Research ArticleOptimization of Base Location and PatrolRoutes for Unmanned Aerial Vehicles in Border IntelligenceSurveillance and Reconnaissance

Yao Liu1 Zhong Liu1 Jianmai Shi 1 Guohua Wu2 and Chao Chen1

1Science and Technology on Information Systems Engineering Laboratory College of System EngineeringNational University of Defense Technology Changsha 410073 China2School of Traffic and Transportation Engineering Central South University Changsha 410075 China

Correspondence should be addressed to Jianmai Shi jianmaishigmailcom

Received 1 October 2018 Revised 5 January 2019 Accepted 13 January 2019 Published 23 January 2019

Academic Editor Juan C Cano

Copyright copy 2019 Yao Liu et al This is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The location-routing problem (LRP) of unmanned aerial vehicles (UAV) in border patrol for Intelligence Surveillance andReconnaissance is investigated where the locations of UAV base stations and the UAV flying routes for visiting the targets inborder area are jointly optimized The capacity of the base station and the endurance of the UAV are considered A binary integerprogramming model is developed to formulate the problem and two heuristic algorithms combined with local search strategiesare designed for solving the problem The experiment design for simulating the distribution of stations and targets in border isproposed for generating random test instances Also an example based on the practical border in Guangxi is presented to illustratethe problem and the solution approach The performance of the two algorithms is analysed and compared through randomlygenerated instances

1 Introduction

Border patrol is one of military Intelligence Surveillanceand Reconnaissance (ISR) missions In many ISR missionsespecially monitoring mission Unmanned Aerial Vehicles(UAVs) have become a natural choice with the deploymentof air surveillance technology [1 2] In border patrol someareas located on or inside the borderline which have the highrates of illegal activities would be focused Thus it is feasibleto deploy UAVs to detect the targets regularly and ferry theinformation such as images videos sensor data etc to basestations

However patrol mission faces severe challenges withrampant crimes such as smuggling And an increasinglyconcern is raised with more diversified forms of crimes Tobe able to cope with the complexity and diversity of threatseffectively much higher requirements need to be satisfied toensure the peace and security near the borderline such ashigh patrol efficiency and fast reaction speed Furthermoredue to the harsh environment and complex geographical

conditions it is dangerous for border guards to patrolmanually And the widespread use of the camera is alsodifficult with its high costTherefore it is meaningful to applythe unmanned aerial vehicles (UAVs) to the border patrol

Even though unmanned patrol is of great significancethere are still some challenges Initially the capacity con-straints of base stations should be taken into account Tomake full use of each established station it is not practicablefor the amount of its UAVs to be under a lower limit whileit is also unreasonable to exceed an upper limit with thelimitations of military ranks Moreover since more than onebase station should be established to ensure the missioncomplement both the amount and the location of basestations need to be optimized Meanwhile the flight paths ofUAVs are also supposed to be jointly planned These factorsare all involved tominimize the total cost which increases thecomplexity of the problem

After considering the above-mentioned factors thispaper provides a solution for border patrol which is struc-tured as follows Section 2 presents the literature review and

HindawiJournal of Advanced TransportationVolume 2019 Article ID 9063232 13 pageshttpsdoiorg10115520199063232

2 Journal of Advanced Transportation

Section 3 illustrates the main assumptions and constructs theoptimization model Section 4 introduces two constructiveheuristics and the local search improving strategies Theexperimental design and computational results are proposedin Section 5 At last Section 6 presents the conclusion andfuture works

2 Literature Review

In regard to location-routing problem there are many schol-ars doing the research after Jacobsen and Madsen [3] inte-grated the study of locations and routing in 1980 Tuzun et al[4] promoted that LRP is an NP-hard problem Min et al[5] proposed a classification of location-routing problemsbased on facility capacities vehicle capacities and so onAfterwards LRP with capacity constraints on depots andvehicles was considered more often called capacitated LRP(CLRP) [6] Due to the complexity of the problem a few exactapproaches are available such as branch-and-cut algorithm[7] and column generation approach [8] but can only be usedto solve small instances Therefore heuristics are designedwhich can present an appropriate solution in acceptablerunning time for the large-scale instances Barreto et al [9]proposed a constructive heuristic and employed clusteringanalysis There are also many metaheuristics based on neigh-bourhood search [10] Greedy randomized adaptive searchprocedure (GRASP) is designed [11] and even improved withevolutionary local search (ELS) [12] Hybrid genetic algo-rithms (GA) [13] simulated annealing heuristic [14] and two-phase hybrid heuristics [15] are also proposed Neverthelessonly the upper bound of the depotrsquos capacity is consideredin most of the current literatures It is not economical norappropriate if the depotrsquos capacity occupied actually is toosmall Thus this paper takes the lower bound of the depotrsquoscapacity into account to ensure the efficient utilization ofthe depotrsquos capacity Besides most current researches areconducted in the commercial background such as parceldelivery and the potential depots are located within theregion and the customers are usually around the depots Butin some situations such as border patrol the potential basestations are always located inside the border while the targetsare located in the border lines

For the route planning of UAVs many researches havebeen carried out In 2004 Harder et al [16] put forward thegeneral architecture of UAVsrsquo route problem and designed thecomponents of the architecture The constraints of ammuni-tion load are first considered by Shetty et al [17] To schemethe attack path in the war the main idea is distributing theattack targets to different UAVs and visiting targets in thesequence of importance-differentiationMufalli et al [18] alsotake the limitations of drone payload into account and usethe column-generated heuristics for both sensor selectionand flight path Besides multiple vehicles and time windowsare solved [19] As for the military applications unmannedcombat aerial vehicles are applied to destruct predeterminedtargets with the constraints of munitions [17] MoreoverAvellar Gustavo S C et al [20] present a solution for theproblem of using a group of unmanned air vehicles (UAVs)

equipped with image sensors to gather intelligence infor-mation which the objective is to minimum time coverageof ground areas Persistent Intelligence Surveillance andReconnaissance (PISR) routing problem is also considered byminimizing the time of delivering the collected data to thecontrol station [2] Unfortunately most of these researchesare based on the traditional routing problem with little touchand exploration on the optimization of base location andflight path

From the current literature there are a few studies on thelocation-routing problem for UAVs with mainly two havinginvestigated it The first one is that Inci Sarıcicek et al [21]studied border patrols of UAVs in Turkey in 2014 which usesa two-stage solution method leading to ineffectiveness ofintegrating the base location into path planning The secondone is in 2016 Yakıcı [22] studied the base location andpath planning under the background of maritime targetreconnaissance However the constraints of the amount ofUAVs are not contained in his study

In this paper both capacity constraints on base stationsand endurance limitations on UAVs are taken into accountin the location-routing problem And a programming modeland two heuristic algorithms are constructed to solve theproblem

3 Model Formulation

In the border patrol mission there exist a set of potentialbase stations and a set of determined patrol targets distributedin the border area Considering the capacity constraints ofbases and the endurance limitations of UAVs the objectiveof mission planning is to locate the base stations and planthe UAVsrsquo routes in an effort to minimize the overall costFor starters this section presents the assumptions defines theproblem and builds the mathematical model

31 Problem Assumptions

(i) Assume that all UAVs are in the same type whichmeans that they have same fight endurance and flyingspeed

(ii) The flying speed of UAVs is assumed to be constant(iii) The UAV must depart from and return to the same

base station The situation of swapping the UAVsbetween different stations is not considered

(iv) Each UAV can visit multiple targets while each targetcan only be visited by one UAV

(v) Patrol cost for eachmile is only concerned with UAVrsquosproperty Uncertain or unexpected situations such asweather changes are not taken into consideration

32 Problem Description Figure 1 presents an example of theoptimization problem for the UAV base location and patrolroutes In patrol missions a series of base stations with thecorresponding equipment are essential These stations areestablished inside the borderline can be reconstructed withthe existing sentry posts for reducing the construction cost orbe built near the border to reduce the flight distance of UAVs

Journal of Advanced Transportation 3

Flight Paths

Potential Bases

Patrol Targets

Figure 1 Sketch map for UAV border patrol

Thus the set of all potential locations can be constituted as119872 = 1 2 119898 Once a base station is determined theequipped facilities such as takeoff and recovery device wouldgenerate a fixed establishing cost 119862119894 (119894 isin 119872) Furthermoreunder the considerations of economic cost and militaryestablishment there exists a limitation on the capacity of basestations For each base station it is not reasonable for theamount of its UAVs to be under the lower limit 119886119871 which thestation would be underutilized nor to exceed the upper limit119886119880 with the limitations of military ranks

Another necessary element in this problem is patroltargets which are some small areas located on or inside theborderline where have the high rates of illegal activities likesmuggling Since the sensor of the drone detects one area atone time these areas can be simplified into nodes Then weget a set119873 = 1 2 119899 All target points in this set must bedetected once in this mission And the distance 119889119894119895 betweenany two targets (or target and base) 119894 119895 (119894 119895 isin 119872 cup 119873) isknown Moreover UAVs would be consumed some servicetime to spy on each target denoted by 119904119894 (119894 isin 119873)

As for UAVs 119881 = 1 2 V is used to denote the setof all UAVs Since UAVs require maintenance before andafter usage there is a fixed use cost 119865119896 (119896 isin 119881) It couldbe different for each UAV but with all UAVs in the sametype it is assumed to be constant to simplify the calculationFurthermore knowing that UAVs would fly at a constantspeed the flying time 119889119894119895 from node 119894 to node two nodes119895 (119894 119895 isin 119872 cup 119873) can be given Besides the total timecontaining flying time and service time cannot exceed theUAVsrsquo maximum flight duration 119863

The final objective function is formed via the sum of threeprimary costs (1) minimize the base establishing cost (2)accomplish the patrol mission with as few drones as possible(3)minimize the flight cost of UAVs

33 Mathematical Model The parameters and variables usedin the model are listed as follows

Sets119872 = 1 2 119898 set of all potential base stations119873 = 1 2 119899 set of all patrol targets119881 = 1 2 V set of all UAVs

Parameters119862119894 fixed establishing cost of base 119894 (119894 isin 119872)119865119896 fixed use cost of UAV 119896 (119896 isin 119881)119902 unit patrol cost of UAVs per kilometre119889119894119895 the distance between two targets (or target andbase) 119894 119895 (119894 119895 isin 119872 cup119873)119905119894119895 the flying time between two targets (or target andbase) 119894 119895 (119894 119895 isin 119872 cup119873)119904119894 detecting time for target 119894 (119894 isin 119873)119886119880 upper limit of the capacity of bases119886119871 lower limit of the capacity of bases119863 the UAVsrsquo maximum flight duration

Decision Variables119909119894119895119896 = 1 if UAV 119896 (119896 isin 119881) fly from node 119894 to 119895(119894 119895 isin119872 cup119873) 0 otherwise119910119894 = 1 if a base station is determined to be built onnode 119894 (119894 isin 119872) 0 otherwise119911119894119896 auxiliary variable for subtour elimination con-straints in the route of UAV 119896 (119896 isin 119881)

min sum119894isin119872

119862119894119910119894 + sum119894isin119872cup119873

sum119895isin119872cup119873

sum119896isin119881

119902119889119894119895119909119894119895119896

+ sum119896isin119881

119865119896sum119894isin119872

sum119895isin119873

119909119894119895119896(1)

St sum119896isin119881

sum119894isin119872cup119873

119909119894119895119896 = sum119896isin119881

sum119894isin119872cup119873

119909119895119894119896 119895 isin 119872 cup 119873 (2)

sum119896isin119881

sum119895isin119872cup119873

119909119894119895119896 = 1 119894 isin 119873 (3)

sum119894isin119872cup119873

sum119895isin119872cup119873

(119905119894119895 + 119904119894) 119909119894119895119896 le 119863 119896 isin 119881 (4)

sum119894isin119873

sum119895isin119872

119909119894119895119896 le 1 119896 isin 119881 (5)

sum119895isin119873

sum119896isin119881

119909119894119895119896 le 119886119880119910119894 119894 isin 119872 (6)

sum119895isin119873

sum119896isin119881

119909119894119895119896 ge 119886119871119910119894 119894 isin 119872 (7)

sum119894isin119873

119909119894119895119896 = sum119894isin119873

119909119895119894119896 119895 isin 119872 119896 isin 119881 (8)

4 Journal of Advanced Transportation

(1) Allocate targets allocate every target to its nearest station(2) Sort base sort base stations by the number of allocated targets(3) while (unvisited targets) do(4) Select the base with the most targets(5) Detect targets with Nearest Neighbour(6) if (unvisited targets in this base) then(7) Reallocate allocate the remaining targets to the second nearest station(8) end if(9) end while(10) while (bases with the number of UAVs lower than limit) do(11) Select the base with the least targets and close the station(12) Reallocate allocate targets of the station to the nearest neighbour station(13) Re-detect targets add the new targets for the neighbour station(14) end while

Algorithm 1 Heuristic based on clustering and nearest point search

119911119894119896 minus 119911119895119896 + |119873| 119909119894119895119896 le |119873| minus 1

119894 119895 isin 119873 119896 isin 119881(9)

119909119894119895119896 isin 0 1 119894 119895 isin 119872 cup 119873 119896 isin 119881 (10)

119910119894 isin 0 1 119894 isin 119872 (11)

119911119894119896 ge 0 119894 isin 119873 119896 isin 119881 (12)

The objective function (1) minimizes the sum of base estab-lishing cost UAVsrsquo use cost and its patrol cost Constraint (2)expresses the limitation in flow conservation Constraint (3)ensures that each target point must be visited and assignedto only one UAV Constraint (4) restricts the time elapsed ineach UAVrsquos flight containing both flying time and detectingtime Constraint (5) requires that each UAV can be scheduledatmost once in onemission planning Constraints (6) and (7)define the limitations on the capacity of base station of whichthe number of equipped UAVs cannot exceed the upper andlower limit Constraint (8) makes sure that each UAV mustturn back to the base station which it departs from Subtourelimination constrains are expressed in (9) Constraints (10)to (12) declare the variable domains

4 Algorithms

In this section two different hybrid heuristics are introducedto construct the feasible solution nearest point searchingalgorithm or saving algorithm Then neighbourhood searchserves as an optimization tool to finalize the optimizationsolution

41 Hybrid Heuristics

411 Heuristic Based on Clustering and Nearest Point Search(H1) Heuristic based on clustering and nearest point search(H1) utilizes the strategy of Nearest Neighbour NearestNeighbour is a well-known constructive search algorithmthat is one of the earliest methods proposed for TSP problems[23] It adopts the principle of selecting the next nearestunvisited node until all nodes have been covered It runs

fast however the optimality of the tours it produces highlydepends on the layout of the given nodes

In H1 every target point is allocated to the nearest basestation at first Then for each station which has assignedtargets the path of UAV is arranged one by one until allassigned targets are detected or the number of UAVs reachesthe upper limit of the station If there are unvisited targetsthen allocate the remaining points to the second neareststation At last there is a check function to find whether thereare some stations that the number of UAVs does not reachlower limit If so close the station and reallocate the targets

The corresponding pseudocode is shown in H1 and thedetailed explanation of the heuristic is shown in Algorithm 1

As shown in pseudocode every target is allocated to itsnearest station with the known positions of the potential basestations and target points (Line (1)) Then sort the selectedbase stations (Line (2)) and plan the path of UAVs in eachstation While detecting the targets prioritize the base withthemost targets (Line (4)) As for the details (Line (5)) launchone UAV at a time and choose the nearest unvisited targetas the next access point Judge whether the UAV can returnback to the original station after visiting the next point Ifso the UAV travels to the next point and keeps detectingwhile turning back to the start if not Repeat the step until allassigned targets are detected or the number of UAVs reachesthe upper limit of the station At this time check whetherthere is assigned targets unvisited after sending out all UAVs(Line (6)) If so allocate the remaining targets to the secondnearest station (Line (7))

After all targets have been detected find whether thereare some stations not having enough numbers of UAVs (Line(10)) If so give priority to the base with the least targetsand close the station (Line (11)) Then allocate targets of thestation to the Nearest Neighbour station (Line (12)) Afterthat redetect targets for the newneighbour station (Line (13))like what have done in Line (5)

412 Heuristic Based on Clustering and CW Saving Search(H2) Clarke and Wright proposed the saving algorithm in1964 [24] This algorithm provides an easy way to solve the

Journal of Advanced Transportation 5

(1) Allocate targets allocate every target to its nearest station(2) Sort base sort base stations by the number of allocated targets(3) while (unvisited targets) do(4) Select the base with the most targets and calculate the saving matrix(5) Detect targets with CW(6) if (unvisited targets in this base) then(7) Reallocate allocate the remaining targets to the second nearest station(8) end if(9) end while(10) while (bases with the number of UAVs lower than limit) do(11) Select the base with the least targets and close the station(12) Reallocate allocate targets of the station to the nearest neighbour station(13) Re-detect targets add the new targets for the neighbour station(14) end while

Algorithm 2 Heuristic based on clustering and CW saving search

vehicle routing problem but it considers neither the locationproblem nor the restriction on the numbers of vehicles

Similar to H1 heuristic based on clustering and CW sav-ing search (H2) first allocates each target point to its nearestbase station and has a check function at last Different fromH1 using Nearest Neighbour CW saving search algorithmis applied in H2 while planning paths to detect targets Thecorresponding pseudocode is shown in H2 and the detailedexplanation of the heuristic is shown in Algorithm 2

Since the overall framework of H2 is similar to thatof H1 the same process will not be repeated in this partAfter selecting the base with the most targets calculate thecorresponding distance matrix and saving matrix (Line (4))In terms of the details (Line (5)) launch one UAV at atime Refer to the saving matrix and merge the target pointsas many as possible under the limitation of UAVsrsquo flightendurance which would generate a flight path for a UAVRepeat the step until all assigned targets are detected or allUAVs have been sent out Moreover CW saving search alsoworks in redetecting targets in Line (13)

42 Neighbourhood Search Improvement Although the hy-brid heuristics can construct a feasible solution quickly thesolution still has room for improvement For example somestations can be replaced by another station or some otherstations and some UAV routes still can be optimized Thusneighbourhood search is introduced to optimize the solutionobtained through the heuristics in Section 41 and reducethe overall cost The framework of neighbourhood search isdisplayed in the pseudocode shown in Algorithm 3

Given an initial solution119904 the main process iterates overthe parameter 119894 until it reaches the preset value of maximumiterations 119894119898119886119909 (Line (1)) In each interaction a solution s1015840would be generated through the operation of closing base sta-tions which would be described in Section 421 Then fromLine (5) to Line (16) local search is performed After initializ-ing the neighbourhood list (Line (5)) the local search will notend until running all neighbourhoods without improvement(Line (7)) Neighbourhood list would be explored exhaus-tively every time which returns the best improvement s1015840

(1) Require s 119894119898119886119909(2) 119894 larr997888 1(3) while 119894 le 119894119898119886119909 do(4) s1015840 larr997888 CloseBaseStation(s)(5) Initialize Neighborhood List (N)(6) k larr997888 1(7) while k le N do(8) Find the best neighbor s1015840 isinN(s)(9) if s1015840 lt s then(10) slarr997888 s1015840(11) ReinitializeN(12) k larr997888 1(13) else(14) klarr997888 k + 1(15) end if(16) end while(17) 119894 larr997888 119894 + 1(18) end while

Algorithm 3 Neighbourhood search

(Line (8)) Comparedwith the current solution s if s1015840 is betterthen s1015840 is the new solution and reinitialize the neighbourhoodlist which would restart the counter k (Lines (9)ndash(12)) Theneighbourhoods used in this part are detailed in Sections422ndash424

Therefore combining two heuristics with the neighbour-hood research respectively we can produce two algorithmsand generate two optimal solutions

421 Operation of Closing the Base Station In the feasiblesolutions there exists a possibility that some base stationshave not fully utilized the UAVs Therefore it might usefulto reduce the establishing cost through shutting down somestations As Figure 2 shows just two UAVs are launched forboth station A and station B which have not dispatched allUAVs At this time we can try to close one of these twostations and find whether these targets can be detected bythe UAVs from only one station If so then station B can

6 Journal of Advanced Transportation

Flight Paths

Potential BasesPatrol Targets

A

B

A

B

Figure 2 The operation of closing the base station

Flight Paths

Potential BasesPatrol Targets

A1

2

3A

12

3

Figure 3The operation of Opt2

Flight Paths

Potential BasesPatrol Targets

A

1

2

3 4

56

A

1

2

3 4

56

Figure 4 The operation of exchanging targets

be closed Furthermore after closing the base station theflight paths in station A would be rearranged To save thecalculation time Nearest Neighbourhood algorithm is usedwhich is displayed in Figure 2

422 Neighbourhood 1 Opt2 This neighbourhood relocatestwo targets on one flight path in a tentative solution Thisoperation is mainly meant to reduce the cross-over routes or

overlapping routes In Figure 3 the initial route is 1 997888rarr 2 997888rarr3 Then points 2 and 3 are selected and their positions areswapped to see whether there is a better solution

423 Neighbourhood 2 Exchange Targets This neighbour-hood is set to swap a target with another one which locateson another path in a tentative solution The two paths canbelong to the same station or two adjacent stations Figure 4

Journal of Advanced Transportation 7

Flight Paths

Potential BasesPatrol Targets

A

B

12

3

4

56

7

8

9A

B

12

3

4

56

7

8

9(b)

A

B

12

3

4

56

7

8

9(a)

Figure 5 The operation of insertion

presents the situation that two targets are in different pathsof one station After exchanging the points 3 and 4 the flightdistance of both two flight paths would be decreased whichcould help lower the flight cost

424 Neighbourhood 3 Insertion This neighbourhood re-moves a target and reinserts it in other position in a tentativesolution which may change the owner base station ofthe target Figure 5(a) illustrates a relatively straightforwardmove in one station Additionally the path represented byFigure 5(b) relocates the target 6 from station B to station A

5 Experiment Design and Results

In this section experiments are designed based on actualcharacteristics of border patrol and two algorithms are testedwith the constructed cases

51 Experiment Design When designing the experiment theparticularity of border patrol should be taken into accountSince the detection goal is part of borderline themission areashould be set as an irregular strip area Thus as displayed inFigure 6 it is assumed that the detection area is a rectanglewith aspect ratio of 2 1

In the mission planning the target points should belocated on the borderlinewhile the base stations are inside theborderline It means that there would be a boundary betweenpotential bases and target points which is different from thecases in delivery system Therefore a random curve is first

8

20

25

24

3 5

17

14

1115

19

18

23 21

13

16

6

4

1

2

12

22

107

9

Target Points

Potential BaseStations

0

20

40

60

80

100

120

140

50 100 150 200 2500Figure 6 Experiment case generated under limited conditions

generated as a boundary (note this boundary differs fromthe borderline the border is in the area of target points)Then base stations and target points are separately generatedon both sides of the boundary which is the dotted line inFigure 6 Five potential base stations are below the boundaryline while twenty target points are above it

As the target points are abstracted from a small area onthe borderline they should not be too close to each otherotherwise two points could be merged into one node It issame for the potential stations It would be impractical tobuild two stations in a close range For the purpose of thischaracteristic all nodes are generated one by one Take thebase stations as an example every time a new station isproduced the distance between the station and every existingstation would be judged If the distance is too short the

8 Journal of Advanced Transportation

Table 1 Detailed parameters of two typical UVAs

Parameters UAV 1 UAV 2

Fuselage 07 meters in length 175 meters in length2 meters in wingspan 175 meters in length

Body Weight 85 kg 15 kgPayload 15 kg 4 kg

Flight Speed 80-120 km h maximum 158 km hpatrol 295 km h

Flight Altitude working 100-500 meters working 300 metersMission Radius 70 km 30 kmFlight Endurance 25 hours ge 4 hours

Table 2 Detailed comparison between feasible solution and improved solution of H1-NS

Feasible solution by H1 Improved solution after NSBase UAV Route Base UAV Route

1 1 1997888rarr9997888rarr7997888rarr10997888rarr1 1 1 1997888rarr9997888rarr7997888rarr10997888rarr12 1997888rarr18997888rarr14997888rarr23997888rarr1 2 1997888rarr14997888rarr23997888rarr18997888rarr19997888rarr1

4

1 4997888rarr15997888rarr11997888rarr13997888rarr4

4

1 4997888rarr15997888rarr11997888rarr21997888rarr42 4997888rarr16997888rarr12997888rarr6997888rarr4 2 4997888rarr16997888rarr12997888rarr6997888rarr43 4997888rarr25997888rarr21997888rarr4 3 4997888rarr13997888rarr25997888rarr44 4997888rarr19997888rarr4

51 5997888rarr24997888rarr8997888rarr5

51 5997888rarr24997888rarr8997888rarr5

2 5997888rarr17997888rarr20997888rarr5 2 5997888rarr17997888rarr22997888rarr20997888rarr53 5997888rarr22997888rarr5

Cost 372992 Cost 274386

position would be abandoned and regenerated until there areenough base stations

The parameters of UAVmainly refer to the public param-eters from two typical UAVs which have been applied toborder patrol The detailed parameter is presented in Table 1After some proper randomization the experiment parame-ters are generated such as the flight endurance patrol speedand so on

52 Experiment Result With the experiment data generatedtwo algorithms are tested and compared with each other Forthe sake of illustration H1-NS represents the combination ofthe heuristic based on clustering and nearest point search(H1) and the neighbourhood search while H2-NS containsthe heuristic based on clustering and CW saving search (H2)and the neighbourhood search

521 Results of H1-NS on Test Case Take a small-scale case(5 base stations and 20 target points) generated randomlyFigure 7(a) shows the feasible solution given by H1 while theimproved solution is provided after neighbourhood search asFigure 7(b) depicts

In Figure 7(a) it is can be seen that the performanceof Nearest Neighbour is flawed Obviously when the UAVdepartures from Station 5 and then visits Target 17 and Target20 the rest of energy cannot support it to return to the base ifcontinuing detecting Target 22 which causes one more UAVto be sent to specially visit Target 22

However after neighbourhood search the solution isimproved a lot Some fight paths are merged and adjustedwhich reduces the number of UAVs used as well as the flightdistance of UAV For example the routes 5997888rarr17997888rarr20997888rarr5and 5997888rarr22997888rarr5 aremerged into 5997888rarr17997888rarr22997888rarr20997888rarr5 Andthe detecting order of Target 14 and 23 is interchangeddecreasing the UAVrsquos redundant flight Although the numberof stations has not changed the number of drones hasdecreased after optimization Only 7 UAVs are used in thefinal solution which is two less than that of the initialsolution As displayed in Table 2 the overall costs have beendecreased from 372992 to 274386 down by 26 percent prov-ing the feasibility of H1 and effectiveness of neighbourhoodsearch

522 Results of H2-NS on Test Case The same case is alsoapplied to test H2-NS The feasible solution given by H2is presented by Figure 8(a) and the improved after NS inFigure 8(b)

The conclusion can be drawn that the CW saving algo-rithm has utilized the flight endurance as far as possiblewhich is fairly obvious in the feasible solution Comparedwith the cost of feasible solution in H1 H2 reduces the costfrom 372992 to 336496

After the adjustment of the neighbourhood search thestructure of the solution has changed a lot Although thenumber of the UAVs has not decreased the base station 1 is

Journal of Advanced Transportation 9

Table 3 Detailed comparison between feasible solution and improved solution of H2-NS

Feasible solution by H1 Improved solution after NSBase UAV Route Base UAV Route

1 1 1997888rarr9997888rarr10997888rarr1 1 1 1997888rarr9997888rarr7997888rarr10997888rarr12 1997888rarr18997888rarr23997888rarr14997888rarr7997888rarr1 2 1997888rarr14997888rarr23997888rarr18997888rarr19997888rarr1

4

1 4997888rarr13997888rarr25997888rarr21997888rarr19997888rarr4

4

1 4997888rarr11997888rarr25997888rarr21997888rarr19997888rarr42 4997888rarr15997888rarr11997888rarr4 2 4997888rarr15997888rarr18997888rarr23997888rarr14997888rarr4

3 4997888rarr16997888rarr6997888rarr12997888rarr4 3 4997888rarr16997888rarr13997888rarr6997888rarr12997888rarr44 4997888rarr9997888rarr4

51 5997888rarr24997888rarr8997888rarr5

51 5997888rarr24997888rarr8997888rarr5

2 5997888rarr17997888rarr20997888rarr22997888rarr5 2 5997888rarr17997888rarr20997888rarr22997888rarr53 5997888rarr7997888rarr10997888rarr5

Cost 336496 Cost 189061

0

20

40

60

80

100

120

140

50 100 150 200 2500(a) Feasible solution given by H1

50 100 150 200 25000

20

40

60

80

100

120

140

(b) Improved solution after NS

Figure 7 Illustration of the results of H1-NS for the small-scaleexample

closed and replaced by the other two stations which reducethe base establishing cost

The detailed comparison is shown in Table 3 The overallcosts have been reduced from 336496 to 189061 dropping by44 Therefore H2-NS seems to be more accurate than H1-NS and can solve the problem better

523 Comparison See Table 4

53 Example Based on the Sino-Vietnamese Border In thissection a practical border is used as the example case andsolved by the preceding algorithms

50 100 150 200 25000

20

40

60

80

100

120

140

(a) Feasible solution given by H1

50 100 150 200 25000

20

40

60

80

100

120

140

(b) Improved solution after NS

Figure 8 Illustration of the results of H2-NS for the small-scaleexample

As is shown in Figure 9 there are about 8 cities and 103towns bordering in Guangxi Zhuang Autonomous RegionWith the development of economy and the implementationof opening-up policy especially under ldquoBelt and Roadrdquoinitiative Guangxi develops an increasingly flourishing bor-der trade However smuggling also increases at the sametime Since the border area is mainly delimited by riversor mountains and has few natural barriers this part of theborder is prone to smuggling which is difficult to monitorAccording to the official report 6726 smuggling cases wereseized in Guangxi in 2006 Thus it is meaningful to applyUAVs on the border patrol which can improve the patrol

10 Journal of Advanced Transportation

Table4Algorith

mcomparis

onin

caseso

fthree

scales

CaseS

cale

H1-N

SH2-NS

Costo

ffeasib

lesolutio

nCosto

fimproved

solutio

nTime10and-2

(s)

Costo

ffeasib

lesolutio

nCosto

fimproved

solutio

nTime10and-2

(s)

5sta

tions

amp20

targets

348882

300435

2325

336890

238473

3928

386308

3364

162392

362091

263009

3815

372992

274386

2463

336496

1890

613786

322293

273432

2313

287293

239058

3682

372327

2764

202342

325443

179350

3871

372439

274322

2335

336807

238975

5487

372369

273543

1892

337965

240234

3635

361322

261822

2247

348843

250545

3670

372538

322555

2327

336976

237811

3787

384262

285167

2196

336890

237784

3811

20sta

tions

amp50

targets

842265

692451

3037

793872

5440

586950

731291

631663

3081

681403

531504

6895

792129

592620

4232

754694

505265

6627

730762

631054

306

4670777

471234

7285

730340

630746

3149

681039

481442

7002

856295

6560

523173

792201

492593

7867

807587

608259

3128

733063

483691

7419

8040

06654817

3503

719919

520651

7432

828288

628671

3385

732245

482620

7494

804770

655033

2620

719798

570285

7242

50sta

tions

amp100targets

1340

095

1028130

1040

1196218

791338

4590

1272888

923026

0993

121940

6819554

4819

1314565

952735

1061

1143538

843628

4490

1396086

946150

1073

1308837

858909

4931

1197487

897623

1064

1075171

725519

5414

1430365

1091920

1012

1368315

818606

4525

1331166

1031168

1049

1219333

819335

4508

1354155

1004

220

1000

1208915

809037

4550

1418603

1080944

1029

1319784

869953

444

61343357

943478

1023

1256920

807064

4897

Journal of Advanced Transportation 11

Table 5 Comparison between two results of practical cases

H1-NS H2-NSCost of feasiblesolution

Cost of improvedsolution Time 10and-2 (s) Cost of feasible

solutionCost of improved

solution Time 10and-2 (s)

817492 619800 3091 837997 480309 6840

Table 6 Detailed bases and flight paths of the final solution

Base UAV Route

31 3997888rarr21997888rarr22997888rarr32 3997888rarr23997888rarr24997888rarr33 3997888rarr25997888rarr27997888rarr26997888rarr3

61 6997888rarr28997888rarr29997888rarr30997888rarr62 6997888rarr31997888rarr32997888rarr33997888rarr34997888rarr35997888rarr63 6997888rarr36997888rarr37997888rarr6

8 1 8997888rarr38997888rarr39997888rarr40997888rarr41997888rarr82 8997888rarr42997888rarr43997888rarr44997888rarr45997888rarr8

11 1 11997888rarr46997888rarr47997888rarr48997888rarr49997888rarr50997888rarr112 11997888rarr51997888rarr52997888rarr53997888rarr11

15 1 15997888rarr54997888rarr55997888rarr56997888rarr57997888rarr152 15997888rarr58997888rarr59997888rarr60997888rarr15

181 18997888rarr61997888rarr62997888rarr182 18997888rarr63997888rarr64997888rarr65997888rarr67997888rarr66997888rarr183 18997888rarr68997888rarr70997888rarr69997888rarr18

Figure 9 The map of Guangxi Zhuang Autonomous Region (themarked red line is the Guangxi section of the Sino-Vietnameseborder)

efficiency and reaction speed Therefore take the Guangxisection of the border as an example

As displayed in Figure 10 with the ranging tool of GoogleMap the linear distance of this part is about 320 km ThenPaint software is used to discretize this line Fifty target pointsaremarked on the border and twenty base stations are chosenrandomly inside the line Furthermore the relative positionsof these 70 nodes are obtained via the pixel measurement

Figure 10 Guangxi section of the Sino-Vietnamese border with theranging tool

It is assumed that all targets and potential bases arelocated in the area of 320 kilometres multiplied by 160 kilo-metres Mapping these nodes into this area the distributionmap looks like Figure 11 The blue dots are target points andthe red blocks are potential base stations

Two algorithms are applied to solve the practical caseThe results are shown in Table 5 Since the result of H2-NSis obviously superior to another one take the result of H2-NS as the final solution in which the cost is 480309 and thecalculation takes 006840 seconds

The potential base stations are numbered 1 through 20when the target points are represented by 21 to 70 Then thedetailed bases and flight paths can be listed in Table 6 andthe corresponding route map is shown in Figure 12 The finalresult selects 6 bases and launches 15 UAVs

12 Journal of Advanced Transportation

50 100 150 200 250 300 35000

20

40

60

80

100

120

140

Figure 11 50 target points and 20 base stations after discretization

50 100 150 200 250 300 35000

20

40

60

80

100

120

140

Figure 12 The route map of the final solution

6 Conclusions

In this paper considering the background of border patrolfor ISR the capacity constraints of bases are involved inthe multidepot location-routing problem Hence a modifiedmathematical model has been presented The primary objec-tive of this research is to develop an efficient approach forsolving this kind of problem Thus two hybrid heuristicswith neighbourhood search are promoted One is based onclustering and nearest point search and the other one is basedon clustering and CW saving search

In addition experiments have been carried out to com-pare the performance of two algorithms It can be addictedthat neighbourhood search plays an optimizing role to thesolution And the heuristic based on CW saving searchprovides a better solution while consuming more time thanthe other one Furthermore an example based on a practicalborderline is proposed Both algorithms are applied to solvethe border patrol on the practical borderline and provide thefinal solution

Finally two improvements in solving this kind of problemcan be envisaged First the current neighbourhood searchcan be scaled up to find a global optimal solution Secondmore variants of this kind of problem can be exploited Forexample dynamic detecting could be added

Data Availability

The data used to support the findings of this study are avail-able from the corresponding author upon request

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

The research is supported by the National Natural ScienceFoundation of China (no 71771215 and no 71471174)

References

[1] LMiao L Zhen SWangW Lv and X Qu ldquoUnmanned AerialVehicle Scheduling Problem for TrafficMonitoringrdquoComputersamp Industrial Engineering vol 122 pp 15ndash23 2018

[2] S G Manyam S Rasmussen D W Casbeer K Kalyanam andS Manickam ldquoMulti-UAV routing for persistent intelligencesurveillance amp reconnaissance missionsrdquo in Proceedings of the2017 International Conference on Unmanned Aircraft SystemsICUAS 2017 pp 573ndash580 June 2017

[3] S K Jacobsen and O B G Madsen ldquoA comparative study ofheuristics for a two-level routing-location problemrdquo EuropeanJournal of Operational Research vol 5 no 6 pp 378ndash387 1980

[4] D Tuzun and L I Burke ldquoTwo-phase tabu search approach tothe location routing problemrdquo European Journal of OperationalResearch vol 116 no 1 pp 87ndash99 1999

[5] H Min V Jayaraman and R Srivastava ldquoCombined location-routing problems a synthesis and future research directionsrdquoEuropean Journal of Operational Research vol 108 no 1 pp 1ndash15 1998

[6] G Nagy and S Salhi ldquoLocation-routing issues models andmethodsrdquoEuropean Journal ofOperational Research vol 177 no2 pp 649ndash672 2007

[7] J-M Belenguer E Benavent C Prins C Prodhon and RW Calvoc ldquoA Branch-and-Cut method for the CapacitatedLocation-Routing Problemrdquo Computers amp Operations Researchvol 38 no 6 pp 931ndash941 2011

[8] Z Akca R T Berger and T K Ralphs ldquoA branch-and-pricealgorithm for combined location and routing problems undercapacity restrictionsrdquo Operations Research Computer ScienceInterfaces Series vol 47 pp 309ndash330 2009

[9] S Barreto C Ferreira J Paixao and B S Santos ldquoUsing clus-tering analysis in a capacitated location-routing problemrdquoEuropean Journal of Operational Research vol 179 no 3 pp968ndash977 2007

[10] C Prodhon and C Prins ldquoA survey of recent research onlocation-routing problemsrdquo European Journal of OperationalResearch vol 238 no 1 pp 1ndash17 2014

[11] C Prins C Prodhon and RWolfer-Calvo ldquoSolving the capaci-tated location-routing problemby aGRASP complemented by alearning process and a path relinkingrdquo 4OR AQuarterly Journalof Operations Research vol 4 no 3 pp 221ndash238 2006

[12] C Duhamel P Lacomme C Prins and C Prodhon ldquoAGRASPtimesELS approach for the capacitated location-routingproblemrdquo Computers amp Operations Research vol 37 no 11 pp1912ndash1923 2010

[13] R B Lopes C Ferreira and B S Santos ldquoA simple and effectiveevolutionary algorithm for the capacitated location-routingproblemrdquo Computers amp Operations Research vol 70 pp 155ndash162 2016

Journal of Advanced Transportation 13

[14] V F Yu S-W Lin W Lee and C-J Ting ldquoA simulated anneal-ing heuristic for the capacitated location routing problemrdquoComputers amp Industrial Engineering vol 58 no 2 pp 288ndash2992010

[15] J W Escobar R Linfati and P Toth ldquoA two-phase hybridheuristic algorithm for the capacitated location-routing prob-lemrdquoComputers ampOperations Research vol 40 no 1 pp 70ndash792013

[16] R W Harder R R Hill and J T Moore ldquoA Java universalvehicle router for routing unmanned aerial vehiclesrdquo Interna-tional Transactions in Operational Research vol 11 no 3 pp259ndash275 2004

[17] V K Shetty M Sudit and R Nagi ldquoPriority-based assignmentand routing of a fleet of unmanned combat aerial vehiclesrdquoComputers amp Operations Research vol 35 no 6 pp 1813ndash18282008

[18] F Mufalli R Batta and R Nagi ldquoSimultaneous sensor selectionand routing of unmanned aerial vehicles for complex missionplansrdquo Computers amp Operations Research vol 39 no 11 pp2787ndash2799 2012

[19] A M Ham ldquoIntegrated scheduling of m-truck m-drone andm-depot constrained by time-window drop-pickup and m-visit using constraint programmingrdquo Transportation ResearchPart C Emerging Technologies vol 91 pp 1ndash14 2018

[20] G S C Avellar G A S Pereira L C A Pimenta and P IscoldldquoMulti-UAV routing for area coverage and remote sensing withminimum timerdquo Sensors vol 15 no 11 pp 27783ndash27803 2015

[21] I Sarıcicek and Y Akkus ldquoUnmanned aerial vehicle hub-location and routing for monitoring geographic bordersrdquoApplied Mathematical Modelling Simulation and Computationfor Engineering and Environmental Systems vol 39 no 14 pp3939ndash3953 2015

[22] E Yakıcı ldquoSolving location and routing problem for UAVsrdquoComputers amp Industrial Engineering vol 102 pp 294ndash301 2016

[23] T M Cover and P E Hart ldquoNearest neighbor pattern classifi-cationrdquo IEEE Transactions on Information Theory vol 13 no 1pp 21ndash27 1967

[24] G Clarke and J W Wright ldquoScheduling of vehicles from acentral depot to a number of delivery pointsrdquo INFORMS 1964

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Journal of Advanced Transportation 3

Flight Paths

Potential Bases

Patrol Targets

Figure 1 Sketch map for UAV border patrol

Thus the set of all potential locations can be constituted as119872 = 1 2 119898 Once a base station is determined theequipped facilities such as takeoff and recovery device wouldgenerate a fixed establishing cost 119862119894 (119894 isin 119872) Furthermoreunder the considerations of economic cost and militaryestablishment there exists a limitation on the capacity of basestations For each base station it is not reasonable for theamount of its UAVs to be under the lower limit 119886119871 which thestation would be underutilized nor to exceed the upper limit119886119880 with the limitations of military ranks

Another necessary element in this problem is patroltargets which are some small areas located on or inside theborderline where have the high rates of illegal activities likesmuggling Since the sensor of the drone detects one area atone time these areas can be simplified into nodes Then weget a set119873 = 1 2 119899 All target points in this set must bedetected once in this mission And the distance 119889119894119895 betweenany two targets (or target and base) 119894 119895 (119894 119895 isin 119872 cup 119873) isknown Moreover UAVs would be consumed some servicetime to spy on each target denoted by 119904119894 (119894 isin 119873)

As for UAVs 119881 = 1 2 V is used to denote the setof all UAVs Since UAVs require maintenance before andafter usage there is a fixed use cost 119865119896 (119896 isin 119881) It couldbe different for each UAV but with all UAVs in the sametype it is assumed to be constant to simplify the calculationFurthermore knowing that UAVs would fly at a constantspeed the flying time 119889119894119895 from node 119894 to node two nodes119895 (119894 119895 isin 119872 cup 119873) can be given Besides the total timecontaining flying time and service time cannot exceed theUAVsrsquo maximum flight duration 119863

The final objective function is formed via the sum of threeprimary costs (1) minimize the base establishing cost (2)accomplish the patrol mission with as few drones as possible(3)minimize the flight cost of UAVs

33 Mathematical Model The parameters and variables usedin the model are listed as follows

Sets119872 = 1 2 119898 set of all potential base stations119873 = 1 2 119899 set of all patrol targets119881 = 1 2 V set of all UAVs

Parameters119862119894 fixed establishing cost of base 119894 (119894 isin 119872)119865119896 fixed use cost of UAV 119896 (119896 isin 119881)119902 unit patrol cost of UAVs per kilometre119889119894119895 the distance between two targets (or target andbase) 119894 119895 (119894 119895 isin 119872 cup119873)119905119894119895 the flying time between two targets (or target andbase) 119894 119895 (119894 119895 isin 119872 cup119873)119904119894 detecting time for target 119894 (119894 isin 119873)119886119880 upper limit of the capacity of bases119886119871 lower limit of the capacity of bases119863 the UAVsrsquo maximum flight duration

Decision Variables119909119894119895119896 = 1 if UAV 119896 (119896 isin 119881) fly from node 119894 to 119895(119894 119895 isin119872 cup119873) 0 otherwise119910119894 = 1 if a base station is determined to be built onnode 119894 (119894 isin 119872) 0 otherwise119911119894119896 auxiliary variable for subtour elimination con-straints in the route of UAV 119896 (119896 isin 119881)

min sum119894isin119872

119862119894119910119894 + sum119894isin119872cup119873

sum119895isin119872cup119873

sum119896isin119881

119902119889119894119895119909119894119895119896

+ sum119896isin119881

119865119896sum119894isin119872

sum119895isin119873

119909119894119895119896(1)

St sum119896isin119881

sum119894isin119872cup119873

119909119894119895119896 = sum119896isin119881

sum119894isin119872cup119873

119909119895119894119896 119895 isin 119872 cup 119873 (2)

sum119896isin119881

sum119895isin119872cup119873

119909119894119895119896 = 1 119894 isin 119873 (3)

sum119894isin119872cup119873

sum119895isin119872cup119873

(119905119894119895 + 119904119894) 119909119894119895119896 le 119863 119896 isin 119881 (4)

sum119894isin119873

sum119895isin119872

119909119894119895119896 le 1 119896 isin 119881 (5)

sum119895isin119873

sum119896isin119881

119909119894119895119896 le 119886119880119910119894 119894 isin 119872 (6)

sum119895isin119873

sum119896isin119881

119909119894119895119896 ge 119886119871119910119894 119894 isin 119872 (7)

sum119894isin119873

119909119894119895119896 = sum119894isin119873

119909119895119894119896 119895 isin 119872 119896 isin 119881 (8)

4 Journal of Advanced Transportation

(1) Allocate targets allocate every target to its nearest station(2) Sort base sort base stations by the number of allocated targets(3) while (unvisited targets) do(4) Select the base with the most targets(5) Detect targets with Nearest Neighbour(6) if (unvisited targets in this base) then(7) Reallocate allocate the remaining targets to the second nearest station(8) end if(9) end while(10) while (bases with the number of UAVs lower than limit) do(11) Select the base with the least targets and close the station(12) Reallocate allocate targets of the station to the nearest neighbour station(13) Re-detect targets add the new targets for the neighbour station(14) end while

Algorithm 1 Heuristic based on clustering and nearest point search

119911119894119896 minus 119911119895119896 + |119873| 119909119894119895119896 le |119873| minus 1

119894 119895 isin 119873 119896 isin 119881(9)

119909119894119895119896 isin 0 1 119894 119895 isin 119872 cup 119873 119896 isin 119881 (10)

119910119894 isin 0 1 119894 isin 119872 (11)

119911119894119896 ge 0 119894 isin 119873 119896 isin 119881 (12)

The objective function (1) minimizes the sum of base estab-lishing cost UAVsrsquo use cost and its patrol cost Constraint (2)expresses the limitation in flow conservation Constraint (3)ensures that each target point must be visited and assignedto only one UAV Constraint (4) restricts the time elapsed ineach UAVrsquos flight containing both flying time and detectingtime Constraint (5) requires that each UAV can be scheduledatmost once in onemission planning Constraints (6) and (7)define the limitations on the capacity of base station of whichthe number of equipped UAVs cannot exceed the upper andlower limit Constraint (8) makes sure that each UAV mustturn back to the base station which it departs from Subtourelimination constrains are expressed in (9) Constraints (10)to (12) declare the variable domains

4 Algorithms

In this section two different hybrid heuristics are introducedto construct the feasible solution nearest point searchingalgorithm or saving algorithm Then neighbourhood searchserves as an optimization tool to finalize the optimizationsolution

41 Hybrid Heuristics

411 Heuristic Based on Clustering and Nearest Point Search(H1) Heuristic based on clustering and nearest point search(H1) utilizes the strategy of Nearest Neighbour NearestNeighbour is a well-known constructive search algorithmthat is one of the earliest methods proposed for TSP problems[23] It adopts the principle of selecting the next nearestunvisited node until all nodes have been covered It runs

fast however the optimality of the tours it produces highlydepends on the layout of the given nodes

In H1 every target point is allocated to the nearest basestation at first Then for each station which has assignedtargets the path of UAV is arranged one by one until allassigned targets are detected or the number of UAVs reachesthe upper limit of the station If there are unvisited targetsthen allocate the remaining points to the second neareststation At last there is a check function to find whether thereare some stations that the number of UAVs does not reachlower limit If so close the station and reallocate the targets

The corresponding pseudocode is shown in H1 and thedetailed explanation of the heuristic is shown in Algorithm 1

As shown in pseudocode every target is allocated to itsnearest station with the known positions of the potential basestations and target points (Line (1)) Then sort the selectedbase stations (Line (2)) and plan the path of UAVs in eachstation While detecting the targets prioritize the base withthemost targets (Line (4)) As for the details (Line (5)) launchone UAV at a time and choose the nearest unvisited targetas the next access point Judge whether the UAV can returnback to the original station after visiting the next point Ifso the UAV travels to the next point and keeps detectingwhile turning back to the start if not Repeat the step until allassigned targets are detected or the number of UAVs reachesthe upper limit of the station At this time check whetherthere is assigned targets unvisited after sending out all UAVs(Line (6)) If so allocate the remaining targets to the secondnearest station (Line (7))

After all targets have been detected find whether thereare some stations not having enough numbers of UAVs (Line(10)) If so give priority to the base with the least targetsand close the station (Line (11)) Then allocate targets of thestation to the Nearest Neighbour station (Line (12)) Afterthat redetect targets for the newneighbour station (Line (13))like what have done in Line (5)

412 Heuristic Based on Clustering and CW Saving Search(H2) Clarke and Wright proposed the saving algorithm in1964 [24] This algorithm provides an easy way to solve the

Journal of Advanced Transportation 5

(1) Allocate targets allocate every target to its nearest station(2) Sort base sort base stations by the number of allocated targets(3) while (unvisited targets) do(4) Select the base with the most targets and calculate the saving matrix(5) Detect targets with CW(6) if (unvisited targets in this base) then(7) Reallocate allocate the remaining targets to the second nearest station(8) end if(9) end while(10) while (bases with the number of UAVs lower than limit) do(11) Select the base with the least targets and close the station(12) Reallocate allocate targets of the station to the nearest neighbour station(13) Re-detect targets add the new targets for the neighbour station(14) end while

Algorithm 2 Heuristic based on clustering and CW saving search

vehicle routing problem but it considers neither the locationproblem nor the restriction on the numbers of vehicles

Similar to H1 heuristic based on clustering and CW sav-ing search (H2) first allocates each target point to its nearestbase station and has a check function at last Different fromH1 using Nearest Neighbour CW saving search algorithmis applied in H2 while planning paths to detect targets Thecorresponding pseudocode is shown in H2 and the detailedexplanation of the heuristic is shown in Algorithm 2

Since the overall framework of H2 is similar to thatof H1 the same process will not be repeated in this partAfter selecting the base with the most targets calculate thecorresponding distance matrix and saving matrix (Line (4))In terms of the details (Line (5)) launch one UAV at atime Refer to the saving matrix and merge the target pointsas many as possible under the limitation of UAVsrsquo flightendurance which would generate a flight path for a UAVRepeat the step until all assigned targets are detected or allUAVs have been sent out Moreover CW saving search alsoworks in redetecting targets in Line (13)

42 Neighbourhood Search Improvement Although the hy-brid heuristics can construct a feasible solution quickly thesolution still has room for improvement For example somestations can be replaced by another station or some otherstations and some UAV routes still can be optimized Thusneighbourhood search is introduced to optimize the solutionobtained through the heuristics in Section 41 and reducethe overall cost The framework of neighbourhood search isdisplayed in the pseudocode shown in Algorithm 3

Given an initial solution119904 the main process iterates overthe parameter 119894 until it reaches the preset value of maximumiterations 119894119898119886119909 (Line (1)) In each interaction a solution s1015840would be generated through the operation of closing base sta-tions which would be described in Section 421 Then fromLine (5) to Line (16) local search is performed After initializ-ing the neighbourhood list (Line (5)) the local search will notend until running all neighbourhoods without improvement(Line (7)) Neighbourhood list would be explored exhaus-tively every time which returns the best improvement s1015840

(1) Require s 119894119898119886119909(2) 119894 larr997888 1(3) while 119894 le 119894119898119886119909 do(4) s1015840 larr997888 CloseBaseStation(s)(5) Initialize Neighborhood List (N)(6) k larr997888 1(7) while k le N do(8) Find the best neighbor s1015840 isinN(s)(9) if s1015840 lt s then(10) slarr997888 s1015840(11) ReinitializeN(12) k larr997888 1(13) else(14) klarr997888 k + 1(15) end if(16) end while(17) 119894 larr997888 119894 + 1(18) end while

Algorithm 3 Neighbourhood search

(Line (8)) Comparedwith the current solution s if s1015840 is betterthen s1015840 is the new solution and reinitialize the neighbourhoodlist which would restart the counter k (Lines (9)ndash(12)) Theneighbourhoods used in this part are detailed in Sections422ndash424

Therefore combining two heuristics with the neighbour-hood research respectively we can produce two algorithmsand generate two optimal solutions

421 Operation of Closing the Base Station In the feasiblesolutions there exists a possibility that some base stationshave not fully utilized the UAVs Therefore it might usefulto reduce the establishing cost through shutting down somestations As Figure 2 shows just two UAVs are launched forboth station A and station B which have not dispatched allUAVs At this time we can try to close one of these twostations and find whether these targets can be detected bythe UAVs from only one station If so then station B can

6 Journal of Advanced Transportation

Flight Paths

Potential BasesPatrol Targets

A

B

A

B

Figure 2 The operation of closing the base station

Flight Paths

Potential BasesPatrol Targets

A1

2

3A

12

3

Figure 3The operation of Opt2

Flight Paths

Potential BasesPatrol Targets

A

1

2

3 4

56

A

1

2

3 4

56

Figure 4 The operation of exchanging targets

be closed Furthermore after closing the base station theflight paths in station A would be rearranged To save thecalculation time Nearest Neighbourhood algorithm is usedwhich is displayed in Figure 2

422 Neighbourhood 1 Opt2 This neighbourhood relocatestwo targets on one flight path in a tentative solution Thisoperation is mainly meant to reduce the cross-over routes or

overlapping routes In Figure 3 the initial route is 1 997888rarr 2 997888rarr3 Then points 2 and 3 are selected and their positions areswapped to see whether there is a better solution

423 Neighbourhood 2 Exchange Targets This neighbour-hood is set to swap a target with another one which locateson another path in a tentative solution The two paths canbelong to the same station or two adjacent stations Figure 4

Journal of Advanced Transportation 7

Flight Paths

Potential BasesPatrol Targets

A

B

12

3

4

56

7

8

9A

B

12

3

4

56

7

8

9(b)

A

B

12

3

4

56

7

8

9(a)

Figure 5 The operation of insertion

presents the situation that two targets are in different pathsof one station After exchanging the points 3 and 4 the flightdistance of both two flight paths would be decreased whichcould help lower the flight cost

424 Neighbourhood 3 Insertion This neighbourhood re-moves a target and reinserts it in other position in a tentativesolution which may change the owner base station ofthe target Figure 5(a) illustrates a relatively straightforwardmove in one station Additionally the path represented byFigure 5(b) relocates the target 6 from station B to station A

5 Experiment Design and Results

In this section experiments are designed based on actualcharacteristics of border patrol and two algorithms are testedwith the constructed cases

51 Experiment Design When designing the experiment theparticularity of border patrol should be taken into accountSince the detection goal is part of borderline themission areashould be set as an irregular strip area Thus as displayed inFigure 6 it is assumed that the detection area is a rectanglewith aspect ratio of 2 1

In the mission planning the target points should belocated on the borderlinewhile the base stations are inside theborderline It means that there would be a boundary betweenpotential bases and target points which is different from thecases in delivery system Therefore a random curve is first

8

20

25

24

3 5

17

14

1115

19

18

23 21

13

16

6

4

1

2

12

22

107

9

Target Points

Potential BaseStations

0

20

40

60

80

100

120

140

50 100 150 200 2500Figure 6 Experiment case generated under limited conditions

generated as a boundary (note this boundary differs fromthe borderline the border is in the area of target points)Then base stations and target points are separately generatedon both sides of the boundary which is the dotted line inFigure 6 Five potential base stations are below the boundaryline while twenty target points are above it

As the target points are abstracted from a small area onthe borderline they should not be too close to each otherotherwise two points could be merged into one node It issame for the potential stations It would be impractical tobuild two stations in a close range For the purpose of thischaracteristic all nodes are generated one by one Take thebase stations as an example every time a new station isproduced the distance between the station and every existingstation would be judged If the distance is too short the

8 Journal of Advanced Transportation

Table 1 Detailed parameters of two typical UVAs

Parameters UAV 1 UAV 2

Fuselage 07 meters in length 175 meters in length2 meters in wingspan 175 meters in length

Body Weight 85 kg 15 kgPayload 15 kg 4 kg

Flight Speed 80-120 km h maximum 158 km hpatrol 295 km h

Flight Altitude working 100-500 meters working 300 metersMission Radius 70 km 30 kmFlight Endurance 25 hours ge 4 hours

Table 2 Detailed comparison between feasible solution and improved solution of H1-NS

Feasible solution by H1 Improved solution after NSBase UAV Route Base UAV Route

1 1 1997888rarr9997888rarr7997888rarr10997888rarr1 1 1 1997888rarr9997888rarr7997888rarr10997888rarr12 1997888rarr18997888rarr14997888rarr23997888rarr1 2 1997888rarr14997888rarr23997888rarr18997888rarr19997888rarr1

4

1 4997888rarr15997888rarr11997888rarr13997888rarr4

4

1 4997888rarr15997888rarr11997888rarr21997888rarr42 4997888rarr16997888rarr12997888rarr6997888rarr4 2 4997888rarr16997888rarr12997888rarr6997888rarr43 4997888rarr25997888rarr21997888rarr4 3 4997888rarr13997888rarr25997888rarr44 4997888rarr19997888rarr4

51 5997888rarr24997888rarr8997888rarr5

51 5997888rarr24997888rarr8997888rarr5

2 5997888rarr17997888rarr20997888rarr5 2 5997888rarr17997888rarr22997888rarr20997888rarr53 5997888rarr22997888rarr5

Cost 372992 Cost 274386

position would be abandoned and regenerated until there areenough base stations

The parameters of UAVmainly refer to the public param-eters from two typical UAVs which have been applied toborder patrol The detailed parameter is presented in Table 1After some proper randomization the experiment parame-ters are generated such as the flight endurance patrol speedand so on

52 Experiment Result With the experiment data generatedtwo algorithms are tested and compared with each other Forthe sake of illustration H1-NS represents the combination ofthe heuristic based on clustering and nearest point search(H1) and the neighbourhood search while H2-NS containsthe heuristic based on clustering and CW saving search (H2)and the neighbourhood search

521 Results of H1-NS on Test Case Take a small-scale case(5 base stations and 20 target points) generated randomlyFigure 7(a) shows the feasible solution given by H1 while theimproved solution is provided after neighbourhood search asFigure 7(b) depicts

In Figure 7(a) it is can be seen that the performanceof Nearest Neighbour is flawed Obviously when the UAVdepartures from Station 5 and then visits Target 17 and Target20 the rest of energy cannot support it to return to the base ifcontinuing detecting Target 22 which causes one more UAVto be sent to specially visit Target 22

However after neighbourhood search the solution isimproved a lot Some fight paths are merged and adjustedwhich reduces the number of UAVs used as well as the flightdistance of UAV For example the routes 5997888rarr17997888rarr20997888rarr5and 5997888rarr22997888rarr5 aremerged into 5997888rarr17997888rarr22997888rarr20997888rarr5 Andthe detecting order of Target 14 and 23 is interchangeddecreasing the UAVrsquos redundant flight Although the numberof stations has not changed the number of drones hasdecreased after optimization Only 7 UAVs are used in thefinal solution which is two less than that of the initialsolution As displayed in Table 2 the overall costs have beendecreased from 372992 to 274386 down by 26 percent prov-ing the feasibility of H1 and effectiveness of neighbourhoodsearch

522 Results of H2-NS on Test Case The same case is alsoapplied to test H2-NS The feasible solution given by H2is presented by Figure 8(a) and the improved after NS inFigure 8(b)

The conclusion can be drawn that the CW saving algo-rithm has utilized the flight endurance as far as possiblewhich is fairly obvious in the feasible solution Comparedwith the cost of feasible solution in H1 H2 reduces the costfrom 372992 to 336496

After the adjustment of the neighbourhood search thestructure of the solution has changed a lot Although thenumber of the UAVs has not decreased the base station 1 is

Journal of Advanced Transportation 9

Table 3 Detailed comparison between feasible solution and improved solution of H2-NS

Feasible solution by H1 Improved solution after NSBase UAV Route Base UAV Route

1 1 1997888rarr9997888rarr10997888rarr1 1 1 1997888rarr9997888rarr7997888rarr10997888rarr12 1997888rarr18997888rarr23997888rarr14997888rarr7997888rarr1 2 1997888rarr14997888rarr23997888rarr18997888rarr19997888rarr1

4

1 4997888rarr13997888rarr25997888rarr21997888rarr19997888rarr4

4

1 4997888rarr11997888rarr25997888rarr21997888rarr19997888rarr42 4997888rarr15997888rarr11997888rarr4 2 4997888rarr15997888rarr18997888rarr23997888rarr14997888rarr4

3 4997888rarr16997888rarr6997888rarr12997888rarr4 3 4997888rarr16997888rarr13997888rarr6997888rarr12997888rarr44 4997888rarr9997888rarr4

51 5997888rarr24997888rarr8997888rarr5

51 5997888rarr24997888rarr8997888rarr5

2 5997888rarr17997888rarr20997888rarr22997888rarr5 2 5997888rarr17997888rarr20997888rarr22997888rarr53 5997888rarr7997888rarr10997888rarr5

Cost 336496 Cost 189061

0

20

40

60

80

100

120

140

50 100 150 200 2500(a) Feasible solution given by H1

50 100 150 200 25000

20

40

60

80

100

120

140

(b) Improved solution after NS

Figure 7 Illustration of the results of H1-NS for the small-scaleexample

closed and replaced by the other two stations which reducethe base establishing cost

The detailed comparison is shown in Table 3 The overallcosts have been reduced from 336496 to 189061 dropping by44 Therefore H2-NS seems to be more accurate than H1-NS and can solve the problem better

523 Comparison See Table 4

53 Example Based on the Sino-Vietnamese Border In thissection a practical border is used as the example case andsolved by the preceding algorithms

50 100 150 200 25000

20

40

60

80

100

120

140

(a) Feasible solution given by H1

50 100 150 200 25000

20

40

60

80

100

120

140

(b) Improved solution after NS

Figure 8 Illustration of the results of H2-NS for the small-scaleexample

As is shown in Figure 9 there are about 8 cities and 103towns bordering in Guangxi Zhuang Autonomous RegionWith the development of economy and the implementationof opening-up policy especially under ldquoBelt and Roadrdquoinitiative Guangxi develops an increasingly flourishing bor-der trade However smuggling also increases at the sametime Since the border area is mainly delimited by riversor mountains and has few natural barriers this part of theborder is prone to smuggling which is difficult to monitorAccording to the official report 6726 smuggling cases wereseized in Guangxi in 2006 Thus it is meaningful to applyUAVs on the border patrol which can improve the patrol

10 Journal of Advanced Transportation

Table4Algorith

mcomparis

onin

caseso

fthree

scales

CaseS

cale

H1-N

SH2-NS

Costo

ffeasib

lesolutio

nCosto

fimproved

solutio

nTime10and-2

(s)

Costo

ffeasib

lesolutio

nCosto

fimproved

solutio

nTime10and-2

(s)

5sta

tions

amp20

targets

348882

300435

2325

336890

238473

3928

386308

3364

162392

362091

263009

3815

372992

274386

2463

336496

1890

613786

322293

273432

2313

287293

239058

3682

372327

2764

202342

325443

179350

3871

372439

274322

2335

336807

238975

5487

372369

273543

1892

337965

240234

3635

361322

261822

2247

348843

250545

3670

372538

322555

2327

336976

237811

3787

384262

285167

2196

336890

237784

3811

20sta

tions

amp50

targets

842265

692451

3037

793872

5440

586950

731291

631663

3081

681403

531504

6895

792129

592620

4232

754694

505265

6627

730762

631054

306

4670777

471234

7285

730340

630746

3149

681039

481442

7002

856295

6560

523173

792201

492593

7867

807587

608259

3128

733063

483691

7419

8040

06654817

3503

719919

520651

7432

828288

628671

3385

732245

482620

7494

804770

655033

2620

719798

570285

7242

50sta

tions

amp100targets

1340

095

1028130

1040

1196218

791338

4590

1272888

923026

0993

121940

6819554

4819

1314565

952735

1061

1143538

843628

4490

1396086

946150

1073

1308837

858909

4931

1197487

897623

1064

1075171

725519

5414

1430365

1091920

1012

1368315

818606

4525

1331166

1031168

1049

1219333

819335

4508

1354155

1004

220

1000

1208915

809037

4550

1418603

1080944

1029

1319784

869953

444

61343357

943478

1023

1256920

807064

4897

Journal of Advanced Transportation 11

Table 5 Comparison between two results of practical cases

H1-NS H2-NSCost of feasiblesolution

Cost of improvedsolution Time 10and-2 (s) Cost of feasible

solutionCost of improved

solution Time 10and-2 (s)

817492 619800 3091 837997 480309 6840

Table 6 Detailed bases and flight paths of the final solution

Base UAV Route

31 3997888rarr21997888rarr22997888rarr32 3997888rarr23997888rarr24997888rarr33 3997888rarr25997888rarr27997888rarr26997888rarr3

61 6997888rarr28997888rarr29997888rarr30997888rarr62 6997888rarr31997888rarr32997888rarr33997888rarr34997888rarr35997888rarr63 6997888rarr36997888rarr37997888rarr6

8 1 8997888rarr38997888rarr39997888rarr40997888rarr41997888rarr82 8997888rarr42997888rarr43997888rarr44997888rarr45997888rarr8

11 1 11997888rarr46997888rarr47997888rarr48997888rarr49997888rarr50997888rarr112 11997888rarr51997888rarr52997888rarr53997888rarr11

15 1 15997888rarr54997888rarr55997888rarr56997888rarr57997888rarr152 15997888rarr58997888rarr59997888rarr60997888rarr15

181 18997888rarr61997888rarr62997888rarr182 18997888rarr63997888rarr64997888rarr65997888rarr67997888rarr66997888rarr183 18997888rarr68997888rarr70997888rarr69997888rarr18

Figure 9 The map of Guangxi Zhuang Autonomous Region (themarked red line is the Guangxi section of the Sino-Vietnameseborder)

efficiency and reaction speed Therefore take the Guangxisection of the border as an example

As displayed in Figure 10 with the ranging tool of GoogleMap the linear distance of this part is about 320 km ThenPaint software is used to discretize this line Fifty target pointsaremarked on the border and twenty base stations are chosenrandomly inside the line Furthermore the relative positionsof these 70 nodes are obtained via the pixel measurement

Figure 10 Guangxi section of the Sino-Vietnamese border with theranging tool

It is assumed that all targets and potential bases arelocated in the area of 320 kilometres multiplied by 160 kilo-metres Mapping these nodes into this area the distributionmap looks like Figure 11 The blue dots are target points andthe red blocks are potential base stations

Two algorithms are applied to solve the practical caseThe results are shown in Table 5 Since the result of H2-NSis obviously superior to another one take the result of H2-NS as the final solution in which the cost is 480309 and thecalculation takes 006840 seconds

The potential base stations are numbered 1 through 20when the target points are represented by 21 to 70 Then thedetailed bases and flight paths can be listed in Table 6 andthe corresponding route map is shown in Figure 12 The finalresult selects 6 bases and launches 15 UAVs

12 Journal of Advanced Transportation

50 100 150 200 250 300 35000

20

40

60

80

100

120

140

Figure 11 50 target points and 20 base stations after discretization

50 100 150 200 250 300 35000

20

40

60

80

100

120

140

Figure 12 The route map of the final solution

6 Conclusions

In this paper considering the background of border patrolfor ISR the capacity constraints of bases are involved inthe multidepot location-routing problem Hence a modifiedmathematical model has been presented The primary objec-tive of this research is to develop an efficient approach forsolving this kind of problem Thus two hybrid heuristicswith neighbourhood search are promoted One is based onclustering and nearest point search and the other one is basedon clustering and CW saving search

In addition experiments have been carried out to com-pare the performance of two algorithms It can be addictedthat neighbourhood search plays an optimizing role to thesolution And the heuristic based on CW saving searchprovides a better solution while consuming more time thanthe other one Furthermore an example based on a practicalborderline is proposed Both algorithms are applied to solvethe border patrol on the practical borderline and provide thefinal solution

Finally two improvements in solving this kind of problemcan be envisaged First the current neighbourhood searchcan be scaled up to find a global optimal solution Secondmore variants of this kind of problem can be exploited Forexample dynamic detecting could be added

Data Availability

The data used to support the findings of this study are avail-able from the corresponding author upon request

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

The research is supported by the National Natural ScienceFoundation of China (no 71771215 and no 71471174)

References

[1] LMiao L Zhen SWangW Lv and X Qu ldquoUnmanned AerialVehicle Scheduling Problem for TrafficMonitoringrdquoComputersamp Industrial Engineering vol 122 pp 15ndash23 2018

[2] S G Manyam S Rasmussen D W Casbeer K Kalyanam andS Manickam ldquoMulti-UAV routing for persistent intelligencesurveillance amp reconnaissance missionsrdquo in Proceedings of the2017 International Conference on Unmanned Aircraft SystemsICUAS 2017 pp 573ndash580 June 2017

[3] S K Jacobsen and O B G Madsen ldquoA comparative study ofheuristics for a two-level routing-location problemrdquo EuropeanJournal of Operational Research vol 5 no 6 pp 378ndash387 1980

[4] D Tuzun and L I Burke ldquoTwo-phase tabu search approach tothe location routing problemrdquo European Journal of OperationalResearch vol 116 no 1 pp 87ndash99 1999

[5] H Min V Jayaraman and R Srivastava ldquoCombined location-routing problems a synthesis and future research directionsrdquoEuropean Journal of Operational Research vol 108 no 1 pp 1ndash15 1998

[6] G Nagy and S Salhi ldquoLocation-routing issues models andmethodsrdquoEuropean Journal ofOperational Research vol 177 no2 pp 649ndash672 2007

[7] J-M Belenguer E Benavent C Prins C Prodhon and RW Calvoc ldquoA Branch-and-Cut method for the CapacitatedLocation-Routing Problemrdquo Computers amp Operations Researchvol 38 no 6 pp 931ndash941 2011

[8] Z Akca R T Berger and T K Ralphs ldquoA branch-and-pricealgorithm for combined location and routing problems undercapacity restrictionsrdquo Operations Research Computer ScienceInterfaces Series vol 47 pp 309ndash330 2009

[9] S Barreto C Ferreira J Paixao and B S Santos ldquoUsing clus-tering analysis in a capacitated location-routing problemrdquoEuropean Journal of Operational Research vol 179 no 3 pp968ndash977 2007

[10] C Prodhon and C Prins ldquoA survey of recent research onlocation-routing problemsrdquo European Journal of OperationalResearch vol 238 no 1 pp 1ndash17 2014

[11] C Prins C Prodhon and RWolfer-Calvo ldquoSolving the capaci-tated location-routing problemby aGRASP complemented by alearning process and a path relinkingrdquo 4OR AQuarterly Journalof Operations Research vol 4 no 3 pp 221ndash238 2006

[12] C Duhamel P Lacomme C Prins and C Prodhon ldquoAGRASPtimesELS approach for the capacitated location-routingproblemrdquo Computers amp Operations Research vol 37 no 11 pp1912ndash1923 2010

[13] R B Lopes C Ferreira and B S Santos ldquoA simple and effectiveevolutionary algorithm for the capacitated location-routingproblemrdquo Computers amp Operations Research vol 70 pp 155ndash162 2016

Journal of Advanced Transportation 13

[14] V F Yu S-W Lin W Lee and C-J Ting ldquoA simulated anneal-ing heuristic for the capacitated location routing problemrdquoComputers amp Industrial Engineering vol 58 no 2 pp 288ndash2992010

[15] J W Escobar R Linfati and P Toth ldquoA two-phase hybridheuristic algorithm for the capacitated location-routing prob-lemrdquoComputers ampOperations Research vol 40 no 1 pp 70ndash792013

[16] R W Harder R R Hill and J T Moore ldquoA Java universalvehicle router for routing unmanned aerial vehiclesrdquo Interna-tional Transactions in Operational Research vol 11 no 3 pp259ndash275 2004

[17] V K Shetty M Sudit and R Nagi ldquoPriority-based assignmentand routing of a fleet of unmanned combat aerial vehiclesrdquoComputers amp Operations Research vol 35 no 6 pp 1813ndash18282008

[18] F Mufalli R Batta and R Nagi ldquoSimultaneous sensor selectionand routing of unmanned aerial vehicles for complex missionplansrdquo Computers amp Operations Research vol 39 no 11 pp2787ndash2799 2012

[19] A M Ham ldquoIntegrated scheduling of m-truck m-drone andm-depot constrained by time-window drop-pickup and m-visit using constraint programmingrdquo Transportation ResearchPart C Emerging Technologies vol 91 pp 1ndash14 2018

[20] G S C Avellar G A S Pereira L C A Pimenta and P IscoldldquoMulti-UAV routing for area coverage and remote sensing withminimum timerdquo Sensors vol 15 no 11 pp 27783ndash27803 2015

[21] I Sarıcicek and Y Akkus ldquoUnmanned aerial vehicle hub-location and routing for monitoring geographic bordersrdquoApplied Mathematical Modelling Simulation and Computationfor Engineering and Environmental Systems vol 39 no 14 pp3939ndash3953 2015

[22] E Yakıcı ldquoSolving location and routing problem for UAVsrdquoComputers amp Industrial Engineering vol 102 pp 294ndash301 2016

[23] T M Cover and P E Hart ldquoNearest neighbor pattern classifi-cationrdquo IEEE Transactions on Information Theory vol 13 no 1pp 21ndash27 1967

[24] G Clarke and J W Wright ldquoScheduling of vehicles from acentral depot to a number of delivery pointsrdquo INFORMS 1964

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4 Journal of Advanced Transportation

(1) Allocate targets allocate every target to its nearest station(2) Sort base sort base stations by the number of allocated targets(3) while (unvisited targets) do(4) Select the base with the most targets(5) Detect targets with Nearest Neighbour(6) if (unvisited targets in this base) then(7) Reallocate allocate the remaining targets to the second nearest station(8) end if(9) end while(10) while (bases with the number of UAVs lower than limit) do(11) Select the base with the least targets and close the station(12) Reallocate allocate targets of the station to the nearest neighbour station(13) Re-detect targets add the new targets for the neighbour station(14) end while

Algorithm 1 Heuristic based on clustering and nearest point search

119911119894119896 minus 119911119895119896 + |119873| 119909119894119895119896 le |119873| minus 1

119894 119895 isin 119873 119896 isin 119881(9)

119909119894119895119896 isin 0 1 119894 119895 isin 119872 cup 119873 119896 isin 119881 (10)

119910119894 isin 0 1 119894 isin 119872 (11)

119911119894119896 ge 0 119894 isin 119873 119896 isin 119881 (12)

The objective function (1) minimizes the sum of base estab-lishing cost UAVsrsquo use cost and its patrol cost Constraint (2)expresses the limitation in flow conservation Constraint (3)ensures that each target point must be visited and assignedto only one UAV Constraint (4) restricts the time elapsed ineach UAVrsquos flight containing both flying time and detectingtime Constraint (5) requires that each UAV can be scheduledatmost once in onemission planning Constraints (6) and (7)define the limitations on the capacity of base station of whichthe number of equipped UAVs cannot exceed the upper andlower limit Constraint (8) makes sure that each UAV mustturn back to the base station which it departs from Subtourelimination constrains are expressed in (9) Constraints (10)to (12) declare the variable domains

4 Algorithms

In this section two different hybrid heuristics are introducedto construct the feasible solution nearest point searchingalgorithm or saving algorithm Then neighbourhood searchserves as an optimization tool to finalize the optimizationsolution

41 Hybrid Heuristics

411 Heuristic Based on Clustering and Nearest Point Search(H1) Heuristic based on clustering and nearest point search(H1) utilizes the strategy of Nearest Neighbour NearestNeighbour is a well-known constructive search algorithmthat is one of the earliest methods proposed for TSP problems[23] It adopts the principle of selecting the next nearestunvisited node until all nodes have been covered It runs

fast however the optimality of the tours it produces highlydepends on the layout of the given nodes

In H1 every target point is allocated to the nearest basestation at first Then for each station which has assignedtargets the path of UAV is arranged one by one until allassigned targets are detected or the number of UAVs reachesthe upper limit of the station If there are unvisited targetsthen allocate the remaining points to the second neareststation At last there is a check function to find whether thereare some stations that the number of UAVs does not reachlower limit If so close the station and reallocate the targets

The corresponding pseudocode is shown in H1 and thedetailed explanation of the heuristic is shown in Algorithm 1

As shown in pseudocode every target is allocated to itsnearest station with the known positions of the potential basestations and target points (Line (1)) Then sort the selectedbase stations (Line (2)) and plan the path of UAVs in eachstation While detecting the targets prioritize the base withthemost targets (Line (4)) As for the details (Line (5)) launchone UAV at a time and choose the nearest unvisited targetas the next access point Judge whether the UAV can returnback to the original station after visiting the next point Ifso the UAV travels to the next point and keeps detectingwhile turning back to the start if not Repeat the step until allassigned targets are detected or the number of UAVs reachesthe upper limit of the station At this time check whetherthere is assigned targets unvisited after sending out all UAVs(Line (6)) If so allocate the remaining targets to the secondnearest station (Line (7))

After all targets have been detected find whether thereare some stations not having enough numbers of UAVs (Line(10)) If so give priority to the base with the least targetsand close the station (Line (11)) Then allocate targets of thestation to the Nearest Neighbour station (Line (12)) Afterthat redetect targets for the newneighbour station (Line (13))like what have done in Line (5)

412 Heuristic Based on Clustering and CW Saving Search(H2) Clarke and Wright proposed the saving algorithm in1964 [24] This algorithm provides an easy way to solve the

Journal of Advanced Transportation 5

(1) Allocate targets allocate every target to its nearest station(2) Sort base sort base stations by the number of allocated targets(3) while (unvisited targets) do(4) Select the base with the most targets and calculate the saving matrix(5) Detect targets with CW(6) if (unvisited targets in this base) then(7) Reallocate allocate the remaining targets to the second nearest station(8) end if(9) end while(10) while (bases with the number of UAVs lower than limit) do(11) Select the base with the least targets and close the station(12) Reallocate allocate targets of the station to the nearest neighbour station(13) Re-detect targets add the new targets for the neighbour station(14) end while

Algorithm 2 Heuristic based on clustering and CW saving search

vehicle routing problem but it considers neither the locationproblem nor the restriction on the numbers of vehicles

Similar to H1 heuristic based on clustering and CW sav-ing search (H2) first allocates each target point to its nearestbase station and has a check function at last Different fromH1 using Nearest Neighbour CW saving search algorithmis applied in H2 while planning paths to detect targets Thecorresponding pseudocode is shown in H2 and the detailedexplanation of the heuristic is shown in Algorithm 2

Since the overall framework of H2 is similar to thatof H1 the same process will not be repeated in this partAfter selecting the base with the most targets calculate thecorresponding distance matrix and saving matrix (Line (4))In terms of the details (Line (5)) launch one UAV at atime Refer to the saving matrix and merge the target pointsas many as possible under the limitation of UAVsrsquo flightendurance which would generate a flight path for a UAVRepeat the step until all assigned targets are detected or allUAVs have been sent out Moreover CW saving search alsoworks in redetecting targets in Line (13)

42 Neighbourhood Search Improvement Although the hy-brid heuristics can construct a feasible solution quickly thesolution still has room for improvement For example somestations can be replaced by another station or some otherstations and some UAV routes still can be optimized Thusneighbourhood search is introduced to optimize the solutionobtained through the heuristics in Section 41 and reducethe overall cost The framework of neighbourhood search isdisplayed in the pseudocode shown in Algorithm 3

Given an initial solution119904 the main process iterates overthe parameter 119894 until it reaches the preset value of maximumiterations 119894119898119886119909 (Line (1)) In each interaction a solution s1015840would be generated through the operation of closing base sta-tions which would be described in Section 421 Then fromLine (5) to Line (16) local search is performed After initializ-ing the neighbourhood list (Line (5)) the local search will notend until running all neighbourhoods without improvement(Line (7)) Neighbourhood list would be explored exhaus-tively every time which returns the best improvement s1015840

(1) Require s 119894119898119886119909(2) 119894 larr997888 1(3) while 119894 le 119894119898119886119909 do(4) s1015840 larr997888 CloseBaseStation(s)(5) Initialize Neighborhood List (N)(6) k larr997888 1(7) while k le N do(8) Find the best neighbor s1015840 isinN(s)(9) if s1015840 lt s then(10) slarr997888 s1015840(11) ReinitializeN(12) k larr997888 1(13) else(14) klarr997888 k + 1(15) end if(16) end while(17) 119894 larr997888 119894 + 1(18) end while

Algorithm 3 Neighbourhood search

(Line (8)) Comparedwith the current solution s if s1015840 is betterthen s1015840 is the new solution and reinitialize the neighbourhoodlist which would restart the counter k (Lines (9)ndash(12)) Theneighbourhoods used in this part are detailed in Sections422ndash424

Therefore combining two heuristics with the neighbour-hood research respectively we can produce two algorithmsand generate two optimal solutions

421 Operation of Closing the Base Station In the feasiblesolutions there exists a possibility that some base stationshave not fully utilized the UAVs Therefore it might usefulto reduce the establishing cost through shutting down somestations As Figure 2 shows just two UAVs are launched forboth station A and station B which have not dispatched allUAVs At this time we can try to close one of these twostations and find whether these targets can be detected bythe UAVs from only one station If so then station B can

6 Journal of Advanced Transportation

Flight Paths

Potential BasesPatrol Targets

A

B

A

B

Figure 2 The operation of closing the base station

Flight Paths

Potential BasesPatrol Targets

A1

2

3A

12

3

Figure 3The operation of Opt2

Flight Paths

Potential BasesPatrol Targets

A

1

2

3 4

56

A

1

2

3 4

56

Figure 4 The operation of exchanging targets

be closed Furthermore after closing the base station theflight paths in station A would be rearranged To save thecalculation time Nearest Neighbourhood algorithm is usedwhich is displayed in Figure 2

422 Neighbourhood 1 Opt2 This neighbourhood relocatestwo targets on one flight path in a tentative solution Thisoperation is mainly meant to reduce the cross-over routes or

overlapping routes In Figure 3 the initial route is 1 997888rarr 2 997888rarr3 Then points 2 and 3 are selected and their positions areswapped to see whether there is a better solution

423 Neighbourhood 2 Exchange Targets This neighbour-hood is set to swap a target with another one which locateson another path in a tentative solution The two paths canbelong to the same station or two adjacent stations Figure 4

Journal of Advanced Transportation 7

Flight Paths

Potential BasesPatrol Targets

A

B

12

3

4

56

7

8

9A

B

12

3

4

56

7

8

9(b)

A

B

12

3

4

56

7

8

9(a)

Figure 5 The operation of insertion

presents the situation that two targets are in different pathsof one station After exchanging the points 3 and 4 the flightdistance of both two flight paths would be decreased whichcould help lower the flight cost

424 Neighbourhood 3 Insertion This neighbourhood re-moves a target and reinserts it in other position in a tentativesolution which may change the owner base station ofthe target Figure 5(a) illustrates a relatively straightforwardmove in one station Additionally the path represented byFigure 5(b) relocates the target 6 from station B to station A

5 Experiment Design and Results

In this section experiments are designed based on actualcharacteristics of border patrol and two algorithms are testedwith the constructed cases

51 Experiment Design When designing the experiment theparticularity of border patrol should be taken into accountSince the detection goal is part of borderline themission areashould be set as an irregular strip area Thus as displayed inFigure 6 it is assumed that the detection area is a rectanglewith aspect ratio of 2 1

In the mission planning the target points should belocated on the borderlinewhile the base stations are inside theborderline It means that there would be a boundary betweenpotential bases and target points which is different from thecases in delivery system Therefore a random curve is first

8

20

25

24

3 5

17

14

1115

19

18

23 21

13

16

6

4

1

2

12

22

107

9

Target Points

Potential BaseStations

0

20

40

60

80

100

120

140

50 100 150 200 2500Figure 6 Experiment case generated under limited conditions

generated as a boundary (note this boundary differs fromthe borderline the border is in the area of target points)Then base stations and target points are separately generatedon both sides of the boundary which is the dotted line inFigure 6 Five potential base stations are below the boundaryline while twenty target points are above it

As the target points are abstracted from a small area onthe borderline they should not be too close to each otherotherwise two points could be merged into one node It issame for the potential stations It would be impractical tobuild two stations in a close range For the purpose of thischaracteristic all nodes are generated one by one Take thebase stations as an example every time a new station isproduced the distance between the station and every existingstation would be judged If the distance is too short the

8 Journal of Advanced Transportation

Table 1 Detailed parameters of two typical UVAs

Parameters UAV 1 UAV 2

Fuselage 07 meters in length 175 meters in length2 meters in wingspan 175 meters in length

Body Weight 85 kg 15 kgPayload 15 kg 4 kg

Flight Speed 80-120 km h maximum 158 km hpatrol 295 km h

Flight Altitude working 100-500 meters working 300 metersMission Radius 70 km 30 kmFlight Endurance 25 hours ge 4 hours

Table 2 Detailed comparison between feasible solution and improved solution of H1-NS

Feasible solution by H1 Improved solution after NSBase UAV Route Base UAV Route

1 1 1997888rarr9997888rarr7997888rarr10997888rarr1 1 1 1997888rarr9997888rarr7997888rarr10997888rarr12 1997888rarr18997888rarr14997888rarr23997888rarr1 2 1997888rarr14997888rarr23997888rarr18997888rarr19997888rarr1

4

1 4997888rarr15997888rarr11997888rarr13997888rarr4

4

1 4997888rarr15997888rarr11997888rarr21997888rarr42 4997888rarr16997888rarr12997888rarr6997888rarr4 2 4997888rarr16997888rarr12997888rarr6997888rarr43 4997888rarr25997888rarr21997888rarr4 3 4997888rarr13997888rarr25997888rarr44 4997888rarr19997888rarr4

51 5997888rarr24997888rarr8997888rarr5

51 5997888rarr24997888rarr8997888rarr5

2 5997888rarr17997888rarr20997888rarr5 2 5997888rarr17997888rarr22997888rarr20997888rarr53 5997888rarr22997888rarr5

Cost 372992 Cost 274386

position would be abandoned and regenerated until there areenough base stations

The parameters of UAVmainly refer to the public param-eters from two typical UAVs which have been applied toborder patrol The detailed parameter is presented in Table 1After some proper randomization the experiment parame-ters are generated such as the flight endurance patrol speedand so on

52 Experiment Result With the experiment data generatedtwo algorithms are tested and compared with each other Forthe sake of illustration H1-NS represents the combination ofthe heuristic based on clustering and nearest point search(H1) and the neighbourhood search while H2-NS containsthe heuristic based on clustering and CW saving search (H2)and the neighbourhood search

521 Results of H1-NS on Test Case Take a small-scale case(5 base stations and 20 target points) generated randomlyFigure 7(a) shows the feasible solution given by H1 while theimproved solution is provided after neighbourhood search asFigure 7(b) depicts

In Figure 7(a) it is can be seen that the performanceof Nearest Neighbour is flawed Obviously when the UAVdepartures from Station 5 and then visits Target 17 and Target20 the rest of energy cannot support it to return to the base ifcontinuing detecting Target 22 which causes one more UAVto be sent to specially visit Target 22

However after neighbourhood search the solution isimproved a lot Some fight paths are merged and adjustedwhich reduces the number of UAVs used as well as the flightdistance of UAV For example the routes 5997888rarr17997888rarr20997888rarr5and 5997888rarr22997888rarr5 aremerged into 5997888rarr17997888rarr22997888rarr20997888rarr5 Andthe detecting order of Target 14 and 23 is interchangeddecreasing the UAVrsquos redundant flight Although the numberof stations has not changed the number of drones hasdecreased after optimization Only 7 UAVs are used in thefinal solution which is two less than that of the initialsolution As displayed in Table 2 the overall costs have beendecreased from 372992 to 274386 down by 26 percent prov-ing the feasibility of H1 and effectiveness of neighbourhoodsearch

522 Results of H2-NS on Test Case The same case is alsoapplied to test H2-NS The feasible solution given by H2is presented by Figure 8(a) and the improved after NS inFigure 8(b)

The conclusion can be drawn that the CW saving algo-rithm has utilized the flight endurance as far as possiblewhich is fairly obvious in the feasible solution Comparedwith the cost of feasible solution in H1 H2 reduces the costfrom 372992 to 336496

After the adjustment of the neighbourhood search thestructure of the solution has changed a lot Although thenumber of the UAVs has not decreased the base station 1 is

Journal of Advanced Transportation 9

Table 3 Detailed comparison between feasible solution and improved solution of H2-NS

Feasible solution by H1 Improved solution after NSBase UAV Route Base UAV Route

1 1 1997888rarr9997888rarr10997888rarr1 1 1 1997888rarr9997888rarr7997888rarr10997888rarr12 1997888rarr18997888rarr23997888rarr14997888rarr7997888rarr1 2 1997888rarr14997888rarr23997888rarr18997888rarr19997888rarr1

4

1 4997888rarr13997888rarr25997888rarr21997888rarr19997888rarr4

4

1 4997888rarr11997888rarr25997888rarr21997888rarr19997888rarr42 4997888rarr15997888rarr11997888rarr4 2 4997888rarr15997888rarr18997888rarr23997888rarr14997888rarr4

3 4997888rarr16997888rarr6997888rarr12997888rarr4 3 4997888rarr16997888rarr13997888rarr6997888rarr12997888rarr44 4997888rarr9997888rarr4

51 5997888rarr24997888rarr8997888rarr5

51 5997888rarr24997888rarr8997888rarr5

2 5997888rarr17997888rarr20997888rarr22997888rarr5 2 5997888rarr17997888rarr20997888rarr22997888rarr53 5997888rarr7997888rarr10997888rarr5

Cost 336496 Cost 189061

0

20

40

60

80

100

120

140

50 100 150 200 2500(a) Feasible solution given by H1

50 100 150 200 25000

20

40

60

80

100

120

140

(b) Improved solution after NS

Figure 7 Illustration of the results of H1-NS for the small-scaleexample

closed and replaced by the other two stations which reducethe base establishing cost

The detailed comparison is shown in Table 3 The overallcosts have been reduced from 336496 to 189061 dropping by44 Therefore H2-NS seems to be more accurate than H1-NS and can solve the problem better

523 Comparison See Table 4

53 Example Based on the Sino-Vietnamese Border In thissection a practical border is used as the example case andsolved by the preceding algorithms

50 100 150 200 25000

20

40

60

80

100

120

140

(a) Feasible solution given by H1

50 100 150 200 25000

20

40

60

80

100

120

140

(b) Improved solution after NS

Figure 8 Illustration of the results of H2-NS for the small-scaleexample

As is shown in Figure 9 there are about 8 cities and 103towns bordering in Guangxi Zhuang Autonomous RegionWith the development of economy and the implementationof opening-up policy especially under ldquoBelt and Roadrdquoinitiative Guangxi develops an increasingly flourishing bor-der trade However smuggling also increases at the sametime Since the border area is mainly delimited by riversor mountains and has few natural barriers this part of theborder is prone to smuggling which is difficult to monitorAccording to the official report 6726 smuggling cases wereseized in Guangxi in 2006 Thus it is meaningful to applyUAVs on the border patrol which can improve the patrol

10 Journal of Advanced Transportation

Table4Algorith

mcomparis

onin

caseso

fthree

scales

CaseS

cale

H1-N

SH2-NS

Costo

ffeasib

lesolutio

nCosto

fimproved

solutio

nTime10and-2

(s)

Costo

ffeasib

lesolutio

nCosto

fimproved

solutio

nTime10and-2

(s)

5sta

tions

amp20

targets

348882

300435

2325

336890

238473

3928

386308

3364

162392

362091

263009

3815

372992

274386

2463

336496

1890

613786

322293

273432

2313

287293

239058

3682

372327

2764

202342

325443

179350

3871

372439

274322

2335

336807

238975

5487

372369

273543

1892

337965

240234

3635

361322

261822

2247

348843

250545

3670

372538

322555

2327

336976

237811

3787

384262

285167

2196

336890

237784

3811

20sta

tions

amp50

targets

842265

692451

3037

793872

5440

586950

731291

631663

3081

681403

531504

6895

792129

592620

4232

754694

505265

6627

730762

631054

306

4670777

471234

7285

730340

630746

3149

681039

481442

7002

856295

6560

523173

792201

492593

7867

807587

608259

3128

733063

483691

7419

8040

06654817

3503

719919

520651

7432

828288

628671

3385

732245

482620

7494

804770

655033

2620

719798

570285

7242

50sta

tions

amp100targets

1340

095

1028130

1040

1196218

791338

4590

1272888

923026

0993

121940

6819554

4819

1314565

952735

1061

1143538

843628

4490

1396086

946150

1073

1308837

858909

4931

1197487

897623

1064

1075171

725519

5414

1430365

1091920

1012

1368315

818606

4525

1331166

1031168

1049

1219333

819335

4508

1354155

1004

220

1000

1208915

809037

4550

1418603

1080944

1029

1319784

869953

444

61343357

943478

1023

1256920

807064

4897

Journal of Advanced Transportation 11

Table 5 Comparison between two results of practical cases

H1-NS H2-NSCost of feasiblesolution

Cost of improvedsolution Time 10and-2 (s) Cost of feasible

solutionCost of improved

solution Time 10and-2 (s)

817492 619800 3091 837997 480309 6840

Table 6 Detailed bases and flight paths of the final solution

Base UAV Route

31 3997888rarr21997888rarr22997888rarr32 3997888rarr23997888rarr24997888rarr33 3997888rarr25997888rarr27997888rarr26997888rarr3

61 6997888rarr28997888rarr29997888rarr30997888rarr62 6997888rarr31997888rarr32997888rarr33997888rarr34997888rarr35997888rarr63 6997888rarr36997888rarr37997888rarr6

8 1 8997888rarr38997888rarr39997888rarr40997888rarr41997888rarr82 8997888rarr42997888rarr43997888rarr44997888rarr45997888rarr8

11 1 11997888rarr46997888rarr47997888rarr48997888rarr49997888rarr50997888rarr112 11997888rarr51997888rarr52997888rarr53997888rarr11

15 1 15997888rarr54997888rarr55997888rarr56997888rarr57997888rarr152 15997888rarr58997888rarr59997888rarr60997888rarr15

181 18997888rarr61997888rarr62997888rarr182 18997888rarr63997888rarr64997888rarr65997888rarr67997888rarr66997888rarr183 18997888rarr68997888rarr70997888rarr69997888rarr18

Figure 9 The map of Guangxi Zhuang Autonomous Region (themarked red line is the Guangxi section of the Sino-Vietnameseborder)

efficiency and reaction speed Therefore take the Guangxisection of the border as an example

As displayed in Figure 10 with the ranging tool of GoogleMap the linear distance of this part is about 320 km ThenPaint software is used to discretize this line Fifty target pointsaremarked on the border and twenty base stations are chosenrandomly inside the line Furthermore the relative positionsof these 70 nodes are obtained via the pixel measurement

Figure 10 Guangxi section of the Sino-Vietnamese border with theranging tool

It is assumed that all targets and potential bases arelocated in the area of 320 kilometres multiplied by 160 kilo-metres Mapping these nodes into this area the distributionmap looks like Figure 11 The blue dots are target points andthe red blocks are potential base stations

Two algorithms are applied to solve the practical caseThe results are shown in Table 5 Since the result of H2-NSis obviously superior to another one take the result of H2-NS as the final solution in which the cost is 480309 and thecalculation takes 006840 seconds

The potential base stations are numbered 1 through 20when the target points are represented by 21 to 70 Then thedetailed bases and flight paths can be listed in Table 6 andthe corresponding route map is shown in Figure 12 The finalresult selects 6 bases and launches 15 UAVs

12 Journal of Advanced Transportation

50 100 150 200 250 300 35000

20

40

60

80

100

120

140

Figure 11 50 target points and 20 base stations after discretization

50 100 150 200 250 300 35000

20

40

60

80

100

120

140

Figure 12 The route map of the final solution

6 Conclusions

In this paper considering the background of border patrolfor ISR the capacity constraints of bases are involved inthe multidepot location-routing problem Hence a modifiedmathematical model has been presented The primary objec-tive of this research is to develop an efficient approach forsolving this kind of problem Thus two hybrid heuristicswith neighbourhood search are promoted One is based onclustering and nearest point search and the other one is basedon clustering and CW saving search

In addition experiments have been carried out to com-pare the performance of two algorithms It can be addictedthat neighbourhood search plays an optimizing role to thesolution And the heuristic based on CW saving searchprovides a better solution while consuming more time thanthe other one Furthermore an example based on a practicalborderline is proposed Both algorithms are applied to solvethe border patrol on the practical borderline and provide thefinal solution

Finally two improvements in solving this kind of problemcan be envisaged First the current neighbourhood searchcan be scaled up to find a global optimal solution Secondmore variants of this kind of problem can be exploited Forexample dynamic detecting could be added

Data Availability

The data used to support the findings of this study are avail-able from the corresponding author upon request

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

The research is supported by the National Natural ScienceFoundation of China (no 71771215 and no 71471174)

References

[1] LMiao L Zhen SWangW Lv and X Qu ldquoUnmanned AerialVehicle Scheduling Problem for TrafficMonitoringrdquoComputersamp Industrial Engineering vol 122 pp 15ndash23 2018

[2] S G Manyam S Rasmussen D W Casbeer K Kalyanam andS Manickam ldquoMulti-UAV routing for persistent intelligencesurveillance amp reconnaissance missionsrdquo in Proceedings of the2017 International Conference on Unmanned Aircraft SystemsICUAS 2017 pp 573ndash580 June 2017

[3] S K Jacobsen and O B G Madsen ldquoA comparative study ofheuristics for a two-level routing-location problemrdquo EuropeanJournal of Operational Research vol 5 no 6 pp 378ndash387 1980

[4] D Tuzun and L I Burke ldquoTwo-phase tabu search approach tothe location routing problemrdquo European Journal of OperationalResearch vol 116 no 1 pp 87ndash99 1999

[5] H Min V Jayaraman and R Srivastava ldquoCombined location-routing problems a synthesis and future research directionsrdquoEuropean Journal of Operational Research vol 108 no 1 pp 1ndash15 1998

[6] G Nagy and S Salhi ldquoLocation-routing issues models andmethodsrdquoEuropean Journal ofOperational Research vol 177 no2 pp 649ndash672 2007

[7] J-M Belenguer E Benavent C Prins C Prodhon and RW Calvoc ldquoA Branch-and-Cut method for the CapacitatedLocation-Routing Problemrdquo Computers amp Operations Researchvol 38 no 6 pp 931ndash941 2011

[8] Z Akca R T Berger and T K Ralphs ldquoA branch-and-pricealgorithm for combined location and routing problems undercapacity restrictionsrdquo Operations Research Computer ScienceInterfaces Series vol 47 pp 309ndash330 2009

[9] S Barreto C Ferreira J Paixao and B S Santos ldquoUsing clus-tering analysis in a capacitated location-routing problemrdquoEuropean Journal of Operational Research vol 179 no 3 pp968ndash977 2007

[10] C Prodhon and C Prins ldquoA survey of recent research onlocation-routing problemsrdquo European Journal of OperationalResearch vol 238 no 1 pp 1ndash17 2014

[11] C Prins C Prodhon and RWolfer-Calvo ldquoSolving the capaci-tated location-routing problemby aGRASP complemented by alearning process and a path relinkingrdquo 4OR AQuarterly Journalof Operations Research vol 4 no 3 pp 221ndash238 2006

[12] C Duhamel P Lacomme C Prins and C Prodhon ldquoAGRASPtimesELS approach for the capacitated location-routingproblemrdquo Computers amp Operations Research vol 37 no 11 pp1912ndash1923 2010

[13] R B Lopes C Ferreira and B S Santos ldquoA simple and effectiveevolutionary algorithm for the capacitated location-routingproblemrdquo Computers amp Operations Research vol 70 pp 155ndash162 2016

Journal of Advanced Transportation 13

[14] V F Yu S-W Lin W Lee and C-J Ting ldquoA simulated anneal-ing heuristic for the capacitated location routing problemrdquoComputers amp Industrial Engineering vol 58 no 2 pp 288ndash2992010

[15] J W Escobar R Linfati and P Toth ldquoA two-phase hybridheuristic algorithm for the capacitated location-routing prob-lemrdquoComputers ampOperations Research vol 40 no 1 pp 70ndash792013

[16] R W Harder R R Hill and J T Moore ldquoA Java universalvehicle router for routing unmanned aerial vehiclesrdquo Interna-tional Transactions in Operational Research vol 11 no 3 pp259ndash275 2004

[17] V K Shetty M Sudit and R Nagi ldquoPriority-based assignmentand routing of a fleet of unmanned combat aerial vehiclesrdquoComputers amp Operations Research vol 35 no 6 pp 1813ndash18282008

[18] F Mufalli R Batta and R Nagi ldquoSimultaneous sensor selectionand routing of unmanned aerial vehicles for complex missionplansrdquo Computers amp Operations Research vol 39 no 11 pp2787ndash2799 2012

[19] A M Ham ldquoIntegrated scheduling of m-truck m-drone andm-depot constrained by time-window drop-pickup and m-visit using constraint programmingrdquo Transportation ResearchPart C Emerging Technologies vol 91 pp 1ndash14 2018

[20] G S C Avellar G A S Pereira L C A Pimenta and P IscoldldquoMulti-UAV routing for area coverage and remote sensing withminimum timerdquo Sensors vol 15 no 11 pp 27783ndash27803 2015

[21] I Sarıcicek and Y Akkus ldquoUnmanned aerial vehicle hub-location and routing for monitoring geographic bordersrdquoApplied Mathematical Modelling Simulation and Computationfor Engineering and Environmental Systems vol 39 no 14 pp3939ndash3953 2015

[22] E Yakıcı ldquoSolving location and routing problem for UAVsrdquoComputers amp Industrial Engineering vol 102 pp 294ndash301 2016

[23] T M Cover and P E Hart ldquoNearest neighbor pattern classifi-cationrdquo IEEE Transactions on Information Theory vol 13 no 1pp 21ndash27 1967

[24] G Clarke and J W Wright ldquoScheduling of vehicles from acentral depot to a number of delivery pointsrdquo INFORMS 1964

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Journal of Advanced Transportation 5

(1) Allocate targets allocate every target to its nearest station(2) Sort base sort base stations by the number of allocated targets(3) while (unvisited targets) do(4) Select the base with the most targets and calculate the saving matrix(5) Detect targets with CW(6) if (unvisited targets in this base) then(7) Reallocate allocate the remaining targets to the second nearest station(8) end if(9) end while(10) while (bases with the number of UAVs lower than limit) do(11) Select the base with the least targets and close the station(12) Reallocate allocate targets of the station to the nearest neighbour station(13) Re-detect targets add the new targets for the neighbour station(14) end while

Algorithm 2 Heuristic based on clustering and CW saving search

vehicle routing problem but it considers neither the locationproblem nor the restriction on the numbers of vehicles

Similar to H1 heuristic based on clustering and CW sav-ing search (H2) first allocates each target point to its nearestbase station and has a check function at last Different fromH1 using Nearest Neighbour CW saving search algorithmis applied in H2 while planning paths to detect targets Thecorresponding pseudocode is shown in H2 and the detailedexplanation of the heuristic is shown in Algorithm 2

Since the overall framework of H2 is similar to thatof H1 the same process will not be repeated in this partAfter selecting the base with the most targets calculate thecorresponding distance matrix and saving matrix (Line (4))In terms of the details (Line (5)) launch one UAV at atime Refer to the saving matrix and merge the target pointsas many as possible under the limitation of UAVsrsquo flightendurance which would generate a flight path for a UAVRepeat the step until all assigned targets are detected or allUAVs have been sent out Moreover CW saving search alsoworks in redetecting targets in Line (13)

42 Neighbourhood Search Improvement Although the hy-brid heuristics can construct a feasible solution quickly thesolution still has room for improvement For example somestations can be replaced by another station or some otherstations and some UAV routes still can be optimized Thusneighbourhood search is introduced to optimize the solutionobtained through the heuristics in Section 41 and reducethe overall cost The framework of neighbourhood search isdisplayed in the pseudocode shown in Algorithm 3

Given an initial solution119904 the main process iterates overthe parameter 119894 until it reaches the preset value of maximumiterations 119894119898119886119909 (Line (1)) In each interaction a solution s1015840would be generated through the operation of closing base sta-tions which would be described in Section 421 Then fromLine (5) to Line (16) local search is performed After initializ-ing the neighbourhood list (Line (5)) the local search will notend until running all neighbourhoods without improvement(Line (7)) Neighbourhood list would be explored exhaus-tively every time which returns the best improvement s1015840

(1) Require s 119894119898119886119909(2) 119894 larr997888 1(3) while 119894 le 119894119898119886119909 do(4) s1015840 larr997888 CloseBaseStation(s)(5) Initialize Neighborhood List (N)(6) k larr997888 1(7) while k le N do(8) Find the best neighbor s1015840 isinN(s)(9) if s1015840 lt s then(10) slarr997888 s1015840(11) ReinitializeN(12) k larr997888 1(13) else(14) klarr997888 k + 1(15) end if(16) end while(17) 119894 larr997888 119894 + 1(18) end while

Algorithm 3 Neighbourhood search

(Line (8)) Comparedwith the current solution s if s1015840 is betterthen s1015840 is the new solution and reinitialize the neighbourhoodlist which would restart the counter k (Lines (9)ndash(12)) Theneighbourhoods used in this part are detailed in Sections422ndash424

Therefore combining two heuristics with the neighbour-hood research respectively we can produce two algorithmsand generate two optimal solutions

421 Operation of Closing the Base Station In the feasiblesolutions there exists a possibility that some base stationshave not fully utilized the UAVs Therefore it might usefulto reduce the establishing cost through shutting down somestations As Figure 2 shows just two UAVs are launched forboth station A and station B which have not dispatched allUAVs At this time we can try to close one of these twostations and find whether these targets can be detected bythe UAVs from only one station If so then station B can

6 Journal of Advanced Transportation

Flight Paths

Potential BasesPatrol Targets

A

B

A

B

Figure 2 The operation of closing the base station

Flight Paths

Potential BasesPatrol Targets

A1

2

3A

12

3

Figure 3The operation of Opt2

Flight Paths

Potential BasesPatrol Targets

A

1

2

3 4

56

A

1

2

3 4

56

Figure 4 The operation of exchanging targets

be closed Furthermore after closing the base station theflight paths in station A would be rearranged To save thecalculation time Nearest Neighbourhood algorithm is usedwhich is displayed in Figure 2

422 Neighbourhood 1 Opt2 This neighbourhood relocatestwo targets on one flight path in a tentative solution Thisoperation is mainly meant to reduce the cross-over routes or

overlapping routes In Figure 3 the initial route is 1 997888rarr 2 997888rarr3 Then points 2 and 3 are selected and their positions areswapped to see whether there is a better solution

423 Neighbourhood 2 Exchange Targets This neighbour-hood is set to swap a target with another one which locateson another path in a tentative solution The two paths canbelong to the same station or two adjacent stations Figure 4

Journal of Advanced Transportation 7

Flight Paths

Potential BasesPatrol Targets

A

B

12

3

4

56

7

8

9A

B

12

3

4

56

7

8

9(b)

A

B

12

3

4

56

7

8

9(a)

Figure 5 The operation of insertion

presents the situation that two targets are in different pathsof one station After exchanging the points 3 and 4 the flightdistance of both two flight paths would be decreased whichcould help lower the flight cost

424 Neighbourhood 3 Insertion This neighbourhood re-moves a target and reinserts it in other position in a tentativesolution which may change the owner base station ofthe target Figure 5(a) illustrates a relatively straightforwardmove in one station Additionally the path represented byFigure 5(b) relocates the target 6 from station B to station A

5 Experiment Design and Results

In this section experiments are designed based on actualcharacteristics of border patrol and two algorithms are testedwith the constructed cases

51 Experiment Design When designing the experiment theparticularity of border patrol should be taken into accountSince the detection goal is part of borderline themission areashould be set as an irregular strip area Thus as displayed inFigure 6 it is assumed that the detection area is a rectanglewith aspect ratio of 2 1

In the mission planning the target points should belocated on the borderlinewhile the base stations are inside theborderline It means that there would be a boundary betweenpotential bases and target points which is different from thecases in delivery system Therefore a random curve is first

8

20

25

24

3 5

17

14

1115

19

18

23 21

13

16

6

4

1

2

12

22

107

9

Target Points

Potential BaseStations

0

20

40

60

80

100

120

140

50 100 150 200 2500Figure 6 Experiment case generated under limited conditions

generated as a boundary (note this boundary differs fromthe borderline the border is in the area of target points)Then base stations and target points are separately generatedon both sides of the boundary which is the dotted line inFigure 6 Five potential base stations are below the boundaryline while twenty target points are above it

As the target points are abstracted from a small area onthe borderline they should not be too close to each otherotherwise two points could be merged into one node It issame for the potential stations It would be impractical tobuild two stations in a close range For the purpose of thischaracteristic all nodes are generated one by one Take thebase stations as an example every time a new station isproduced the distance between the station and every existingstation would be judged If the distance is too short the

8 Journal of Advanced Transportation

Table 1 Detailed parameters of two typical UVAs

Parameters UAV 1 UAV 2

Fuselage 07 meters in length 175 meters in length2 meters in wingspan 175 meters in length

Body Weight 85 kg 15 kgPayload 15 kg 4 kg

Flight Speed 80-120 km h maximum 158 km hpatrol 295 km h

Flight Altitude working 100-500 meters working 300 metersMission Radius 70 km 30 kmFlight Endurance 25 hours ge 4 hours

Table 2 Detailed comparison between feasible solution and improved solution of H1-NS

Feasible solution by H1 Improved solution after NSBase UAV Route Base UAV Route

1 1 1997888rarr9997888rarr7997888rarr10997888rarr1 1 1 1997888rarr9997888rarr7997888rarr10997888rarr12 1997888rarr18997888rarr14997888rarr23997888rarr1 2 1997888rarr14997888rarr23997888rarr18997888rarr19997888rarr1

4

1 4997888rarr15997888rarr11997888rarr13997888rarr4

4

1 4997888rarr15997888rarr11997888rarr21997888rarr42 4997888rarr16997888rarr12997888rarr6997888rarr4 2 4997888rarr16997888rarr12997888rarr6997888rarr43 4997888rarr25997888rarr21997888rarr4 3 4997888rarr13997888rarr25997888rarr44 4997888rarr19997888rarr4

51 5997888rarr24997888rarr8997888rarr5

51 5997888rarr24997888rarr8997888rarr5

2 5997888rarr17997888rarr20997888rarr5 2 5997888rarr17997888rarr22997888rarr20997888rarr53 5997888rarr22997888rarr5

Cost 372992 Cost 274386

position would be abandoned and regenerated until there areenough base stations

The parameters of UAVmainly refer to the public param-eters from two typical UAVs which have been applied toborder patrol The detailed parameter is presented in Table 1After some proper randomization the experiment parame-ters are generated such as the flight endurance patrol speedand so on

52 Experiment Result With the experiment data generatedtwo algorithms are tested and compared with each other Forthe sake of illustration H1-NS represents the combination ofthe heuristic based on clustering and nearest point search(H1) and the neighbourhood search while H2-NS containsthe heuristic based on clustering and CW saving search (H2)and the neighbourhood search

521 Results of H1-NS on Test Case Take a small-scale case(5 base stations and 20 target points) generated randomlyFigure 7(a) shows the feasible solution given by H1 while theimproved solution is provided after neighbourhood search asFigure 7(b) depicts

In Figure 7(a) it is can be seen that the performanceof Nearest Neighbour is flawed Obviously when the UAVdepartures from Station 5 and then visits Target 17 and Target20 the rest of energy cannot support it to return to the base ifcontinuing detecting Target 22 which causes one more UAVto be sent to specially visit Target 22

However after neighbourhood search the solution isimproved a lot Some fight paths are merged and adjustedwhich reduces the number of UAVs used as well as the flightdistance of UAV For example the routes 5997888rarr17997888rarr20997888rarr5and 5997888rarr22997888rarr5 aremerged into 5997888rarr17997888rarr22997888rarr20997888rarr5 Andthe detecting order of Target 14 and 23 is interchangeddecreasing the UAVrsquos redundant flight Although the numberof stations has not changed the number of drones hasdecreased after optimization Only 7 UAVs are used in thefinal solution which is two less than that of the initialsolution As displayed in Table 2 the overall costs have beendecreased from 372992 to 274386 down by 26 percent prov-ing the feasibility of H1 and effectiveness of neighbourhoodsearch

522 Results of H2-NS on Test Case The same case is alsoapplied to test H2-NS The feasible solution given by H2is presented by Figure 8(a) and the improved after NS inFigure 8(b)

The conclusion can be drawn that the CW saving algo-rithm has utilized the flight endurance as far as possiblewhich is fairly obvious in the feasible solution Comparedwith the cost of feasible solution in H1 H2 reduces the costfrom 372992 to 336496

After the adjustment of the neighbourhood search thestructure of the solution has changed a lot Although thenumber of the UAVs has not decreased the base station 1 is

Journal of Advanced Transportation 9

Table 3 Detailed comparison between feasible solution and improved solution of H2-NS

Feasible solution by H1 Improved solution after NSBase UAV Route Base UAV Route

1 1 1997888rarr9997888rarr10997888rarr1 1 1 1997888rarr9997888rarr7997888rarr10997888rarr12 1997888rarr18997888rarr23997888rarr14997888rarr7997888rarr1 2 1997888rarr14997888rarr23997888rarr18997888rarr19997888rarr1

4

1 4997888rarr13997888rarr25997888rarr21997888rarr19997888rarr4

4

1 4997888rarr11997888rarr25997888rarr21997888rarr19997888rarr42 4997888rarr15997888rarr11997888rarr4 2 4997888rarr15997888rarr18997888rarr23997888rarr14997888rarr4

3 4997888rarr16997888rarr6997888rarr12997888rarr4 3 4997888rarr16997888rarr13997888rarr6997888rarr12997888rarr44 4997888rarr9997888rarr4

51 5997888rarr24997888rarr8997888rarr5

51 5997888rarr24997888rarr8997888rarr5

2 5997888rarr17997888rarr20997888rarr22997888rarr5 2 5997888rarr17997888rarr20997888rarr22997888rarr53 5997888rarr7997888rarr10997888rarr5

Cost 336496 Cost 189061

0

20

40

60

80

100

120

140

50 100 150 200 2500(a) Feasible solution given by H1

50 100 150 200 25000

20

40

60

80

100

120

140

(b) Improved solution after NS

Figure 7 Illustration of the results of H1-NS for the small-scaleexample

closed and replaced by the other two stations which reducethe base establishing cost

The detailed comparison is shown in Table 3 The overallcosts have been reduced from 336496 to 189061 dropping by44 Therefore H2-NS seems to be more accurate than H1-NS and can solve the problem better

523 Comparison See Table 4

53 Example Based on the Sino-Vietnamese Border In thissection a practical border is used as the example case andsolved by the preceding algorithms

50 100 150 200 25000

20

40

60

80

100

120

140

(a) Feasible solution given by H1

50 100 150 200 25000

20

40

60

80

100

120

140

(b) Improved solution after NS

Figure 8 Illustration of the results of H2-NS for the small-scaleexample

As is shown in Figure 9 there are about 8 cities and 103towns bordering in Guangxi Zhuang Autonomous RegionWith the development of economy and the implementationof opening-up policy especially under ldquoBelt and Roadrdquoinitiative Guangxi develops an increasingly flourishing bor-der trade However smuggling also increases at the sametime Since the border area is mainly delimited by riversor mountains and has few natural barriers this part of theborder is prone to smuggling which is difficult to monitorAccording to the official report 6726 smuggling cases wereseized in Guangxi in 2006 Thus it is meaningful to applyUAVs on the border patrol which can improve the patrol

10 Journal of Advanced Transportation

Table4Algorith

mcomparis

onin

caseso

fthree

scales

CaseS

cale

H1-N

SH2-NS

Costo

ffeasib

lesolutio

nCosto

fimproved

solutio

nTime10and-2

(s)

Costo

ffeasib

lesolutio

nCosto

fimproved

solutio

nTime10and-2

(s)

5sta

tions

amp20

targets

348882

300435

2325

336890

238473

3928

386308

3364

162392

362091

263009

3815

372992

274386

2463

336496

1890

613786

322293

273432

2313

287293

239058

3682

372327

2764

202342

325443

179350

3871

372439

274322

2335

336807

238975

5487

372369

273543

1892

337965

240234

3635

361322

261822

2247

348843

250545

3670

372538

322555

2327

336976

237811

3787

384262

285167

2196

336890

237784

3811

20sta

tions

amp50

targets

842265

692451

3037

793872

5440

586950

731291

631663

3081

681403

531504

6895

792129

592620

4232

754694

505265

6627

730762

631054

306

4670777

471234

7285

730340

630746

3149

681039

481442

7002

856295

6560

523173

792201

492593

7867

807587

608259

3128

733063

483691

7419

8040

06654817

3503

719919

520651

7432

828288

628671

3385

732245

482620

7494

804770

655033

2620

719798

570285

7242

50sta

tions

amp100targets

1340

095

1028130

1040

1196218

791338

4590

1272888

923026

0993

121940

6819554

4819

1314565

952735

1061

1143538

843628

4490

1396086

946150

1073

1308837

858909

4931

1197487

897623

1064

1075171

725519

5414

1430365

1091920

1012

1368315

818606

4525

1331166

1031168

1049

1219333

819335

4508

1354155

1004

220

1000

1208915

809037

4550

1418603

1080944

1029

1319784

869953

444

61343357

943478

1023

1256920

807064

4897

Journal of Advanced Transportation 11

Table 5 Comparison between two results of practical cases

H1-NS H2-NSCost of feasiblesolution

Cost of improvedsolution Time 10and-2 (s) Cost of feasible

solutionCost of improved

solution Time 10and-2 (s)

817492 619800 3091 837997 480309 6840

Table 6 Detailed bases and flight paths of the final solution

Base UAV Route

31 3997888rarr21997888rarr22997888rarr32 3997888rarr23997888rarr24997888rarr33 3997888rarr25997888rarr27997888rarr26997888rarr3

61 6997888rarr28997888rarr29997888rarr30997888rarr62 6997888rarr31997888rarr32997888rarr33997888rarr34997888rarr35997888rarr63 6997888rarr36997888rarr37997888rarr6

8 1 8997888rarr38997888rarr39997888rarr40997888rarr41997888rarr82 8997888rarr42997888rarr43997888rarr44997888rarr45997888rarr8

11 1 11997888rarr46997888rarr47997888rarr48997888rarr49997888rarr50997888rarr112 11997888rarr51997888rarr52997888rarr53997888rarr11

15 1 15997888rarr54997888rarr55997888rarr56997888rarr57997888rarr152 15997888rarr58997888rarr59997888rarr60997888rarr15

181 18997888rarr61997888rarr62997888rarr182 18997888rarr63997888rarr64997888rarr65997888rarr67997888rarr66997888rarr183 18997888rarr68997888rarr70997888rarr69997888rarr18

Figure 9 The map of Guangxi Zhuang Autonomous Region (themarked red line is the Guangxi section of the Sino-Vietnameseborder)

efficiency and reaction speed Therefore take the Guangxisection of the border as an example

As displayed in Figure 10 with the ranging tool of GoogleMap the linear distance of this part is about 320 km ThenPaint software is used to discretize this line Fifty target pointsaremarked on the border and twenty base stations are chosenrandomly inside the line Furthermore the relative positionsof these 70 nodes are obtained via the pixel measurement

Figure 10 Guangxi section of the Sino-Vietnamese border with theranging tool

It is assumed that all targets and potential bases arelocated in the area of 320 kilometres multiplied by 160 kilo-metres Mapping these nodes into this area the distributionmap looks like Figure 11 The blue dots are target points andthe red blocks are potential base stations

Two algorithms are applied to solve the practical caseThe results are shown in Table 5 Since the result of H2-NSis obviously superior to another one take the result of H2-NS as the final solution in which the cost is 480309 and thecalculation takes 006840 seconds

The potential base stations are numbered 1 through 20when the target points are represented by 21 to 70 Then thedetailed bases and flight paths can be listed in Table 6 andthe corresponding route map is shown in Figure 12 The finalresult selects 6 bases and launches 15 UAVs

12 Journal of Advanced Transportation

50 100 150 200 250 300 35000

20

40

60

80

100

120

140

Figure 11 50 target points and 20 base stations after discretization

50 100 150 200 250 300 35000

20

40

60

80

100

120

140

Figure 12 The route map of the final solution

6 Conclusions

In this paper considering the background of border patrolfor ISR the capacity constraints of bases are involved inthe multidepot location-routing problem Hence a modifiedmathematical model has been presented The primary objec-tive of this research is to develop an efficient approach forsolving this kind of problem Thus two hybrid heuristicswith neighbourhood search are promoted One is based onclustering and nearest point search and the other one is basedon clustering and CW saving search

In addition experiments have been carried out to com-pare the performance of two algorithms It can be addictedthat neighbourhood search plays an optimizing role to thesolution And the heuristic based on CW saving searchprovides a better solution while consuming more time thanthe other one Furthermore an example based on a practicalborderline is proposed Both algorithms are applied to solvethe border patrol on the practical borderline and provide thefinal solution

Finally two improvements in solving this kind of problemcan be envisaged First the current neighbourhood searchcan be scaled up to find a global optimal solution Secondmore variants of this kind of problem can be exploited Forexample dynamic detecting could be added

Data Availability

The data used to support the findings of this study are avail-able from the corresponding author upon request

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

The research is supported by the National Natural ScienceFoundation of China (no 71771215 and no 71471174)

References

[1] LMiao L Zhen SWangW Lv and X Qu ldquoUnmanned AerialVehicle Scheduling Problem for TrafficMonitoringrdquoComputersamp Industrial Engineering vol 122 pp 15ndash23 2018

[2] S G Manyam S Rasmussen D W Casbeer K Kalyanam andS Manickam ldquoMulti-UAV routing for persistent intelligencesurveillance amp reconnaissance missionsrdquo in Proceedings of the2017 International Conference on Unmanned Aircraft SystemsICUAS 2017 pp 573ndash580 June 2017

[3] S K Jacobsen and O B G Madsen ldquoA comparative study ofheuristics for a two-level routing-location problemrdquo EuropeanJournal of Operational Research vol 5 no 6 pp 378ndash387 1980

[4] D Tuzun and L I Burke ldquoTwo-phase tabu search approach tothe location routing problemrdquo European Journal of OperationalResearch vol 116 no 1 pp 87ndash99 1999

[5] H Min V Jayaraman and R Srivastava ldquoCombined location-routing problems a synthesis and future research directionsrdquoEuropean Journal of Operational Research vol 108 no 1 pp 1ndash15 1998

[6] G Nagy and S Salhi ldquoLocation-routing issues models andmethodsrdquoEuropean Journal ofOperational Research vol 177 no2 pp 649ndash672 2007

[7] J-M Belenguer E Benavent C Prins C Prodhon and RW Calvoc ldquoA Branch-and-Cut method for the CapacitatedLocation-Routing Problemrdquo Computers amp Operations Researchvol 38 no 6 pp 931ndash941 2011

[8] Z Akca R T Berger and T K Ralphs ldquoA branch-and-pricealgorithm for combined location and routing problems undercapacity restrictionsrdquo Operations Research Computer ScienceInterfaces Series vol 47 pp 309ndash330 2009

[9] S Barreto C Ferreira J Paixao and B S Santos ldquoUsing clus-tering analysis in a capacitated location-routing problemrdquoEuropean Journal of Operational Research vol 179 no 3 pp968ndash977 2007

[10] C Prodhon and C Prins ldquoA survey of recent research onlocation-routing problemsrdquo European Journal of OperationalResearch vol 238 no 1 pp 1ndash17 2014

[11] C Prins C Prodhon and RWolfer-Calvo ldquoSolving the capaci-tated location-routing problemby aGRASP complemented by alearning process and a path relinkingrdquo 4OR AQuarterly Journalof Operations Research vol 4 no 3 pp 221ndash238 2006

[12] C Duhamel P Lacomme C Prins and C Prodhon ldquoAGRASPtimesELS approach for the capacitated location-routingproblemrdquo Computers amp Operations Research vol 37 no 11 pp1912ndash1923 2010

[13] R B Lopes C Ferreira and B S Santos ldquoA simple and effectiveevolutionary algorithm for the capacitated location-routingproblemrdquo Computers amp Operations Research vol 70 pp 155ndash162 2016

Journal of Advanced Transportation 13

[14] V F Yu S-W Lin W Lee and C-J Ting ldquoA simulated anneal-ing heuristic for the capacitated location routing problemrdquoComputers amp Industrial Engineering vol 58 no 2 pp 288ndash2992010

[15] J W Escobar R Linfati and P Toth ldquoA two-phase hybridheuristic algorithm for the capacitated location-routing prob-lemrdquoComputers ampOperations Research vol 40 no 1 pp 70ndash792013

[16] R W Harder R R Hill and J T Moore ldquoA Java universalvehicle router for routing unmanned aerial vehiclesrdquo Interna-tional Transactions in Operational Research vol 11 no 3 pp259ndash275 2004

[17] V K Shetty M Sudit and R Nagi ldquoPriority-based assignmentand routing of a fleet of unmanned combat aerial vehiclesrdquoComputers amp Operations Research vol 35 no 6 pp 1813ndash18282008

[18] F Mufalli R Batta and R Nagi ldquoSimultaneous sensor selectionand routing of unmanned aerial vehicles for complex missionplansrdquo Computers amp Operations Research vol 39 no 11 pp2787ndash2799 2012

[19] A M Ham ldquoIntegrated scheduling of m-truck m-drone andm-depot constrained by time-window drop-pickup and m-visit using constraint programmingrdquo Transportation ResearchPart C Emerging Technologies vol 91 pp 1ndash14 2018

[20] G S C Avellar G A S Pereira L C A Pimenta and P IscoldldquoMulti-UAV routing for area coverage and remote sensing withminimum timerdquo Sensors vol 15 no 11 pp 27783ndash27803 2015

[21] I Sarıcicek and Y Akkus ldquoUnmanned aerial vehicle hub-location and routing for monitoring geographic bordersrdquoApplied Mathematical Modelling Simulation and Computationfor Engineering and Environmental Systems vol 39 no 14 pp3939ndash3953 2015

[22] E Yakıcı ldquoSolving location and routing problem for UAVsrdquoComputers amp Industrial Engineering vol 102 pp 294ndash301 2016

[23] T M Cover and P E Hart ldquoNearest neighbor pattern classifi-cationrdquo IEEE Transactions on Information Theory vol 13 no 1pp 21ndash27 1967

[24] G Clarke and J W Wright ldquoScheduling of vehicles from acentral depot to a number of delivery pointsrdquo INFORMS 1964

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6 Journal of Advanced Transportation

Flight Paths

Potential BasesPatrol Targets

A

B

A

B

Figure 2 The operation of closing the base station

Flight Paths

Potential BasesPatrol Targets

A1

2

3A

12

3

Figure 3The operation of Opt2

Flight Paths

Potential BasesPatrol Targets

A

1

2

3 4

56

A

1

2

3 4

56

Figure 4 The operation of exchanging targets

be closed Furthermore after closing the base station theflight paths in station A would be rearranged To save thecalculation time Nearest Neighbourhood algorithm is usedwhich is displayed in Figure 2

422 Neighbourhood 1 Opt2 This neighbourhood relocatestwo targets on one flight path in a tentative solution Thisoperation is mainly meant to reduce the cross-over routes or

overlapping routes In Figure 3 the initial route is 1 997888rarr 2 997888rarr3 Then points 2 and 3 are selected and their positions areswapped to see whether there is a better solution

423 Neighbourhood 2 Exchange Targets This neighbour-hood is set to swap a target with another one which locateson another path in a tentative solution The two paths canbelong to the same station or two adjacent stations Figure 4

Journal of Advanced Transportation 7

Flight Paths

Potential BasesPatrol Targets

A

B

12

3

4

56

7

8

9A

B

12

3

4

56

7

8

9(b)

A

B

12

3

4

56

7

8

9(a)

Figure 5 The operation of insertion

presents the situation that two targets are in different pathsof one station After exchanging the points 3 and 4 the flightdistance of both two flight paths would be decreased whichcould help lower the flight cost

424 Neighbourhood 3 Insertion This neighbourhood re-moves a target and reinserts it in other position in a tentativesolution which may change the owner base station ofthe target Figure 5(a) illustrates a relatively straightforwardmove in one station Additionally the path represented byFigure 5(b) relocates the target 6 from station B to station A

5 Experiment Design and Results

In this section experiments are designed based on actualcharacteristics of border patrol and two algorithms are testedwith the constructed cases

51 Experiment Design When designing the experiment theparticularity of border patrol should be taken into accountSince the detection goal is part of borderline themission areashould be set as an irregular strip area Thus as displayed inFigure 6 it is assumed that the detection area is a rectanglewith aspect ratio of 2 1

In the mission planning the target points should belocated on the borderlinewhile the base stations are inside theborderline It means that there would be a boundary betweenpotential bases and target points which is different from thecases in delivery system Therefore a random curve is first

8

20

25

24

3 5

17

14

1115

19

18

23 21

13

16

6

4

1

2

12

22

107

9

Target Points

Potential BaseStations

0

20

40

60

80

100

120

140

50 100 150 200 2500Figure 6 Experiment case generated under limited conditions

generated as a boundary (note this boundary differs fromthe borderline the border is in the area of target points)Then base stations and target points are separately generatedon both sides of the boundary which is the dotted line inFigure 6 Five potential base stations are below the boundaryline while twenty target points are above it

As the target points are abstracted from a small area onthe borderline they should not be too close to each otherotherwise two points could be merged into one node It issame for the potential stations It would be impractical tobuild two stations in a close range For the purpose of thischaracteristic all nodes are generated one by one Take thebase stations as an example every time a new station isproduced the distance between the station and every existingstation would be judged If the distance is too short the

8 Journal of Advanced Transportation

Table 1 Detailed parameters of two typical UVAs

Parameters UAV 1 UAV 2

Fuselage 07 meters in length 175 meters in length2 meters in wingspan 175 meters in length

Body Weight 85 kg 15 kgPayload 15 kg 4 kg

Flight Speed 80-120 km h maximum 158 km hpatrol 295 km h

Flight Altitude working 100-500 meters working 300 metersMission Radius 70 km 30 kmFlight Endurance 25 hours ge 4 hours

Table 2 Detailed comparison between feasible solution and improved solution of H1-NS

Feasible solution by H1 Improved solution after NSBase UAV Route Base UAV Route

1 1 1997888rarr9997888rarr7997888rarr10997888rarr1 1 1 1997888rarr9997888rarr7997888rarr10997888rarr12 1997888rarr18997888rarr14997888rarr23997888rarr1 2 1997888rarr14997888rarr23997888rarr18997888rarr19997888rarr1

4

1 4997888rarr15997888rarr11997888rarr13997888rarr4

4

1 4997888rarr15997888rarr11997888rarr21997888rarr42 4997888rarr16997888rarr12997888rarr6997888rarr4 2 4997888rarr16997888rarr12997888rarr6997888rarr43 4997888rarr25997888rarr21997888rarr4 3 4997888rarr13997888rarr25997888rarr44 4997888rarr19997888rarr4

51 5997888rarr24997888rarr8997888rarr5

51 5997888rarr24997888rarr8997888rarr5

2 5997888rarr17997888rarr20997888rarr5 2 5997888rarr17997888rarr22997888rarr20997888rarr53 5997888rarr22997888rarr5

Cost 372992 Cost 274386

position would be abandoned and regenerated until there areenough base stations

The parameters of UAVmainly refer to the public param-eters from two typical UAVs which have been applied toborder patrol The detailed parameter is presented in Table 1After some proper randomization the experiment parame-ters are generated such as the flight endurance patrol speedand so on

52 Experiment Result With the experiment data generatedtwo algorithms are tested and compared with each other Forthe sake of illustration H1-NS represents the combination ofthe heuristic based on clustering and nearest point search(H1) and the neighbourhood search while H2-NS containsthe heuristic based on clustering and CW saving search (H2)and the neighbourhood search

521 Results of H1-NS on Test Case Take a small-scale case(5 base stations and 20 target points) generated randomlyFigure 7(a) shows the feasible solution given by H1 while theimproved solution is provided after neighbourhood search asFigure 7(b) depicts

In Figure 7(a) it is can be seen that the performanceof Nearest Neighbour is flawed Obviously when the UAVdepartures from Station 5 and then visits Target 17 and Target20 the rest of energy cannot support it to return to the base ifcontinuing detecting Target 22 which causes one more UAVto be sent to specially visit Target 22

However after neighbourhood search the solution isimproved a lot Some fight paths are merged and adjustedwhich reduces the number of UAVs used as well as the flightdistance of UAV For example the routes 5997888rarr17997888rarr20997888rarr5and 5997888rarr22997888rarr5 aremerged into 5997888rarr17997888rarr22997888rarr20997888rarr5 Andthe detecting order of Target 14 and 23 is interchangeddecreasing the UAVrsquos redundant flight Although the numberof stations has not changed the number of drones hasdecreased after optimization Only 7 UAVs are used in thefinal solution which is two less than that of the initialsolution As displayed in Table 2 the overall costs have beendecreased from 372992 to 274386 down by 26 percent prov-ing the feasibility of H1 and effectiveness of neighbourhoodsearch

522 Results of H2-NS on Test Case The same case is alsoapplied to test H2-NS The feasible solution given by H2is presented by Figure 8(a) and the improved after NS inFigure 8(b)

The conclusion can be drawn that the CW saving algo-rithm has utilized the flight endurance as far as possiblewhich is fairly obvious in the feasible solution Comparedwith the cost of feasible solution in H1 H2 reduces the costfrom 372992 to 336496

After the adjustment of the neighbourhood search thestructure of the solution has changed a lot Although thenumber of the UAVs has not decreased the base station 1 is

Journal of Advanced Transportation 9

Table 3 Detailed comparison between feasible solution and improved solution of H2-NS

Feasible solution by H1 Improved solution after NSBase UAV Route Base UAV Route

1 1 1997888rarr9997888rarr10997888rarr1 1 1 1997888rarr9997888rarr7997888rarr10997888rarr12 1997888rarr18997888rarr23997888rarr14997888rarr7997888rarr1 2 1997888rarr14997888rarr23997888rarr18997888rarr19997888rarr1

4

1 4997888rarr13997888rarr25997888rarr21997888rarr19997888rarr4

4

1 4997888rarr11997888rarr25997888rarr21997888rarr19997888rarr42 4997888rarr15997888rarr11997888rarr4 2 4997888rarr15997888rarr18997888rarr23997888rarr14997888rarr4

3 4997888rarr16997888rarr6997888rarr12997888rarr4 3 4997888rarr16997888rarr13997888rarr6997888rarr12997888rarr44 4997888rarr9997888rarr4

51 5997888rarr24997888rarr8997888rarr5

51 5997888rarr24997888rarr8997888rarr5

2 5997888rarr17997888rarr20997888rarr22997888rarr5 2 5997888rarr17997888rarr20997888rarr22997888rarr53 5997888rarr7997888rarr10997888rarr5

Cost 336496 Cost 189061

0

20

40

60

80

100

120

140

50 100 150 200 2500(a) Feasible solution given by H1

50 100 150 200 25000

20

40

60

80

100

120

140

(b) Improved solution after NS

Figure 7 Illustration of the results of H1-NS for the small-scaleexample

closed and replaced by the other two stations which reducethe base establishing cost

The detailed comparison is shown in Table 3 The overallcosts have been reduced from 336496 to 189061 dropping by44 Therefore H2-NS seems to be more accurate than H1-NS and can solve the problem better

523 Comparison See Table 4

53 Example Based on the Sino-Vietnamese Border In thissection a practical border is used as the example case andsolved by the preceding algorithms

50 100 150 200 25000

20

40

60

80

100

120

140

(a) Feasible solution given by H1

50 100 150 200 25000

20

40

60

80

100

120

140

(b) Improved solution after NS

Figure 8 Illustration of the results of H2-NS for the small-scaleexample

As is shown in Figure 9 there are about 8 cities and 103towns bordering in Guangxi Zhuang Autonomous RegionWith the development of economy and the implementationof opening-up policy especially under ldquoBelt and Roadrdquoinitiative Guangxi develops an increasingly flourishing bor-der trade However smuggling also increases at the sametime Since the border area is mainly delimited by riversor mountains and has few natural barriers this part of theborder is prone to smuggling which is difficult to monitorAccording to the official report 6726 smuggling cases wereseized in Guangxi in 2006 Thus it is meaningful to applyUAVs on the border patrol which can improve the patrol

10 Journal of Advanced Transportation

Table4Algorith

mcomparis

onin

caseso

fthree

scales

CaseS

cale

H1-N

SH2-NS

Costo

ffeasib

lesolutio

nCosto

fimproved

solutio

nTime10and-2

(s)

Costo

ffeasib

lesolutio

nCosto

fimproved

solutio

nTime10and-2

(s)

5sta

tions

amp20

targets

348882

300435

2325

336890

238473

3928

386308

3364

162392

362091

263009

3815

372992

274386

2463

336496

1890

613786

322293

273432

2313

287293

239058

3682

372327

2764

202342

325443

179350

3871

372439

274322

2335

336807

238975

5487

372369

273543

1892

337965

240234

3635

361322

261822

2247

348843

250545

3670

372538

322555

2327

336976

237811

3787

384262

285167

2196

336890

237784

3811

20sta

tions

amp50

targets

842265

692451

3037

793872

5440

586950

731291

631663

3081

681403

531504

6895

792129

592620

4232

754694

505265

6627

730762

631054

306

4670777

471234

7285

730340

630746

3149

681039

481442

7002

856295

6560

523173

792201

492593

7867

807587

608259

3128

733063

483691

7419

8040

06654817

3503

719919

520651

7432

828288

628671

3385

732245

482620

7494

804770

655033

2620

719798

570285

7242

50sta

tions

amp100targets

1340

095

1028130

1040

1196218

791338

4590

1272888

923026

0993

121940

6819554

4819

1314565

952735

1061

1143538

843628

4490

1396086

946150

1073

1308837

858909

4931

1197487

897623

1064

1075171

725519

5414

1430365

1091920

1012

1368315

818606

4525

1331166

1031168

1049

1219333

819335

4508

1354155

1004

220

1000

1208915

809037

4550

1418603

1080944

1029

1319784

869953

444

61343357

943478

1023

1256920

807064

4897

Journal of Advanced Transportation 11

Table 5 Comparison between two results of practical cases

H1-NS H2-NSCost of feasiblesolution

Cost of improvedsolution Time 10and-2 (s) Cost of feasible

solutionCost of improved

solution Time 10and-2 (s)

817492 619800 3091 837997 480309 6840

Table 6 Detailed bases and flight paths of the final solution

Base UAV Route

31 3997888rarr21997888rarr22997888rarr32 3997888rarr23997888rarr24997888rarr33 3997888rarr25997888rarr27997888rarr26997888rarr3

61 6997888rarr28997888rarr29997888rarr30997888rarr62 6997888rarr31997888rarr32997888rarr33997888rarr34997888rarr35997888rarr63 6997888rarr36997888rarr37997888rarr6

8 1 8997888rarr38997888rarr39997888rarr40997888rarr41997888rarr82 8997888rarr42997888rarr43997888rarr44997888rarr45997888rarr8

11 1 11997888rarr46997888rarr47997888rarr48997888rarr49997888rarr50997888rarr112 11997888rarr51997888rarr52997888rarr53997888rarr11

15 1 15997888rarr54997888rarr55997888rarr56997888rarr57997888rarr152 15997888rarr58997888rarr59997888rarr60997888rarr15

181 18997888rarr61997888rarr62997888rarr182 18997888rarr63997888rarr64997888rarr65997888rarr67997888rarr66997888rarr183 18997888rarr68997888rarr70997888rarr69997888rarr18

Figure 9 The map of Guangxi Zhuang Autonomous Region (themarked red line is the Guangxi section of the Sino-Vietnameseborder)

efficiency and reaction speed Therefore take the Guangxisection of the border as an example

As displayed in Figure 10 with the ranging tool of GoogleMap the linear distance of this part is about 320 km ThenPaint software is used to discretize this line Fifty target pointsaremarked on the border and twenty base stations are chosenrandomly inside the line Furthermore the relative positionsof these 70 nodes are obtained via the pixel measurement

Figure 10 Guangxi section of the Sino-Vietnamese border with theranging tool

It is assumed that all targets and potential bases arelocated in the area of 320 kilometres multiplied by 160 kilo-metres Mapping these nodes into this area the distributionmap looks like Figure 11 The blue dots are target points andthe red blocks are potential base stations

Two algorithms are applied to solve the practical caseThe results are shown in Table 5 Since the result of H2-NSis obviously superior to another one take the result of H2-NS as the final solution in which the cost is 480309 and thecalculation takes 006840 seconds

The potential base stations are numbered 1 through 20when the target points are represented by 21 to 70 Then thedetailed bases and flight paths can be listed in Table 6 andthe corresponding route map is shown in Figure 12 The finalresult selects 6 bases and launches 15 UAVs

12 Journal of Advanced Transportation

50 100 150 200 250 300 35000

20

40

60

80

100

120

140

Figure 11 50 target points and 20 base stations after discretization

50 100 150 200 250 300 35000

20

40

60

80

100

120

140

Figure 12 The route map of the final solution

6 Conclusions

In this paper considering the background of border patrolfor ISR the capacity constraints of bases are involved inthe multidepot location-routing problem Hence a modifiedmathematical model has been presented The primary objec-tive of this research is to develop an efficient approach forsolving this kind of problem Thus two hybrid heuristicswith neighbourhood search are promoted One is based onclustering and nearest point search and the other one is basedon clustering and CW saving search

In addition experiments have been carried out to com-pare the performance of two algorithms It can be addictedthat neighbourhood search plays an optimizing role to thesolution And the heuristic based on CW saving searchprovides a better solution while consuming more time thanthe other one Furthermore an example based on a practicalborderline is proposed Both algorithms are applied to solvethe border patrol on the practical borderline and provide thefinal solution

Finally two improvements in solving this kind of problemcan be envisaged First the current neighbourhood searchcan be scaled up to find a global optimal solution Secondmore variants of this kind of problem can be exploited Forexample dynamic detecting could be added

Data Availability

The data used to support the findings of this study are avail-able from the corresponding author upon request

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

The research is supported by the National Natural ScienceFoundation of China (no 71771215 and no 71471174)

References

[1] LMiao L Zhen SWangW Lv and X Qu ldquoUnmanned AerialVehicle Scheduling Problem for TrafficMonitoringrdquoComputersamp Industrial Engineering vol 122 pp 15ndash23 2018

[2] S G Manyam S Rasmussen D W Casbeer K Kalyanam andS Manickam ldquoMulti-UAV routing for persistent intelligencesurveillance amp reconnaissance missionsrdquo in Proceedings of the2017 International Conference on Unmanned Aircraft SystemsICUAS 2017 pp 573ndash580 June 2017

[3] S K Jacobsen and O B G Madsen ldquoA comparative study ofheuristics for a two-level routing-location problemrdquo EuropeanJournal of Operational Research vol 5 no 6 pp 378ndash387 1980

[4] D Tuzun and L I Burke ldquoTwo-phase tabu search approach tothe location routing problemrdquo European Journal of OperationalResearch vol 116 no 1 pp 87ndash99 1999

[5] H Min V Jayaraman and R Srivastava ldquoCombined location-routing problems a synthesis and future research directionsrdquoEuropean Journal of Operational Research vol 108 no 1 pp 1ndash15 1998

[6] G Nagy and S Salhi ldquoLocation-routing issues models andmethodsrdquoEuropean Journal ofOperational Research vol 177 no2 pp 649ndash672 2007

[7] J-M Belenguer E Benavent C Prins C Prodhon and RW Calvoc ldquoA Branch-and-Cut method for the CapacitatedLocation-Routing Problemrdquo Computers amp Operations Researchvol 38 no 6 pp 931ndash941 2011

[8] Z Akca R T Berger and T K Ralphs ldquoA branch-and-pricealgorithm for combined location and routing problems undercapacity restrictionsrdquo Operations Research Computer ScienceInterfaces Series vol 47 pp 309ndash330 2009

[9] S Barreto C Ferreira J Paixao and B S Santos ldquoUsing clus-tering analysis in a capacitated location-routing problemrdquoEuropean Journal of Operational Research vol 179 no 3 pp968ndash977 2007

[10] C Prodhon and C Prins ldquoA survey of recent research onlocation-routing problemsrdquo European Journal of OperationalResearch vol 238 no 1 pp 1ndash17 2014

[11] C Prins C Prodhon and RWolfer-Calvo ldquoSolving the capaci-tated location-routing problemby aGRASP complemented by alearning process and a path relinkingrdquo 4OR AQuarterly Journalof Operations Research vol 4 no 3 pp 221ndash238 2006

[12] C Duhamel P Lacomme C Prins and C Prodhon ldquoAGRASPtimesELS approach for the capacitated location-routingproblemrdquo Computers amp Operations Research vol 37 no 11 pp1912ndash1923 2010

[13] R B Lopes C Ferreira and B S Santos ldquoA simple and effectiveevolutionary algorithm for the capacitated location-routingproblemrdquo Computers amp Operations Research vol 70 pp 155ndash162 2016

Journal of Advanced Transportation 13

[14] V F Yu S-W Lin W Lee and C-J Ting ldquoA simulated anneal-ing heuristic for the capacitated location routing problemrdquoComputers amp Industrial Engineering vol 58 no 2 pp 288ndash2992010

[15] J W Escobar R Linfati and P Toth ldquoA two-phase hybridheuristic algorithm for the capacitated location-routing prob-lemrdquoComputers ampOperations Research vol 40 no 1 pp 70ndash792013

[16] R W Harder R R Hill and J T Moore ldquoA Java universalvehicle router for routing unmanned aerial vehiclesrdquo Interna-tional Transactions in Operational Research vol 11 no 3 pp259ndash275 2004

[17] V K Shetty M Sudit and R Nagi ldquoPriority-based assignmentand routing of a fleet of unmanned combat aerial vehiclesrdquoComputers amp Operations Research vol 35 no 6 pp 1813ndash18282008

[18] F Mufalli R Batta and R Nagi ldquoSimultaneous sensor selectionand routing of unmanned aerial vehicles for complex missionplansrdquo Computers amp Operations Research vol 39 no 11 pp2787ndash2799 2012

[19] A M Ham ldquoIntegrated scheduling of m-truck m-drone andm-depot constrained by time-window drop-pickup and m-visit using constraint programmingrdquo Transportation ResearchPart C Emerging Technologies vol 91 pp 1ndash14 2018

[20] G S C Avellar G A S Pereira L C A Pimenta and P IscoldldquoMulti-UAV routing for area coverage and remote sensing withminimum timerdquo Sensors vol 15 no 11 pp 27783ndash27803 2015

[21] I Sarıcicek and Y Akkus ldquoUnmanned aerial vehicle hub-location and routing for monitoring geographic bordersrdquoApplied Mathematical Modelling Simulation and Computationfor Engineering and Environmental Systems vol 39 no 14 pp3939ndash3953 2015

[22] E Yakıcı ldquoSolving location and routing problem for UAVsrdquoComputers amp Industrial Engineering vol 102 pp 294ndash301 2016

[23] T M Cover and P E Hart ldquoNearest neighbor pattern classifi-cationrdquo IEEE Transactions on Information Theory vol 13 no 1pp 21ndash27 1967

[24] G Clarke and J W Wright ldquoScheduling of vehicles from acentral depot to a number of delivery pointsrdquo INFORMS 1964

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Journal of Advanced Transportation 7

Flight Paths

Potential BasesPatrol Targets

A

B

12

3

4

56

7

8

9A

B

12

3

4

56

7

8

9(b)

A

B

12

3

4

56

7

8

9(a)

Figure 5 The operation of insertion

presents the situation that two targets are in different pathsof one station After exchanging the points 3 and 4 the flightdistance of both two flight paths would be decreased whichcould help lower the flight cost

424 Neighbourhood 3 Insertion This neighbourhood re-moves a target and reinserts it in other position in a tentativesolution which may change the owner base station ofthe target Figure 5(a) illustrates a relatively straightforwardmove in one station Additionally the path represented byFigure 5(b) relocates the target 6 from station B to station A

5 Experiment Design and Results

In this section experiments are designed based on actualcharacteristics of border patrol and two algorithms are testedwith the constructed cases

51 Experiment Design When designing the experiment theparticularity of border patrol should be taken into accountSince the detection goal is part of borderline themission areashould be set as an irregular strip area Thus as displayed inFigure 6 it is assumed that the detection area is a rectanglewith aspect ratio of 2 1

In the mission planning the target points should belocated on the borderlinewhile the base stations are inside theborderline It means that there would be a boundary betweenpotential bases and target points which is different from thecases in delivery system Therefore a random curve is first

8

20

25

24

3 5

17

14

1115

19

18

23 21

13

16

6

4

1

2

12

22

107

9

Target Points

Potential BaseStations

0

20

40

60

80

100

120

140

50 100 150 200 2500Figure 6 Experiment case generated under limited conditions

generated as a boundary (note this boundary differs fromthe borderline the border is in the area of target points)Then base stations and target points are separately generatedon both sides of the boundary which is the dotted line inFigure 6 Five potential base stations are below the boundaryline while twenty target points are above it

As the target points are abstracted from a small area onthe borderline they should not be too close to each otherotherwise two points could be merged into one node It issame for the potential stations It would be impractical tobuild two stations in a close range For the purpose of thischaracteristic all nodes are generated one by one Take thebase stations as an example every time a new station isproduced the distance between the station and every existingstation would be judged If the distance is too short the

8 Journal of Advanced Transportation

Table 1 Detailed parameters of two typical UVAs

Parameters UAV 1 UAV 2

Fuselage 07 meters in length 175 meters in length2 meters in wingspan 175 meters in length

Body Weight 85 kg 15 kgPayload 15 kg 4 kg

Flight Speed 80-120 km h maximum 158 km hpatrol 295 km h

Flight Altitude working 100-500 meters working 300 metersMission Radius 70 km 30 kmFlight Endurance 25 hours ge 4 hours

Table 2 Detailed comparison between feasible solution and improved solution of H1-NS

Feasible solution by H1 Improved solution after NSBase UAV Route Base UAV Route

1 1 1997888rarr9997888rarr7997888rarr10997888rarr1 1 1 1997888rarr9997888rarr7997888rarr10997888rarr12 1997888rarr18997888rarr14997888rarr23997888rarr1 2 1997888rarr14997888rarr23997888rarr18997888rarr19997888rarr1

4

1 4997888rarr15997888rarr11997888rarr13997888rarr4

4

1 4997888rarr15997888rarr11997888rarr21997888rarr42 4997888rarr16997888rarr12997888rarr6997888rarr4 2 4997888rarr16997888rarr12997888rarr6997888rarr43 4997888rarr25997888rarr21997888rarr4 3 4997888rarr13997888rarr25997888rarr44 4997888rarr19997888rarr4

51 5997888rarr24997888rarr8997888rarr5

51 5997888rarr24997888rarr8997888rarr5

2 5997888rarr17997888rarr20997888rarr5 2 5997888rarr17997888rarr22997888rarr20997888rarr53 5997888rarr22997888rarr5

Cost 372992 Cost 274386

position would be abandoned and regenerated until there areenough base stations

The parameters of UAVmainly refer to the public param-eters from two typical UAVs which have been applied toborder patrol The detailed parameter is presented in Table 1After some proper randomization the experiment parame-ters are generated such as the flight endurance patrol speedand so on

52 Experiment Result With the experiment data generatedtwo algorithms are tested and compared with each other Forthe sake of illustration H1-NS represents the combination ofthe heuristic based on clustering and nearest point search(H1) and the neighbourhood search while H2-NS containsthe heuristic based on clustering and CW saving search (H2)and the neighbourhood search

521 Results of H1-NS on Test Case Take a small-scale case(5 base stations and 20 target points) generated randomlyFigure 7(a) shows the feasible solution given by H1 while theimproved solution is provided after neighbourhood search asFigure 7(b) depicts

In Figure 7(a) it is can be seen that the performanceof Nearest Neighbour is flawed Obviously when the UAVdepartures from Station 5 and then visits Target 17 and Target20 the rest of energy cannot support it to return to the base ifcontinuing detecting Target 22 which causes one more UAVto be sent to specially visit Target 22

However after neighbourhood search the solution isimproved a lot Some fight paths are merged and adjustedwhich reduces the number of UAVs used as well as the flightdistance of UAV For example the routes 5997888rarr17997888rarr20997888rarr5and 5997888rarr22997888rarr5 aremerged into 5997888rarr17997888rarr22997888rarr20997888rarr5 Andthe detecting order of Target 14 and 23 is interchangeddecreasing the UAVrsquos redundant flight Although the numberof stations has not changed the number of drones hasdecreased after optimization Only 7 UAVs are used in thefinal solution which is two less than that of the initialsolution As displayed in Table 2 the overall costs have beendecreased from 372992 to 274386 down by 26 percent prov-ing the feasibility of H1 and effectiveness of neighbourhoodsearch

522 Results of H2-NS on Test Case The same case is alsoapplied to test H2-NS The feasible solution given by H2is presented by Figure 8(a) and the improved after NS inFigure 8(b)

The conclusion can be drawn that the CW saving algo-rithm has utilized the flight endurance as far as possiblewhich is fairly obvious in the feasible solution Comparedwith the cost of feasible solution in H1 H2 reduces the costfrom 372992 to 336496

After the adjustment of the neighbourhood search thestructure of the solution has changed a lot Although thenumber of the UAVs has not decreased the base station 1 is

Journal of Advanced Transportation 9

Table 3 Detailed comparison between feasible solution and improved solution of H2-NS

Feasible solution by H1 Improved solution after NSBase UAV Route Base UAV Route

1 1 1997888rarr9997888rarr10997888rarr1 1 1 1997888rarr9997888rarr7997888rarr10997888rarr12 1997888rarr18997888rarr23997888rarr14997888rarr7997888rarr1 2 1997888rarr14997888rarr23997888rarr18997888rarr19997888rarr1

4

1 4997888rarr13997888rarr25997888rarr21997888rarr19997888rarr4

4

1 4997888rarr11997888rarr25997888rarr21997888rarr19997888rarr42 4997888rarr15997888rarr11997888rarr4 2 4997888rarr15997888rarr18997888rarr23997888rarr14997888rarr4

3 4997888rarr16997888rarr6997888rarr12997888rarr4 3 4997888rarr16997888rarr13997888rarr6997888rarr12997888rarr44 4997888rarr9997888rarr4

51 5997888rarr24997888rarr8997888rarr5

51 5997888rarr24997888rarr8997888rarr5

2 5997888rarr17997888rarr20997888rarr22997888rarr5 2 5997888rarr17997888rarr20997888rarr22997888rarr53 5997888rarr7997888rarr10997888rarr5

Cost 336496 Cost 189061

0

20

40

60

80

100

120

140

50 100 150 200 2500(a) Feasible solution given by H1

50 100 150 200 25000

20

40

60

80

100

120

140

(b) Improved solution after NS

Figure 7 Illustration of the results of H1-NS for the small-scaleexample

closed and replaced by the other two stations which reducethe base establishing cost

The detailed comparison is shown in Table 3 The overallcosts have been reduced from 336496 to 189061 dropping by44 Therefore H2-NS seems to be more accurate than H1-NS and can solve the problem better

523 Comparison See Table 4

53 Example Based on the Sino-Vietnamese Border In thissection a practical border is used as the example case andsolved by the preceding algorithms

50 100 150 200 25000

20

40

60

80

100

120

140

(a) Feasible solution given by H1

50 100 150 200 25000

20

40

60

80

100

120

140

(b) Improved solution after NS

Figure 8 Illustration of the results of H2-NS for the small-scaleexample

As is shown in Figure 9 there are about 8 cities and 103towns bordering in Guangxi Zhuang Autonomous RegionWith the development of economy and the implementationof opening-up policy especially under ldquoBelt and Roadrdquoinitiative Guangxi develops an increasingly flourishing bor-der trade However smuggling also increases at the sametime Since the border area is mainly delimited by riversor mountains and has few natural barriers this part of theborder is prone to smuggling which is difficult to monitorAccording to the official report 6726 smuggling cases wereseized in Guangxi in 2006 Thus it is meaningful to applyUAVs on the border patrol which can improve the patrol

10 Journal of Advanced Transportation

Table4Algorith

mcomparis

onin

caseso

fthree

scales

CaseS

cale

H1-N

SH2-NS

Costo

ffeasib

lesolutio

nCosto

fimproved

solutio

nTime10and-2

(s)

Costo

ffeasib

lesolutio

nCosto

fimproved

solutio

nTime10and-2

(s)

5sta

tions

amp20

targets

348882

300435

2325

336890

238473

3928

386308

3364

162392

362091

263009

3815

372992

274386

2463

336496

1890

613786

322293

273432

2313

287293

239058

3682

372327

2764

202342

325443

179350

3871

372439

274322

2335

336807

238975

5487

372369

273543

1892

337965

240234

3635

361322

261822

2247

348843

250545

3670

372538

322555

2327

336976

237811

3787

384262

285167

2196

336890

237784

3811

20sta

tions

amp50

targets

842265

692451

3037

793872

5440

586950

731291

631663

3081

681403

531504

6895

792129

592620

4232

754694

505265

6627

730762

631054

306

4670777

471234

7285

730340

630746

3149

681039

481442

7002

856295

6560

523173

792201

492593

7867

807587

608259

3128

733063

483691

7419

8040

06654817

3503

719919

520651

7432

828288

628671

3385

732245

482620

7494

804770

655033

2620

719798

570285

7242

50sta

tions

amp100targets

1340

095

1028130

1040

1196218

791338

4590

1272888

923026

0993

121940

6819554

4819

1314565

952735

1061

1143538

843628

4490

1396086

946150

1073

1308837

858909

4931

1197487

897623

1064

1075171

725519

5414

1430365

1091920

1012

1368315

818606

4525

1331166

1031168

1049

1219333

819335

4508

1354155

1004

220

1000

1208915

809037

4550

1418603

1080944

1029

1319784

869953

444

61343357

943478

1023

1256920

807064

4897

Journal of Advanced Transportation 11

Table 5 Comparison between two results of practical cases

H1-NS H2-NSCost of feasiblesolution

Cost of improvedsolution Time 10and-2 (s) Cost of feasible

solutionCost of improved

solution Time 10and-2 (s)

817492 619800 3091 837997 480309 6840

Table 6 Detailed bases and flight paths of the final solution

Base UAV Route

31 3997888rarr21997888rarr22997888rarr32 3997888rarr23997888rarr24997888rarr33 3997888rarr25997888rarr27997888rarr26997888rarr3

61 6997888rarr28997888rarr29997888rarr30997888rarr62 6997888rarr31997888rarr32997888rarr33997888rarr34997888rarr35997888rarr63 6997888rarr36997888rarr37997888rarr6

8 1 8997888rarr38997888rarr39997888rarr40997888rarr41997888rarr82 8997888rarr42997888rarr43997888rarr44997888rarr45997888rarr8

11 1 11997888rarr46997888rarr47997888rarr48997888rarr49997888rarr50997888rarr112 11997888rarr51997888rarr52997888rarr53997888rarr11

15 1 15997888rarr54997888rarr55997888rarr56997888rarr57997888rarr152 15997888rarr58997888rarr59997888rarr60997888rarr15

181 18997888rarr61997888rarr62997888rarr182 18997888rarr63997888rarr64997888rarr65997888rarr67997888rarr66997888rarr183 18997888rarr68997888rarr70997888rarr69997888rarr18

Figure 9 The map of Guangxi Zhuang Autonomous Region (themarked red line is the Guangxi section of the Sino-Vietnameseborder)

efficiency and reaction speed Therefore take the Guangxisection of the border as an example

As displayed in Figure 10 with the ranging tool of GoogleMap the linear distance of this part is about 320 km ThenPaint software is used to discretize this line Fifty target pointsaremarked on the border and twenty base stations are chosenrandomly inside the line Furthermore the relative positionsof these 70 nodes are obtained via the pixel measurement

Figure 10 Guangxi section of the Sino-Vietnamese border with theranging tool

It is assumed that all targets and potential bases arelocated in the area of 320 kilometres multiplied by 160 kilo-metres Mapping these nodes into this area the distributionmap looks like Figure 11 The blue dots are target points andthe red blocks are potential base stations

Two algorithms are applied to solve the practical caseThe results are shown in Table 5 Since the result of H2-NSis obviously superior to another one take the result of H2-NS as the final solution in which the cost is 480309 and thecalculation takes 006840 seconds

The potential base stations are numbered 1 through 20when the target points are represented by 21 to 70 Then thedetailed bases and flight paths can be listed in Table 6 andthe corresponding route map is shown in Figure 12 The finalresult selects 6 bases and launches 15 UAVs

12 Journal of Advanced Transportation

50 100 150 200 250 300 35000

20

40

60

80

100

120

140

Figure 11 50 target points and 20 base stations after discretization

50 100 150 200 250 300 35000

20

40

60

80

100

120

140

Figure 12 The route map of the final solution

6 Conclusions

In this paper considering the background of border patrolfor ISR the capacity constraints of bases are involved inthe multidepot location-routing problem Hence a modifiedmathematical model has been presented The primary objec-tive of this research is to develop an efficient approach forsolving this kind of problem Thus two hybrid heuristicswith neighbourhood search are promoted One is based onclustering and nearest point search and the other one is basedon clustering and CW saving search

In addition experiments have been carried out to com-pare the performance of two algorithms It can be addictedthat neighbourhood search plays an optimizing role to thesolution And the heuristic based on CW saving searchprovides a better solution while consuming more time thanthe other one Furthermore an example based on a practicalborderline is proposed Both algorithms are applied to solvethe border patrol on the practical borderline and provide thefinal solution

Finally two improvements in solving this kind of problemcan be envisaged First the current neighbourhood searchcan be scaled up to find a global optimal solution Secondmore variants of this kind of problem can be exploited Forexample dynamic detecting could be added

Data Availability

The data used to support the findings of this study are avail-able from the corresponding author upon request

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

The research is supported by the National Natural ScienceFoundation of China (no 71771215 and no 71471174)

References

[1] LMiao L Zhen SWangW Lv and X Qu ldquoUnmanned AerialVehicle Scheduling Problem for TrafficMonitoringrdquoComputersamp Industrial Engineering vol 122 pp 15ndash23 2018

[2] S G Manyam S Rasmussen D W Casbeer K Kalyanam andS Manickam ldquoMulti-UAV routing for persistent intelligencesurveillance amp reconnaissance missionsrdquo in Proceedings of the2017 International Conference on Unmanned Aircraft SystemsICUAS 2017 pp 573ndash580 June 2017

[3] S K Jacobsen and O B G Madsen ldquoA comparative study ofheuristics for a two-level routing-location problemrdquo EuropeanJournal of Operational Research vol 5 no 6 pp 378ndash387 1980

[4] D Tuzun and L I Burke ldquoTwo-phase tabu search approach tothe location routing problemrdquo European Journal of OperationalResearch vol 116 no 1 pp 87ndash99 1999

[5] H Min V Jayaraman and R Srivastava ldquoCombined location-routing problems a synthesis and future research directionsrdquoEuropean Journal of Operational Research vol 108 no 1 pp 1ndash15 1998

[6] G Nagy and S Salhi ldquoLocation-routing issues models andmethodsrdquoEuropean Journal ofOperational Research vol 177 no2 pp 649ndash672 2007

[7] J-M Belenguer E Benavent C Prins C Prodhon and RW Calvoc ldquoA Branch-and-Cut method for the CapacitatedLocation-Routing Problemrdquo Computers amp Operations Researchvol 38 no 6 pp 931ndash941 2011

[8] Z Akca R T Berger and T K Ralphs ldquoA branch-and-pricealgorithm for combined location and routing problems undercapacity restrictionsrdquo Operations Research Computer ScienceInterfaces Series vol 47 pp 309ndash330 2009

[9] S Barreto C Ferreira J Paixao and B S Santos ldquoUsing clus-tering analysis in a capacitated location-routing problemrdquoEuropean Journal of Operational Research vol 179 no 3 pp968ndash977 2007

[10] C Prodhon and C Prins ldquoA survey of recent research onlocation-routing problemsrdquo European Journal of OperationalResearch vol 238 no 1 pp 1ndash17 2014

[11] C Prins C Prodhon and RWolfer-Calvo ldquoSolving the capaci-tated location-routing problemby aGRASP complemented by alearning process and a path relinkingrdquo 4OR AQuarterly Journalof Operations Research vol 4 no 3 pp 221ndash238 2006

[12] C Duhamel P Lacomme C Prins and C Prodhon ldquoAGRASPtimesELS approach for the capacitated location-routingproblemrdquo Computers amp Operations Research vol 37 no 11 pp1912ndash1923 2010

[13] R B Lopes C Ferreira and B S Santos ldquoA simple and effectiveevolutionary algorithm for the capacitated location-routingproblemrdquo Computers amp Operations Research vol 70 pp 155ndash162 2016

Journal of Advanced Transportation 13

[14] V F Yu S-W Lin W Lee and C-J Ting ldquoA simulated anneal-ing heuristic for the capacitated location routing problemrdquoComputers amp Industrial Engineering vol 58 no 2 pp 288ndash2992010

[15] J W Escobar R Linfati and P Toth ldquoA two-phase hybridheuristic algorithm for the capacitated location-routing prob-lemrdquoComputers ampOperations Research vol 40 no 1 pp 70ndash792013

[16] R W Harder R R Hill and J T Moore ldquoA Java universalvehicle router for routing unmanned aerial vehiclesrdquo Interna-tional Transactions in Operational Research vol 11 no 3 pp259ndash275 2004

[17] V K Shetty M Sudit and R Nagi ldquoPriority-based assignmentand routing of a fleet of unmanned combat aerial vehiclesrdquoComputers amp Operations Research vol 35 no 6 pp 1813ndash18282008

[18] F Mufalli R Batta and R Nagi ldquoSimultaneous sensor selectionand routing of unmanned aerial vehicles for complex missionplansrdquo Computers amp Operations Research vol 39 no 11 pp2787ndash2799 2012

[19] A M Ham ldquoIntegrated scheduling of m-truck m-drone andm-depot constrained by time-window drop-pickup and m-visit using constraint programmingrdquo Transportation ResearchPart C Emerging Technologies vol 91 pp 1ndash14 2018

[20] G S C Avellar G A S Pereira L C A Pimenta and P IscoldldquoMulti-UAV routing for area coverage and remote sensing withminimum timerdquo Sensors vol 15 no 11 pp 27783ndash27803 2015

[21] I Sarıcicek and Y Akkus ldquoUnmanned aerial vehicle hub-location and routing for monitoring geographic bordersrdquoApplied Mathematical Modelling Simulation and Computationfor Engineering and Environmental Systems vol 39 no 14 pp3939ndash3953 2015

[22] E Yakıcı ldquoSolving location and routing problem for UAVsrdquoComputers amp Industrial Engineering vol 102 pp 294ndash301 2016

[23] T M Cover and P E Hart ldquoNearest neighbor pattern classifi-cationrdquo IEEE Transactions on Information Theory vol 13 no 1pp 21ndash27 1967

[24] G Clarke and J W Wright ldquoScheduling of vehicles from acentral depot to a number of delivery pointsrdquo INFORMS 1964

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Submit your manuscripts atwwwhindawicom

8 Journal of Advanced Transportation

Table 1 Detailed parameters of two typical UVAs

Parameters UAV 1 UAV 2

Fuselage 07 meters in length 175 meters in length2 meters in wingspan 175 meters in length

Body Weight 85 kg 15 kgPayload 15 kg 4 kg

Flight Speed 80-120 km h maximum 158 km hpatrol 295 km h

Flight Altitude working 100-500 meters working 300 metersMission Radius 70 km 30 kmFlight Endurance 25 hours ge 4 hours

Table 2 Detailed comparison between feasible solution and improved solution of H1-NS

Feasible solution by H1 Improved solution after NSBase UAV Route Base UAV Route

1 1 1997888rarr9997888rarr7997888rarr10997888rarr1 1 1 1997888rarr9997888rarr7997888rarr10997888rarr12 1997888rarr18997888rarr14997888rarr23997888rarr1 2 1997888rarr14997888rarr23997888rarr18997888rarr19997888rarr1

4

1 4997888rarr15997888rarr11997888rarr13997888rarr4

4

1 4997888rarr15997888rarr11997888rarr21997888rarr42 4997888rarr16997888rarr12997888rarr6997888rarr4 2 4997888rarr16997888rarr12997888rarr6997888rarr43 4997888rarr25997888rarr21997888rarr4 3 4997888rarr13997888rarr25997888rarr44 4997888rarr19997888rarr4

51 5997888rarr24997888rarr8997888rarr5

51 5997888rarr24997888rarr8997888rarr5

2 5997888rarr17997888rarr20997888rarr5 2 5997888rarr17997888rarr22997888rarr20997888rarr53 5997888rarr22997888rarr5

Cost 372992 Cost 274386

position would be abandoned and regenerated until there areenough base stations

The parameters of UAVmainly refer to the public param-eters from two typical UAVs which have been applied toborder patrol The detailed parameter is presented in Table 1After some proper randomization the experiment parame-ters are generated such as the flight endurance patrol speedand so on

52 Experiment Result With the experiment data generatedtwo algorithms are tested and compared with each other Forthe sake of illustration H1-NS represents the combination ofthe heuristic based on clustering and nearest point search(H1) and the neighbourhood search while H2-NS containsthe heuristic based on clustering and CW saving search (H2)and the neighbourhood search

521 Results of H1-NS on Test Case Take a small-scale case(5 base stations and 20 target points) generated randomlyFigure 7(a) shows the feasible solution given by H1 while theimproved solution is provided after neighbourhood search asFigure 7(b) depicts

In Figure 7(a) it is can be seen that the performanceof Nearest Neighbour is flawed Obviously when the UAVdepartures from Station 5 and then visits Target 17 and Target20 the rest of energy cannot support it to return to the base ifcontinuing detecting Target 22 which causes one more UAVto be sent to specially visit Target 22

However after neighbourhood search the solution isimproved a lot Some fight paths are merged and adjustedwhich reduces the number of UAVs used as well as the flightdistance of UAV For example the routes 5997888rarr17997888rarr20997888rarr5and 5997888rarr22997888rarr5 aremerged into 5997888rarr17997888rarr22997888rarr20997888rarr5 Andthe detecting order of Target 14 and 23 is interchangeddecreasing the UAVrsquos redundant flight Although the numberof stations has not changed the number of drones hasdecreased after optimization Only 7 UAVs are used in thefinal solution which is two less than that of the initialsolution As displayed in Table 2 the overall costs have beendecreased from 372992 to 274386 down by 26 percent prov-ing the feasibility of H1 and effectiveness of neighbourhoodsearch

522 Results of H2-NS on Test Case The same case is alsoapplied to test H2-NS The feasible solution given by H2is presented by Figure 8(a) and the improved after NS inFigure 8(b)

The conclusion can be drawn that the CW saving algo-rithm has utilized the flight endurance as far as possiblewhich is fairly obvious in the feasible solution Comparedwith the cost of feasible solution in H1 H2 reduces the costfrom 372992 to 336496

After the adjustment of the neighbourhood search thestructure of the solution has changed a lot Although thenumber of the UAVs has not decreased the base station 1 is

Journal of Advanced Transportation 9

Table 3 Detailed comparison between feasible solution and improved solution of H2-NS

Feasible solution by H1 Improved solution after NSBase UAV Route Base UAV Route

1 1 1997888rarr9997888rarr10997888rarr1 1 1 1997888rarr9997888rarr7997888rarr10997888rarr12 1997888rarr18997888rarr23997888rarr14997888rarr7997888rarr1 2 1997888rarr14997888rarr23997888rarr18997888rarr19997888rarr1

4

1 4997888rarr13997888rarr25997888rarr21997888rarr19997888rarr4

4

1 4997888rarr11997888rarr25997888rarr21997888rarr19997888rarr42 4997888rarr15997888rarr11997888rarr4 2 4997888rarr15997888rarr18997888rarr23997888rarr14997888rarr4

3 4997888rarr16997888rarr6997888rarr12997888rarr4 3 4997888rarr16997888rarr13997888rarr6997888rarr12997888rarr44 4997888rarr9997888rarr4

51 5997888rarr24997888rarr8997888rarr5

51 5997888rarr24997888rarr8997888rarr5

2 5997888rarr17997888rarr20997888rarr22997888rarr5 2 5997888rarr17997888rarr20997888rarr22997888rarr53 5997888rarr7997888rarr10997888rarr5

Cost 336496 Cost 189061

0

20

40

60

80

100

120

140

50 100 150 200 2500(a) Feasible solution given by H1

50 100 150 200 25000

20

40

60

80

100

120

140

(b) Improved solution after NS

Figure 7 Illustration of the results of H1-NS for the small-scaleexample

closed and replaced by the other two stations which reducethe base establishing cost

The detailed comparison is shown in Table 3 The overallcosts have been reduced from 336496 to 189061 dropping by44 Therefore H2-NS seems to be more accurate than H1-NS and can solve the problem better

523 Comparison See Table 4

53 Example Based on the Sino-Vietnamese Border In thissection a practical border is used as the example case andsolved by the preceding algorithms

50 100 150 200 25000

20

40

60

80

100

120

140

(a) Feasible solution given by H1

50 100 150 200 25000

20

40

60

80

100

120

140

(b) Improved solution after NS

Figure 8 Illustration of the results of H2-NS for the small-scaleexample

As is shown in Figure 9 there are about 8 cities and 103towns bordering in Guangxi Zhuang Autonomous RegionWith the development of economy and the implementationof opening-up policy especially under ldquoBelt and Roadrdquoinitiative Guangxi develops an increasingly flourishing bor-der trade However smuggling also increases at the sametime Since the border area is mainly delimited by riversor mountains and has few natural barriers this part of theborder is prone to smuggling which is difficult to monitorAccording to the official report 6726 smuggling cases wereseized in Guangxi in 2006 Thus it is meaningful to applyUAVs on the border patrol which can improve the patrol

10 Journal of Advanced Transportation

Table4Algorith

mcomparis

onin

caseso

fthree

scales

CaseS

cale

H1-N

SH2-NS

Costo

ffeasib

lesolutio

nCosto

fimproved

solutio

nTime10and-2

(s)

Costo

ffeasib

lesolutio

nCosto

fimproved

solutio

nTime10and-2

(s)

5sta

tions

amp20

targets

348882

300435

2325

336890

238473

3928

386308

3364

162392

362091

263009

3815

372992

274386

2463

336496

1890

613786

322293

273432

2313

287293

239058

3682

372327

2764

202342

325443

179350

3871

372439

274322

2335

336807

238975

5487

372369

273543

1892

337965

240234

3635

361322

261822

2247

348843

250545

3670

372538

322555

2327

336976

237811

3787

384262

285167

2196

336890

237784

3811

20sta

tions

amp50

targets

842265

692451

3037

793872

5440

586950

731291

631663

3081

681403

531504

6895

792129

592620

4232

754694

505265

6627

730762

631054

306

4670777

471234

7285

730340

630746

3149

681039

481442

7002

856295

6560

523173

792201

492593

7867

807587

608259

3128

733063

483691

7419

8040

06654817

3503

719919

520651

7432

828288

628671

3385

732245

482620

7494

804770

655033

2620

719798

570285

7242

50sta

tions

amp100targets

1340

095

1028130

1040

1196218

791338

4590

1272888

923026

0993

121940

6819554

4819

1314565

952735

1061

1143538

843628

4490

1396086

946150

1073

1308837

858909

4931

1197487

897623

1064

1075171

725519

5414

1430365

1091920

1012

1368315

818606

4525

1331166

1031168

1049

1219333

819335

4508

1354155

1004

220

1000

1208915

809037

4550

1418603

1080944

1029

1319784

869953

444

61343357

943478

1023

1256920

807064

4897

Journal of Advanced Transportation 11

Table 5 Comparison between two results of practical cases

H1-NS H2-NSCost of feasiblesolution

Cost of improvedsolution Time 10and-2 (s) Cost of feasible

solutionCost of improved

solution Time 10and-2 (s)

817492 619800 3091 837997 480309 6840

Table 6 Detailed bases and flight paths of the final solution

Base UAV Route

31 3997888rarr21997888rarr22997888rarr32 3997888rarr23997888rarr24997888rarr33 3997888rarr25997888rarr27997888rarr26997888rarr3

61 6997888rarr28997888rarr29997888rarr30997888rarr62 6997888rarr31997888rarr32997888rarr33997888rarr34997888rarr35997888rarr63 6997888rarr36997888rarr37997888rarr6

8 1 8997888rarr38997888rarr39997888rarr40997888rarr41997888rarr82 8997888rarr42997888rarr43997888rarr44997888rarr45997888rarr8

11 1 11997888rarr46997888rarr47997888rarr48997888rarr49997888rarr50997888rarr112 11997888rarr51997888rarr52997888rarr53997888rarr11

15 1 15997888rarr54997888rarr55997888rarr56997888rarr57997888rarr152 15997888rarr58997888rarr59997888rarr60997888rarr15

181 18997888rarr61997888rarr62997888rarr182 18997888rarr63997888rarr64997888rarr65997888rarr67997888rarr66997888rarr183 18997888rarr68997888rarr70997888rarr69997888rarr18

Figure 9 The map of Guangxi Zhuang Autonomous Region (themarked red line is the Guangxi section of the Sino-Vietnameseborder)

efficiency and reaction speed Therefore take the Guangxisection of the border as an example

As displayed in Figure 10 with the ranging tool of GoogleMap the linear distance of this part is about 320 km ThenPaint software is used to discretize this line Fifty target pointsaremarked on the border and twenty base stations are chosenrandomly inside the line Furthermore the relative positionsof these 70 nodes are obtained via the pixel measurement

Figure 10 Guangxi section of the Sino-Vietnamese border with theranging tool

It is assumed that all targets and potential bases arelocated in the area of 320 kilometres multiplied by 160 kilo-metres Mapping these nodes into this area the distributionmap looks like Figure 11 The blue dots are target points andthe red blocks are potential base stations

Two algorithms are applied to solve the practical caseThe results are shown in Table 5 Since the result of H2-NSis obviously superior to another one take the result of H2-NS as the final solution in which the cost is 480309 and thecalculation takes 006840 seconds

The potential base stations are numbered 1 through 20when the target points are represented by 21 to 70 Then thedetailed bases and flight paths can be listed in Table 6 andthe corresponding route map is shown in Figure 12 The finalresult selects 6 bases and launches 15 UAVs

12 Journal of Advanced Transportation

50 100 150 200 250 300 35000

20

40

60

80

100

120

140

Figure 11 50 target points and 20 base stations after discretization

50 100 150 200 250 300 35000

20

40

60

80

100

120

140

Figure 12 The route map of the final solution

6 Conclusions

In this paper considering the background of border patrolfor ISR the capacity constraints of bases are involved inthe multidepot location-routing problem Hence a modifiedmathematical model has been presented The primary objec-tive of this research is to develop an efficient approach forsolving this kind of problem Thus two hybrid heuristicswith neighbourhood search are promoted One is based onclustering and nearest point search and the other one is basedon clustering and CW saving search

In addition experiments have been carried out to com-pare the performance of two algorithms It can be addictedthat neighbourhood search plays an optimizing role to thesolution And the heuristic based on CW saving searchprovides a better solution while consuming more time thanthe other one Furthermore an example based on a practicalborderline is proposed Both algorithms are applied to solvethe border patrol on the practical borderline and provide thefinal solution

Finally two improvements in solving this kind of problemcan be envisaged First the current neighbourhood searchcan be scaled up to find a global optimal solution Secondmore variants of this kind of problem can be exploited Forexample dynamic detecting could be added

Data Availability

The data used to support the findings of this study are avail-able from the corresponding author upon request

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

The research is supported by the National Natural ScienceFoundation of China (no 71771215 and no 71471174)

References

[1] LMiao L Zhen SWangW Lv and X Qu ldquoUnmanned AerialVehicle Scheduling Problem for TrafficMonitoringrdquoComputersamp Industrial Engineering vol 122 pp 15ndash23 2018

[2] S G Manyam S Rasmussen D W Casbeer K Kalyanam andS Manickam ldquoMulti-UAV routing for persistent intelligencesurveillance amp reconnaissance missionsrdquo in Proceedings of the2017 International Conference on Unmanned Aircraft SystemsICUAS 2017 pp 573ndash580 June 2017

[3] S K Jacobsen and O B G Madsen ldquoA comparative study ofheuristics for a two-level routing-location problemrdquo EuropeanJournal of Operational Research vol 5 no 6 pp 378ndash387 1980

[4] D Tuzun and L I Burke ldquoTwo-phase tabu search approach tothe location routing problemrdquo European Journal of OperationalResearch vol 116 no 1 pp 87ndash99 1999

[5] H Min V Jayaraman and R Srivastava ldquoCombined location-routing problems a synthesis and future research directionsrdquoEuropean Journal of Operational Research vol 108 no 1 pp 1ndash15 1998

[6] G Nagy and S Salhi ldquoLocation-routing issues models andmethodsrdquoEuropean Journal ofOperational Research vol 177 no2 pp 649ndash672 2007

[7] J-M Belenguer E Benavent C Prins C Prodhon and RW Calvoc ldquoA Branch-and-Cut method for the CapacitatedLocation-Routing Problemrdquo Computers amp Operations Researchvol 38 no 6 pp 931ndash941 2011

[8] Z Akca R T Berger and T K Ralphs ldquoA branch-and-pricealgorithm for combined location and routing problems undercapacity restrictionsrdquo Operations Research Computer ScienceInterfaces Series vol 47 pp 309ndash330 2009

[9] S Barreto C Ferreira J Paixao and B S Santos ldquoUsing clus-tering analysis in a capacitated location-routing problemrdquoEuropean Journal of Operational Research vol 179 no 3 pp968ndash977 2007

[10] C Prodhon and C Prins ldquoA survey of recent research onlocation-routing problemsrdquo European Journal of OperationalResearch vol 238 no 1 pp 1ndash17 2014

[11] C Prins C Prodhon and RWolfer-Calvo ldquoSolving the capaci-tated location-routing problemby aGRASP complemented by alearning process and a path relinkingrdquo 4OR AQuarterly Journalof Operations Research vol 4 no 3 pp 221ndash238 2006

[12] C Duhamel P Lacomme C Prins and C Prodhon ldquoAGRASPtimesELS approach for the capacitated location-routingproblemrdquo Computers amp Operations Research vol 37 no 11 pp1912ndash1923 2010

[13] R B Lopes C Ferreira and B S Santos ldquoA simple and effectiveevolutionary algorithm for the capacitated location-routingproblemrdquo Computers amp Operations Research vol 70 pp 155ndash162 2016

Journal of Advanced Transportation 13

[14] V F Yu S-W Lin W Lee and C-J Ting ldquoA simulated anneal-ing heuristic for the capacitated location routing problemrdquoComputers amp Industrial Engineering vol 58 no 2 pp 288ndash2992010

[15] J W Escobar R Linfati and P Toth ldquoA two-phase hybridheuristic algorithm for the capacitated location-routing prob-lemrdquoComputers ampOperations Research vol 40 no 1 pp 70ndash792013

[16] R W Harder R R Hill and J T Moore ldquoA Java universalvehicle router for routing unmanned aerial vehiclesrdquo Interna-tional Transactions in Operational Research vol 11 no 3 pp259ndash275 2004

[17] V K Shetty M Sudit and R Nagi ldquoPriority-based assignmentand routing of a fleet of unmanned combat aerial vehiclesrdquoComputers amp Operations Research vol 35 no 6 pp 1813ndash18282008

[18] F Mufalli R Batta and R Nagi ldquoSimultaneous sensor selectionand routing of unmanned aerial vehicles for complex missionplansrdquo Computers amp Operations Research vol 39 no 11 pp2787ndash2799 2012

[19] A M Ham ldquoIntegrated scheduling of m-truck m-drone andm-depot constrained by time-window drop-pickup and m-visit using constraint programmingrdquo Transportation ResearchPart C Emerging Technologies vol 91 pp 1ndash14 2018

[20] G S C Avellar G A S Pereira L C A Pimenta and P IscoldldquoMulti-UAV routing for area coverage and remote sensing withminimum timerdquo Sensors vol 15 no 11 pp 27783ndash27803 2015

[21] I Sarıcicek and Y Akkus ldquoUnmanned aerial vehicle hub-location and routing for monitoring geographic bordersrdquoApplied Mathematical Modelling Simulation and Computationfor Engineering and Environmental Systems vol 39 no 14 pp3939ndash3953 2015

[22] E Yakıcı ldquoSolving location and routing problem for UAVsrdquoComputers amp Industrial Engineering vol 102 pp 294ndash301 2016

[23] T M Cover and P E Hart ldquoNearest neighbor pattern classifi-cationrdquo IEEE Transactions on Information Theory vol 13 no 1pp 21ndash27 1967

[24] G Clarke and J W Wright ldquoScheduling of vehicles from acentral depot to a number of delivery pointsrdquo INFORMS 1964

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

Journal of Advanced Transportation 9

Table 3 Detailed comparison between feasible solution and improved solution of H2-NS

Feasible solution by H1 Improved solution after NSBase UAV Route Base UAV Route

1 1 1997888rarr9997888rarr10997888rarr1 1 1 1997888rarr9997888rarr7997888rarr10997888rarr12 1997888rarr18997888rarr23997888rarr14997888rarr7997888rarr1 2 1997888rarr14997888rarr23997888rarr18997888rarr19997888rarr1

4

1 4997888rarr13997888rarr25997888rarr21997888rarr19997888rarr4

4

1 4997888rarr11997888rarr25997888rarr21997888rarr19997888rarr42 4997888rarr15997888rarr11997888rarr4 2 4997888rarr15997888rarr18997888rarr23997888rarr14997888rarr4

3 4997888rarr16997888rarr6997888rarr12997888rarr4 3 4997888rarr16997888rarr13997888rarr6997888rarr12997888rarr44 4997888rarr9997888rarr4

51 5997888rarr24997888rarr8997888rarr5

51 5997888rarr24997888rarr8997888rarr5

2 5997888rarr17997888rarr20997888rarr22997888rarr5 2 5997888rarr17997888rarr20997888rarr22997888rarr53 5997888rarr7997888rarr10997888rarr5

Cost 336496 Cost 189061

0

20

40

60

80

100

120

140

50 100 150 200 2500(a) Feasible solution given by H1

50 100 150 200 25000

20

40

60

80

100

120

140

(b) Improved solution after NS

Figure 7 Illustration of the results of H1-NS for the small-scaleexample

closed and replaced by the other two stations which reducethe base establishing cost

The detailed comparison is shown in Table 3 The overallcosts have been reduced from 336496 to 189061 dropping by44 Therefore H2-NS seems to be more accurate than H1-NS and can solve the problem better

523 Comparison See Table 4

53 Example Based on the Sino-Vietnamese Border In thissection a practical border is used as the example case andsolved by the preceding algorithms

50 100 150 200 25000

20

40

60

80

100

120

140

(a) Feasible solution given by H1

50 100 150 200 25000

20

40

60

80

100

120

140

(b) Improved solution after NS

Figure 8 Illustration of the results of H2-NS for the small-scaleexample

As is shown in Figure 9 there are about 8 cities and 103towns bordering in Guangxi Zhuang Autonomous RegionWith the development of economy and the implementationof opening-up policy especially under ldquoBelt and Roadrdquoinitiative Guangxi develops an increasingly flourishing bor-der trade However smuggling also increases at the sametime Since the border area is mainly delimited by riversor mountains and has few natural barriers this part of theborder is prone to smuggling which is difficult to monitorAccording to the official report 6726 smuggling cases wereseized in Guangxi in 2006 Thus it is meaningful to applyUAVs on the border patrol which can improve the patrol

10 Journal of Advanced Transportation

Table4Algorith

mcomparis

onin

caseso

fthree

scales

CaseS

cale

H1-N

SH2-NS

Costo

ffeasib

lesolutio

nCosto

fimproved

solutio

nTime10and-2

(s)

Costo

ffeasib

lesolutio

nCosto

fimproved

solutio

nTime10and-2

(s)

5sta

tions

amp20

targets

348882

300435

2325

336890

238473

3928

386308

3364

162392

362091

263009

3815

372992

274386

2463

336496

1890

613786

322293

273432

2313

287293

239058

3682

372327

2764

202342

325443

179350

3871

372439

274322

2335

336807

238975

5487

372369

273543

1892

337965

240234

3635

361322

261822

2247

348843

250545

3670

372538

322555

2327

336976

237811

3787

384262

285167

2196

336890

237784

3811

20sta

tions

amp50

targets

842265

692451

3037

793872

5440

586950

731291

631663

3081

681403

531504

6895

792129

592620

4232

754694

505265

6627

730762

631054

306

4670777

471234

7285

730340

630746

3149

681039

481442

7002

856295

6560

523173

792201

492593

7867

807587

608259

3128

733063

483691

7419

8040

06654817

3503

719919

520651

7432

828288

628671

3385

732245

482620

7494

804770

655033

2620

719798

570285

7242

50sta

tions

amp100targets

1340

095

1028130

1040

1196218

791338

4590

1272888

923026

0993

121940

6819554

4819

1314565

952735

1061

1143538

843628

4490

1396086

946150

1073

1308837

858909

4931

1197487

897623

1064

1075171

725519

5414

1430365

1091920

1012

1368315

818606

4525

1331166

1031168

1049

1219333

819335

4508

1354155

1004

220

1000

1208915

809037

4550

1418603

1080944

1029

1319784

869953

444

61343357

943478

1023

1256920

807064

4897

Journal of Advanced Transportation 11

Table 5 Comparison between two results of practical cases

H1-NS H2-NSCost of feasiblesolution

Cost of improvedsolution Time 10and-2 (s) Cost of feasible

solutionCost of improved

solution Time 10and-2 (s)

817492 619800 3091 837997 480309 6840

Table 6 Detailed bases and flight paths of the final solution

Base UAV Route

31 3997888rarr21997888rarr22997888rarr32 3997888rarr23997888rarr24997888rarr33 3997888rarr25997888rarr27997888rarr26997888rarr3

61 6997888rarr28997888rarr29997888rarr30997888rarr62 6997888rarr31997888rarr32997888rarr33997888rarr34997888rarr35997888rarr63 6997888rarr36997888rarr37997888rarr6

8 1 8997888rarr38997888rarr39997888rarr40997888rarr41997888rarr82 8997888rarr42997888rarr43997888rarr44997888rarr45997888rarr8

11 1 11997888rarr46997888rarr47997888rarr48997888rarr49997888rarr50997888rarr112 11997888rarr51997888rarr52997888rarr53997888rarr11

15 1 15997888rarr54997888rarr55997888rarr56997888rarr57997888rarr152 15997888rarr58997888rarr59997888rarr60997888rarr15

181 18997888rarr61997888rarr62997888rarr182 18997888rarr63997888rarr64997888rarr65997888rarr67997888rarr66997888rarr183 18997888rarr68997888rarr70997888rarr69997888rarr18

Figure 9 The map of Guangxi Zhuang Autonomous Region (themarked red line is the Guangxi section of the Sino-Vietnameseborder)

efficiency and reaction speed Therefore take the Guangxisection of the border as an example

As displayed in Figure 10 with the ranging tool of GoogleMap the linear distance of this part is about 320 km ThenPaint software is used to discretize this line Fifty target pointsaremarked on the border and twenty base stations are chosenrandomly inside the line Furthermore the relative positionsof these 70 nodes are obtained via the pixel measurement

Figure 10 Guangxi section of the Sino-Vietnamese border with theranging tool

It is assumed that all targets and potential bases arelocated in the area of 320 kilometres multiplied by 160 kilo-metres Mapping these nodes into this area the distributionmap looks like Figure 11 The blue dots are target points andthe red blocks are potential base stations

Two algorithms are applied to solve the practical caseThe results are shown in Table 5 Since the result of H2-NSis obviously superior to another one take the result of H2-NS as the final solution in which the cost is 480309 and thecalculation takes 006840 seconds

The potential base stations are numbered 1 through 20when the target points are represented by 21 to 70 Then thedetailed bases and flight paths can be listed in Table 6 andthe corresponding route map is shown in Figure 12 The finalresult selects 6 bases and launches 15 UAVs

12 Journal of Advanced Transportation

50 100 150 200 250 300 35000

20

40

60

80

100

120

140

Figure 11 50 target points and 20 base stations after discretization

50 100 150 200 250 300 35000

20

40

60

80

100

120

140

Figure 12 The route map of the final solution

6 Conclusions

In this paper considering the background of border patrolfor ISR the capacity constraints of bases are involved inthe multidepot location-routing problem Hence a modifiedmathematical model has been presented The primary objec-tive of this research is to develop an efficient approach forsolving this kind of problem Thus two hybrid heuristicswith neighbourhood search are promoted One is based onclustering and nearest point search and the other one is basedon clustering and CW saving search

In addition experiments have been carried out to com-pare the performance of two algorithms It can be addictedthat neighbourhood search plays an optimizing role to thesolution And the heuristic based on CW saving searchprovides a better solution while consuming more time thanthe other one Furthermore an example based on a practicalborderline is proposed Both algorithms are applied to solvethe border patrol on the practical borderline and provide thefinal solution

Finally two improvements in solving this kind of problemcan be envisaged First the current neighbourhood searchcan be scaled up to find a global optimal solution Secondmore variants of this kind of problem can be exploited Forexample dynamic detecting could be added

Data Availability

The data used to support the findings of this study are avail-able from the corresponding author upon request

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

The research is supported by the National Natural ScienceFoundation of China (no 71771215 and no 71471174)

References

[1] LMiao L Zhen SWangW Lv and X Qu ldquoUnmanned AerialVehicle Scheduling Problem for TrafficMonitoringrdquoComputersamp Industrial Engineering vol 122 pp 15ndash23 2018

[2] S G Manyam S Rasmussen D W Casbeer K Kalyanam andS Manickam ldquoMulti-UAV routing for persistent intelligencesurveillance amp reconnaissance missionsrdquo in Proceedings of the2017 International Conference on Unmanned Aircraft SystemsICUAS 2017 pp 573ndash580 June 2017

[3] S K Jacobsen and O B G Madsen ldquoA comparative study ofheuristics for a two-level routing-location problemrdquo EuropeanJournal of Operational Research vol 5 no 6 pp 378ndash387 1980

[4] D Tuzun and L I Burke ldquoTwo-phase tabu search approach tothe location routing problemrdquo European Journal of OperationalResearch vol 116 no 1 pp 87ndash99 1999

[5] H Min V Jayaraman and R Srivastava ldquoCombined location-routing problems a synthesis and future research directionsrdquoEuropean Journal of Operational Research vol 108 no 1 pp 1ndash15 1998

[6] G Nagy and S Salhi ldquoLocation-routing issues models andmethodsrdquoEuropean Journal ofOperational Research vol 177 no2 pp 649ndash672 2007

[7] J-M Belenguer E Benavent C Prins C Prodhon and RW Calvoc ldquoA Branch-and-Cut method for the CapacitatedLocation-Routing Problemrdquo Computers amp Operations Researchvol 38 no 6 pp 931ndash941 2011

[8] Z Akca R T Berger and T K Ralphs ldquoA branch-and-pricealgorithm for combined location and routing problems undercapacity restrictionsrdquo Operations Research Computer ScienceInterfaces Series vol 47 pp 309ndash330 2009

[9] S Barreto C Ferreira J Paixao and B S Santos ldquoUsing clus-tering analysis in a capacitated location-routing problemrdquoEuropean Journal of Operational Research vol 179 no 3 pp968ndash977 2007

[10] C Prodhon and C Prins ldquoA survey of recent research onlocation-routing problemsrdquo European Journal of OperationalResearch vol 238 no 1 pp 1ndash17 2014

[11] C Prins C Prodhon and RWolfer-Calvo ldquoSolving the capaci-tated location-routing problemby aGRASP complemented by alearning process and a path relinkingrdquo 4OR AQuarterly Journalof Operations Research vol 4 no 3 pp 221ndash238 2006

[12] C Duhamel P Lacomme C Prins and C Prodhon ldquoAGRASPtimesELS approach for the capacitated location-routingproblemrdquo Computers amp Operations Research vol 37 no 11 pp1912ndash1923 2010

[13] R B Lopes C Ferreira and B S Santos ldquoA simple and effectiveevolutionary algorithm for the capacitated location-routingproblemrdquo Computers amp Operations Research vol 70 pp 155ndash162 2016

Journal of Advanced Transportation 13

[14] V F Yu S-W Lin W Lee and C-J Ting ldquoA simulated anneal-ing heuristic for the capacitated location routing problemrdquoComputers amp Industrial Engineering vol 58 no 2 pp 288ndash2992010

[15] J W Escobar R Linfati and P Toth ldquoA two-phase hybridheuristic algorithm for the capacitated location-routing prob-lemrdquoComputers ampOperations Research vol 40 no 1 pp 70ndash792013

[16] R W Harder R R Hill and J T Moore ldquoA Java universalvehicle router for routing unmanned aerial vehiclesrdquo Interna-tional Transactions in Operational Research vol 11 no 3 pp259ndash275 2004

[17] V K Shetty M Sudit and R Nagi ldquoPriority-based assignmentand routing of a fleet of unmanned combat aerial vehiclesrdquoComputers amp Operations Research vol 35 no 6 pp 1813ndash18282008

[18] F Mufalli R Batta and R Nagi ldquoSimultaneous sensor selectionand routing of unmanned aerial vehicles for complex missionplansrdquo Computers amp Operations Research vol 39 no 11 pp2787ndash2799 2012

[19] A M Ham ldquoIntegrated scheduling of m-truck m-drone andm-depot constrained by time-window drop-pickup and m-visit using constraint programmingrdquo Transportation ResearchPart C Emerging Technologies vol 91 pp 1ndash14 2018

[20] G S C Avellar G A S Pereira L C A Pimenta and P IscoldldquoMulti-UAV routing for area coverage and remote sensing withminimum timerdquo Sensors vol 15 no 11 pp 27783ndash27803 2015

[21] I Sarıcicek and Y Akkus ldquoUnmanned aerial vehicle hub-location and routing for monitoring geographic bordersrdquoApplied Mathematical Modelling Simulation and Computationfor Engineering and Environmental Systems vol 39 no 14 pp3939ndash3953 2015

[22] E Yakıcı ldquoSolving location and routing problem for UAVsrdquoComputers amp Industrial Engineering vol 102 pp 294ndash301 2016

[23] T M Cover and P E Hart ldquoNearest neighbor pattern classifi-cationrdquo IEEE Transactions on Information Theory vol 13 no 1pp 21ndash27 1967

[24] G Clarke and J W Wright ldquoScheduling of vehicles from acentral depot to a number of delivery pointsrdquo INFORMS 1964

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

10 Journal of Advanced Transportation

Table4Algorith

mcomparis

onin

caseso

fthree

scales

CaseS

cale

H1-N

SH2-NS

Costo

ffeasib

lesolutio

nCosto

fimproved

solutio

nTime10and-2

(s)

Costo

ffeasib

lesolutio

nCosto

fimproved

solutio

nTime10and-2

(s)

5sta

tions

amp20

targets

348882

300435

2325

336890

238473

3928

386308

3364

162392

362091

263009

3815

372992

274386

2463

336496

1890

613786

322293

273432

2313

287293

239058

3682

372327

2764

202342

325443

179350

3871

372439

274322

2335

336807

238975

5487

372369

273543

1892

337965

240234

3635

361322

261822

2247

348843

250545

3670

372538

322555

2327

336976

237811

3787

384262

285167

2196

336890

237784

3811

20sta

tions

amp50

targets

842265

692451

3037

793872

5440

586950

731291

631663

3081

681403

531504

6895

792129

592620

4232

754694

505265

6627

730762

631054

306

4670777

471234

7285

730340

630746

3149

681039

481442

7002

856295

6560

523173

792201

492593

7867

807587

608259

3128

733063

483691

7419

8040

06654817

3503

719919

520651

7432

828288

628671

3385

732245

482620

7494

804770

655033

2620

719798

570285

7242

50sta

tions

amp100targets

1340

095

1028130

1040

1196218

791338

4590

1272888

923026

0993

121940

6819554

4819

1314565

952735

1061

1143538

843628

4490

1396086

946150

1073

1308837

858909

4931

1197487

897623

1064

1075171

725519

5414

1430365

1091920

1012

1368315

818606

4525

1331166

1031168

1049

1219333

819335

4508

1354155

1004

220

1000

1208915

809037

4550

1418603

1080944

1029

1319784

869953

444

61343357

943478

1023

1256920

807064

4897

Journal of Advanced Transportation 11

Table 5 Comparison between two results of practical cases

H1-NS H2-NSCost of feasiblesolution

Cost of improvedsolution Time 10and-2 (s) Cost of feasible

solutionCost of improved

solution Time 10and-2 (s)

817492 619800 3091 837997 480309 6840

Table 6 Detailed bases and flight paths of the final solution

Base UAV Route

31 3997888rarr21997888rarr22997888rarr32 3997888rarr23997888rarr24997888rarr33 3997888rarr25997888rarr27997888rarr26997888rarr3

61 6997888rarr28997888rarr29997888rarr30997888rarr62 6997888rarr31997888rarr32997888rarr33997888rarr34997888rarr35997888rarr63 6997888rarr36997888rarr37997888rarr6

8 1 8997888rarr38997888rarr39997888rarr40997888rarr41997888rarr82 8997888rarr42997888rarr43997888rarr44997888rarr45997888rarr8

11 1 11997888rarr46997888rarr47997888rarr48997888rarr49997888rarr50997888rarr112 11997888rarr51997888rarr52997888rarr53997888rarr11

15 1 15997888rarr54997888rarr55997888rarr56997888rarr57997888rarr152 15997888rarr58997888rarr59997888rarr60997888rarr15

181 18997888rarr61997888rarr62997888rarr182 18997888rarr63997888rarr64997888rarr65997888rarr67997888rarr66997888rarr183 18997888rarr68997888rarr70997888rarr69997888rarr18

Figure 9 The map of Guangxi Zhuang Autonomous Region (themarked red line is the Guangxi section of the Sino-Vietnameseborder)

efficiency and reaction speed Therefore take the Guangxisection of the border as an example

As displayed in Figure 10 with the ranging tool of GoogleMap the linear distance of this part is about 320 km ThenPaint software is used to discretize this line Fifty target pointsaremarked on the border and twenty base stations are chosenrandomly inside the line Furthermore the relative positionsof these 70 nodes are obtained via the pixel measurement

Figure 10 Guangxi section of the Sino-Vietnamese border with theranging tool

It is assumed that all targets and potential bases arelocated in the area of 320 kilometres multiplied by 160 kilo-metres Mapping these nodes into this area the distributionmap looks like Figure 11 The blue dots are target points andthe red blocks are potential base stations

Two algorithms are applied to solve the practical caseThe results are shown in Table 5 Since the result of H2-NSis obviously superior to another one take the result of H2-NS as the final solution in which the cost is 480309 and thecalculation takes 006840 seconds

The potential base stations are numbered 1 through 20when the target points are represented by 21 to 70 Then thedetailed bases and flight paths can be listed in Table 6 andthe corresponding route map is shown in Figure 12 The finalresult selects 6 bases and launches 15 UAVs

12 Journal of Advanced Transportation

50 100 150 200 250 300 35000

20

40

60

80

100

120

140

Figure 11 50 target points and 20 base stations after discretization

50 100 150 200 250 300 35000

20

40

60

80

100

120

140

Figure 12 The route map of the final solution

6 Conclusions

In this paper considering the background of border patrolfor ISR the capacity constraints of bases are involved inthe multidepot location-routing problem Hence a modifiedmathematical model has been presented The primary objec-tive of this research is to develop an efficient approach forsolving this kind of problem Thus two hybrid heuristicswith neighbourhood search are promoted One is based onclustering and nearest point search and the other one is basedon clustering and CW saving search

In addition experiments have been carried out to com-pare the performance of two algorithms It can be addictedthat neighbourhood search plays an optimizing role to thesolution And the heuristic based on CW saving searchprovides a better solution while consuming more time thanthe other one Furthermore an example based on a practicalborderline is proposed Both algorithms are applied to solvethe border patrol on the practical borderline and provide thefinal solution

Finally two improvements in solving this kind of problemcan be envisaged First the current neighbourhood searchcan be scaled up to find a global optimal solution Secondmore variants of this kind of problem can be exploited Forexample dynamic detecting could be added

Data Availability

The data used to support the findings of this study are avail-able from the corresponding author upon request

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

The research is supported by the National Natural ScienceFoundation of China (no 71771215 and no 71471174)

References

[1] LMiao L Zhen SWangW Lv and X Qu ldquoUnmanned AerialVehicle Scheduling Problem for TrafficMonitoringrdquoComputersamp Industrial Engineering vol 122 pp 15ndash23 2018

[2] S G Manyam S Rasmussen D W Casbeer K Kalyanam andS Manickam ldquoMulti-UAV routing for persistent intelligencesurveillance amp reconnaissance missionsrdquo in Proceedings of the2017 International Conference on Unmanned Aircraft SystemsICUAS 2017 pp 573ndash580 June 2017

[3] S K Jacobsen and O B G Madsen ldquoA comparative study ofheuristics for a two-level routing-location problemrdquo EuropeanJournal of Operational Research vol 5 no 6 pp 378ndash387 1980

[4] D Tuzun and L I Burke ldquoTwo-phase tabu search approach tothe location routing problemrdquo European Journal of OperationalResearch vol 116 no 1 pp 87ndash99 1999

[5] H Min V Jayaraman and R Srivastava ldquoCombined location-routing problems a synthesis and future research directionsrdquoEuropean Journal of Operational Research vol 108 no 1 pp 1ndash15 1998

[6] G Nagy and S Salhi ldquoLocation-routing issues models andmethodsrdquoEuropean Journal ofOperational Research vol 177 no2 pp 649ndash672 2007

[7] J-M Belenguer E Benavent C Prins C Prodhon and RW Calvoc ldquoA Branch-and-Cut method for the CapacitatedLocation-Routing Problemrdquo Computers amp Operations Researchvol 38 no 6 pp 931ndash941 2011

[8] Z Akca R T Berger and T K Ralphs ldquoA branch-and-pricealgorithm for combined location and routing problems undercapacity restrictionsrdquo Operations Research Computer ScienceInterfaces Series vol 47 pp 309ndash330 2009

[9] S Barreto C Ferreira J Paixao and B S Santos ldquoUsing clus-tering analysis in a capacitated location-routing problemrdquoEuropean Journal of Operational Research vol 179 no 3 pp968ndash977 2007

[10] C Prodhon and C Prins ldquoA survey of recent research onlocation-routing problemsrdquo European Journal of OperationalResearch vol 238 no 1 pp 1ndash17 2014

[11] C Prins C Prodhon and RWolfer-Calvo ldquoSolving the capaci-tated location-routing problemby aGRASP complemented by alearning process and a path relinkingrdquo 4OR AQuarterly Journalof Operations Research vol 4 no 3 pp 221ndash238 2006

[12] C Duhamel P Lacomme C Prins and C Prodhon ldquoAGRASPtimesELS approach for the capacitated location-routingproblemrdquo Computers amp Operations Research vol 37 no 11 pp1912ndash1923 2010

[13] R B Lopes C Ferreira and B S Santos ldquoA simple and effectiveevolutionary algorithm for the capacitated location-routingproblemrdquo Computers amp Operations Research vol 70 pp 155ndash162 2016

Journal of Advanced Transportation 13

[14] V F Yu S-W Lin W Lee and C-J Ting ldquoA simulated anneal-ing heuristic for the capacitated location routing problemrdquoComputers amp Industrial Engineering vol 58 no 2 pp 288ndash2992010

[15] J W Escobar R Linfati and P Toth ldquoA two-phase hybridheuristic algorithm for the capacitated location-routing prob-lemrdquoComputers ampOperations Research vol 40 no 1 pp 70ndash792013

[16] R W Harder R R Hill and J T Moore ldquoA Java universalvehicle router for routing unmanned aerial vehiclesrdquo Interna-tional Transactions in Operational Research vol 11 no 3 pp259ndash275 2004

[17] V K Shetty M Sudit and R Nagi ldquoPriority-based assignmentand routing of a fleet of unmanned combat aerial vehiclesrdquoComputers amp Operations Research vol 35 no 6 pp 1813ndash18282008

[18] F Mufalli R Batta and R Nagi ldquoSimultaneous sensor selectionand routing of unmanned aerial vehicles for complex missionplansrdquo Computers amp Operations Research vol 39 no 11 pp2787ndash2799 2012

[19] A M Ham ldquoIntegrated scheduling of m-truck m-drone andm-depot constrained by time-window drop-pickup and m-visit using constraint programmingrdquo Transportation ResearchPart C Emerging Technologies vol 91 pp 1ndash14 2018

[20] G S C Avellar G A S Pereira L C A Pimenta and P IscoldldquoMulti-UAV routing for area coverage and remote sensing withminimum timerdquo Sensors vol 15 no 11 pp 27783ndash27803 2015

[21] I Sarıcicek and Y Akkus ldquoUnmanned aerial vehicle hub-location and routing for monitoring geographic bordersrdquoApplied Mathematical Modelling Simulation and Computationfor Engineering and Environmental Systems vol 39 no 14 pp3939ndash3953 2015

[22] E Yakıcı ldquoSolving location and routing problem for UAVsrdquoComputers amp Industrial Engineering vol 102 pp 294ndash301 2016

[23] T M Cover and P E Hart ldquoNearest neighbor pattern classifi-cationrdquo IEEE Transactions on Information Theory vol 13 no 1pp 21ndash27 1967

[24] G Clarke and J W Wright ldquoScheduling of vehicles from acentral depot to a number of delivery pointsrdquo INFORMS 1964

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

Journal of Advanced Transportation 11

Table 5 Comparison between two results of practical cases

H1-NS H2-NSCost of feasiblesolution

Cost of improvedsolution Time 10and-2 (s) Cost of feasible

solutionCost of improved

solution Time 10and-2 (s)

817492 619800 3091 837997 480309 6840

Table 6 Detailed bases and flight paths of the final solution

Base UAV Route

31 3997888rarr21997888rarr22997888rarr32 3997888rarr23997888rarr24997888rarr33 3997888rarr25997888rarr27997888rarr26997888rarr3

61 6997888rarr28997888rarr29997888rarr30997888rarr62 6997888rarr31997888rarr32997888rarr33997888rarr34997888rarr35997888rarr63 6997888rarr36997888rarr37997888rarr6

8 1 8997888rarr38997888rarr39997888rarr40997888rarr41997888rarr82 8997888rarr42997888rarr43997888rarr44997888rarr45997888rarr8

11 1 11997888rarr46997888rarr47997888rarr48997888rarr49997888rarr50997888rarr112 11997888rarr51997888rarr52997888rarr53997888rarr11

15 1 15997888rarr54997888rarr55997888rarr56997888rarr57997888rarr152 15997888rarr58997888rarr59997888rarr60997888rarr15

181 18997888rarr61997888rarr62997888rarr182 18997888rarr63997888rarr64997888rarr65997888rarr67997888rarr66997888rarr183 18997888rarr68997888rarr70997888rarr69997888rarr18

Figure 9 The map of Guangxi Zhuang Autonomous Region (themarked red line is the Guangxi section of the Sino-Vietnameseborder)

efficiency and reaction speed Therefore take the Guangxisection of the border as an example

As displayed in Figure 10 with the ranging tool of GoogleMap the linear distance of this part is about 320 km ThenPaint software is used to discretize this line Fifty target pointsaremarked on the border and twenty base stations are chosenrandomly inside the line Furthermore the relative positionsof these 70 nodes are obtained via the pixel measurement

Figure 10 Guangxi section of the Sino-Vietnamese border with theranging tool

It is assumed that all targets and potential bases arelocated in the area of 320 kilometres multiplied by 160 kilo-metres Mapping these nodes into this area the distributionmap looks like Figure 11 The blue dots are target points andthe red blocks are potential base stations

Two algorithms are applied to solve the practical caseThe results are shown in Table 5 Since the result of H2-NSis obviously superior to another one take the result of H2-NS as the final solution in which the cost is 480309 and thecalculation takes 006840 seconds

The potential base stations are numbered 1 through 20when the target points are represented by 21 to 70 Then thedetailed bases and flight paths can be listed in Table 6 andthe corresponding route map is shown in Figure 12 The finalresult selects 6 bases and launches 15 UAVs

12 Journal of Advanced Transportation

50 100 150 200 250 300 35000

20

40

60

80

100

120

140

Figure 11 50 target points and 20 base stations after discretization

50 100 150 200 250 300 35000

20

40

60

80

100

120

140

Figure 12 The route map of the final solution

6 Conclusions

In this paper considering the background of border patrolfor ISR the capacity constraints of bases are involved inthe multidepot location-routing problem Hence a modifiedmathematical model has been presented The primary objec-tive of this research is to develop an efficient approach forsolving this kind of problem Thus two hybrid heuristicswith neighbourhood search are promoted One is based onclustering and nearest point search and the other one is basedon clustering and CW saving search

In addition experiments have been carried out to com-pare the performance of two algorithms It can be addictedthat neighbourhood search plays an optimizing role to thesolution And the heuristic based on CW saving searchprovides a better solution while consuming more time thanthe other one Furthermore an example based on a practicalborderline is proposed Both algorithms are applied to solvethe border patrol on the practical borderline and provide thefinal solution

Finally two improvements in solving this kind of problemcan be envisaged First the current neighbourhood searchcan be scaled up to find a global optimal solution Secondmore variants of this kind of problem can be exploited Forexample dynamic detecting could be added

Data Availability

The data used to support the findings of this study are avail-able from the corresponding author upon request

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

The research is supported by the National Natural ScienceFoundation of China (no 71771215 and no 71471174)

References

[1] LMiao L Zhen SWangW Lv and X Qu ldquoUnmanned AerialVehicle Scheduling Problem for TrafficMonitoringrdquoComputersamp Industrial Engineering vol 122 pp 15ndash23 2018

[2] S G Manyam S Rasmussen D W Casbeer K Kalyanam andS Manickam ldquoMulti-UAV routing for persistent intelligencesurveillance amp reconnaissance missionsrdquo in Proceedings of the2017 International Conference on Unmanned Aircraft SystemsICUAS 2017 pp 573ndash580 June 2017

[3] S K Jacobsen and O B G Madsen ldquoA comparative study ofheuristics for a two-level routing-location problemrdquo EuropeanJournal of Operational Research vol 5 no 6 pp 378ndash387 1980

[4] D Tuzun and L I Burke ldquoTwo-phase tabu search approach tothe location routing problemrdquo European Journal of OperationalResearch vol 116 no 1 pp 87ndash99 1999

[5] H Min V Jayaraman and R Srivastava ldquoCombined location-routing problems a synthesis and future research directionsrdquoEuropean Journal of Operational Research vol 108 no 1 pp 1ndash15 1998

[6] G Nagy and S Salhi ldquoLocation-routing issues models andmethodsrdquoEuropean Journal ofOperational Research vol 177 no2 pp 649ndash672 2007

[7] J-M Belenguer E Benavent C Prins C Prodhon and RW Calvoc ldquoA Branch-and-Cut method for the CapacitatedLocation-Routing Problemrdquo Computers amp Operations Researchvol 38 no 6 pp 931ndash941 2011

[8] Z Akca R T Berger and T K Ralphs ldquoA branch-and-pricealgorithm for combined location and routing problems undercapacity restrictionsrdquo Operations Research Computer ScienceInterfaces Series vol 47 pp 309ndash330 2009

[9] S Barreto C Ferreira J Paixao and B S Santos ldquoUsing clus-tering analysis in a capacitated location-routing problemrdquoEuropean Journal of Operational Research vol 179 no 3 pp968ndash977 2007

[10] C Prodhon and C Prins ldquoA survey of recent research onlocation-routing problemsrdquo European Journal of OperationalResearch vol 238 no 1 pp 1ndash17 2014

[11] C Prins C Prodhon and RWolfer-Calvo ldquoSolving the capaci-tated location-routing problemby aGRASP complemented by alearning process and a path relinkingrdquo 4OR AQuarterly Journalof Operations Research vol 4 no 3 pp 221ndash238 2006

[12] C Duhamel P Lacomme C Prins and C Prodhon ldquoAGRASPtimesELS approach for the capacitated location-routingproblemrdquo Computers amp Operations Research vol 37 no 11 pp1912ndash1923 2010

[13] R B Lopes C Ferreira and B S Santos ldquoA simple and effectiveevolutionary algorithm for the capacitated location-routingproblemrdquo Computers amp Operations Research vol 70 pp 155ndash162 2016

Journal of Advanced Transportation 13

[14] V F Yu S-W Lin W Lee and C-J Ting ldquoA simulated anneal-ing heuristic for the capacitated location routing problemrdquoComputers amp Industrial Engineering vol 58 no 2 pp 288ndash2992010

[15] J W Escobar R Linfati and P Toth ldquoA two-phase hybridheuristic algorithm for the capacitated location-routing prob-lemrdquoComputers ampOperations Research vol 40 no 1 pp 70ndash792013

[16] R W Harder R R Hill and J T Moore ldquoA Java universalvehicle router for routing unmanned aerial vehiclesrdquo Interna-tional Transactions in Operational Research vol 11 no 3 pp259ndash275 2004

[17] V K Shetty M Sudit and R Nagi ldquoPriority-based assignmentand routing of a fleet of unmanned combat aerial vehiclesrdquoComputers amp Operations Research vol 35 no 6 pp 1813ndash18282008

[18] F Mufalli R Batta and R Nagi ldquoSimultaneous sensor selectionand routing of unmanned aerial vehicles for complex missionplansrdquo Computers amp Operations Research vol 39 no 11 pp2787ndash2799 2012

[19] A M Ham ldquoIntegrated scheduling of m-truck m-drone andm-depot constrained by time-window drop-pickup and m-visit using constraint programmingrdquo Transportation ResearchPart C Emerging Technologies vol 91 pp 1ndash14 2018

[20] G S C Avellar G A S Pereira L C A Pimenta and P IscoldldquoMulti-UAV routing for area coverage and remote sensing withminimum timerdquo Sensors vol 15 no 11 pp 27783ndash27803 2015

[21] I Sarıcicek and Y Akkus ldquoUnmanned aerial vehicle hub-location and routing for monitoring geographic bordersrdquoApplied Mathematical Modelling Simulation and Computationfor Engineering and Environmental Systems vol 39 no 14 pp3939ndash3953 2015

[22] E Yakıcı ldquoSolving location and routing problem for UAVsrdquoComputers amp Industrial Engineering vol 102 pp 294ndash301 2016

[23] T M Cover and P E Hart ldquoNearest neighbor pattern classifi-cationrdquo IEEE Transactions on Information Theory vol 13 no 1pp 21ndash27 1967

[24] G Clarke and J W Wright ldquoScheduling of vehicles from acentral depot to a number of delivery pointsrdquo INFORMS 1964

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

12 Journal of Advanced Transportation

50 100 150 200 250 300 35000

20

40

60

80

100

120

140

Figure 11 50 target points and 20 base stations after discretization

50 100 150 200 250 300 35000

20

40

60

80

100

120

140

Figure 12 The route map of the final solution

6 Conclusions

In this paper considering the background of border patrolfor ISR the capacity constraints of bases are involved inthe multidepot location-routing problem Hence a modifiedmathematical model has been presented The primary objec-tive of this research is to develop an efficient approach forsolving this kind of problem Thus two hybrid heuristicswith neighbourhood search are promoted One is based onclustering and nearest point search and the other one is basedon clustering and CW saving search

In addition experiments have been carried out to com-pare the performance of two algorithms It can be addictedthat neighbourhood search plays an optimizing role to thesolution And the heuristic based on CW saving searchprovides a better solution while consuming more time thanthe other one Furthermore an example based on a practicalborderline is proposed Both algorithms are applied to solvethe border patrol on the practical borderline and provide thefinal solution

Finally two improvements in solving this kind of problemcan be envisaged First the current neighbourhood searchcan be scaled up to find a global optimal solution Secondmore variants of this kind of problem can be exploited Forexample dynamic detecting could be added

Data Availability

The data used to support the findings of this study are avail-able from the corresponding author upon request

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

The research is supported by the National Natural ScienceFoundation of China (no 71771215 and no 71471174)

References

[1] LMiao L Zhen SWangW Lv and X Qu ldquoUnmanned AerialVehicle Scheduling Problem for TrafficMonitoringrdquoComputersamp Industrial Engineering vol 122 pp 15ndash23 2018

[2] S G Manyam S Rasmussen D W Casbeer K Kalyanam andS Manickam ldquoMulti-UAV routing for persistent intelligencesurveillance amp reconnaissance missionsrdquo in Proceedings of the2017 International Conference on Unmanned Aircraft SystemsICUAS 2017 pp 573ndash580 June 2017

[3] S K Jacobsen and O B G Madsen ldquoA comparative study ofheuristics for a two-level routing-location problemrdquo EuropeanJournal of Operational Research vol 5 no 6 pp 378ndash387 1980

[4] D Tuzun and L I Burke ldquoTwo-phase tabu search approach tothe location routing problemrdquo European Journal of OperationalResearch vol 116 no 1 pp 87ndash99 1999

[5] H Min V Jayaraman and R Srivastava ldquoCombined location-routing problems a synthesis and future research directionsrdquoEuropean Journal of Operational Research vol 108 no 1 pp 1ndash15 1998

[6] G Nagy and S Salhi ldquoLocation-routing issues models andmethodsrdquoEuropean Journal ofOperational Research vol 177 no2 pp 649ndash672 2007

[7] J-M Belenguer E Benavent C Prins C Prodhon and RW Calvoc ldquoA Branch-and-Cut method for the CapacitatedLocation-Routing Problemrdquo Computers amp Operations Researchvol 38 no 6 pp 931ndash941 2011

[8] Z Akca R T Berger and T K Ralphs ldquoA branch-and-pricealgorithm for combined location and routing problems undercapacity restrictionsrdquo Operations Research Computer ScienceInterfaces Series vol 47 pp 309ndash330 2009

[9] S Barreto C Ferreira J Paixao and B S Santos ldquoUsing clus-tering analysis in a capacitated location-routing problemrdquoEuropean Journal of Operational Research vol 179 no 3 pp968ndash977 2007

[10] C Prodhon and C Prins ldquoA survey of recent research onlocation-routing problemsrdquo European Journal of OperationalResearch vol 238 no 1 pp 1ndash17 2014

[11] C Prins C Prodhon and RWolfer-Calvo ldquoSolving the capaci-tated location-routing problemby aGRASP complemented by alearning process and a path relinkingrdquo 4OR AQuarterly Journalof Operations Research vol 4 no 3 pp 221ndash238 2006

[12] C Duhamel P Lacomme C Prins and C Prodhon ldquoAGRASPtimesELS approach for the capacitated location-routingproblemrdquo Computers amp Operations Research vol 37 no 11 pp1912ndash1923 2010

[13] R B Lopes C Ferreira and B S Santos ldquoA simple and effectiveevolutionary algorithm for the capacitated location-routingproblemrdquo Computers amp Operations Research vol 70 pp 155ndash162 2016

Journal of Advanced Transportation 13

[14] V F Yu S-W Lin W Lee and C-J Ting ldquoA simulated anneal-ing heuristic for the capacitated location routing problemrdquoComputers amp Industrial Engineering vol 58 no 2 pp 288ndash2992010

[15] J W Escobar R Linfati and P Toth ldquoA two-phase hybridheuristic algorithm for the capacitated location-routing prob-lemrdquoComputers ampOperations Research vol 40 no 1 pp 70ndash792013

[16] R W Harder R R Hill and J T Moore ldquoA Java universalvehicle router for routing unmanned aerial vehiclesrdquo Interna-tional Transactions in Operational Research vol 11 no 3 pp259ndash275 2004

[17] V K Shetty M Sudit and R Nagi ldquoPriority-based assignmentand routing of a fleet of unmanned combat aerial vehiclesrdquoComputers amp Operations Research vol 35 no 6 pp 1813ndash18282008

[18] F Mufalli R Batta and R Nagi ldquoSimultaneous sensor selectionand routing of unmanned aerial vehicles for complex missionplansrdquo Computers amp Operations Research vol 39 no 11 pp2787ndash2799 2012

[19] A M Ham ldquoIntegrated scheduling of m-truck m-drone andm-depot constrained by time-window drop-pickup and m-visit using constraint programmingrdquo Transportation ResearchPart C Emerging Technologies vol 91 pp 1ndash14 2018

[20] G S C Avellar G A S Pereira L C A Pimenta and P IscoldldquoMulti-UAV routing for area coverage and remote sensing withminimum timerdquo Sensors vol 15 no 11 pp 27783ndash27803 2015

[21] I Sarıcicek and Y Akkus ldquoUnmanned aerial vehicle hub-location and routing for monitoring geographic bordersrdquoApplied Mathematical Modelling Simulation and Computationfor Engineering and Environmental Systems vol 39 no 14 pp3939ndash3953 2015

[22] E Yakıcı ldquoSolving location and routing problem for UAVsrdquoComputers amp Industrial Engineering vol 102 pp 294ndash301 2016

[23] T M Cover and P E Hart ldquoNearest neighbor pattern classifi-cationrdquo IEEE Transactions on Information Theory vol 13 no 1pp 21ndash27 1967

[24] G Clarke and J W Wright ldquoScheduling of vehicles from acentral depot to a number of delivery pointsrdquo INFORMS 1964

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

Journal of Advanced Transportation 13

[14] V F Yu S-W Lin W Lee and C-J Ting ldquoA simulated anneal-ing heuristic for the capacitated location routing problemrdquoComputers amp Industrial Engineering vol 58 no 2 pp 288ndash2992010

[15] J W Escobar R Linfati and P Toth ldquoA two-phase hybridheuristic algorithm for the capacitated location-routing prob-lemrdquoComputers ampOperations Research vol 40 no 1 pp 70ndash792013

[16] R W Harder R R Hill and J T Moore ldquoA Java universalvehicle router for routing unmanned aerial vehiclesrdquo Interna-tional Transactions in Operational Research vol 11 no 3 pp259ndash275 2004

[17] V K Shetty M Sudit and R Nagi ldquoPriority-based assignmentand routing of a fleet of unmanned combat aerial vehiclesrdquoComputers amp Operations Research vol 35 no 6 pp 1813ndash18282008

[18] F Mufalli R Batta and R Nagi ldquoSimultaneous sensor selectionand routing of unmanned aerial vehicles for complex missionplansrdquo Computers amp Operations Research vol 39 no 11 pp2787ndash2799 2012

[19] A M Ham ldquoIntegrated scheduling of m-truck m-drone andm-depot constrained by time-window drop-pickup and m-visit using constraint programmingrdquo Transportation ResearchPart C Emerging Technologies vol 91 pp 1ndash14 2018

[20] G S C Avellar G A S Pereira L C A Pimenta and P IscoldldquoMulti-UAV routing for area coverage and remote sensing withminimum timerdquo Sensors vol 15 no 11 pp 27783ndash27803 2015

[21] I Sarıcicek and Y Akkus ldquoUnmanned aerial vehicle hub-location and routing for monitoring geographic bordersrdquoApplied Mathematical Modelling Simulation and Computationfor Engineering and Environmental Systems vol 39 no 14 pp3939ndash3953 2015

[22] E Yakıcı ldquoSolving location and routing problem for UAVsrdquoComputers amp Industrial Engineering vol 102 pp 294ndash301 2016

[23] T M Cover and P E Hart ldquoNearest neighbor pattern classifi-cationrdquo IEEE Transactions on Information Theory vol 13 no 1pp 21ndash27 1967

[24] G Clarke and J W Wright ldquoScheduling of vehicles from acentral depot to a number of delivery pointsrdquo INFORMS 1964

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom