Research Article Routing Optimization of Intelligent Vehicle in …downloads.hindawi.com/journals/ddns/2014/789754.pdf · 2019-07-31 · colony optimization algorithm. ey gave a mathematical

Research ArticleRouting Optimization of Intelligent Vehiclein Automated Warehouse

Yan-cong Zhou1 Yong-feng Dong2 Hong-mei Xia2 and Jun-hua Gu2

1 School of Information Engineering Tianjin University of Commerce Tianjin 300134 China2 School of Computer Science and Software Hebei University of Technology Tianjin 300401 China

Correspondence should be addressed to Yan-cong Zhou zycong78126com

Received 11 April 2014 Accepted 12 May 2014 Published 16 June 2014

Academic Editor Xiang Li

Copyright copy 2014 Yan-cong Zhou et alThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Routing optimization is a key technology in the intelligent warehouse logistics In order to get an optimal route for warehouseintelligent vehicle routing optimization in complex global dynamic environment is studied A new evolutionary ant colonyalgorithm based on RFID and knowledge-refinement is proposed The new algorithm gets environmental information timelythrough the RFID technology and updates the environmentmap at the same time It adopts elite ant kept fallback and pheromoneslimitation adjustment strategy The current optimal route in population space is optimized based on experiential knowledge Theexperimental results show that the new algorithm has higher convergence speed and can jump out the U-type or V-type obstacletraps easily It can also find the global optimal route or approximate optimal one with higher probability in the complex dynamicenvironment The new algorithm is proved feasible and effective by simulation results

1 Introduction

With the development of factory automation and logisticsautomation traditional production and material handlingare more automated and intelligent and a lot of large-scale storage centers come into being However due to thecomplexity of goods classification frequent turnover largenumber of houses complex road conditions and so onfinding target shelves location in the large-scale storage centeris a very difficult task When working people always need thehelp of memories or carrying signs for tendency guidelinesthe result is inefficient and error-prone and human materialand financial resources are wasted on a certain degreeIntelligent vehicle is a cargo automatically handling car inintelligent transport systems that can meet the requirementsof warehouse and flexible manufacturing systems and it isone of themost crucial parts of thewhole logistics automationand production automation

Generally intelligent vehicle also called automated guidedvehicle is a mobile robot Intelligent vehicle is an integratedsystem which involves computer systems sensors automaticcontrol mechanical communications and other technolo-gies It has beenwidely applied inmany areas such as industry

agriculture military and other fields and is one of the hotresearch issues in the field of robotic applications Intelligentvehicle system is controlled by computer with the charactersof autonomous navigation automatically path planning andexecuting tasks independently avoiding obstacle and has theadvantages of high degree of automation easy schedulingand management safety and reliability and so forth Its goalis to achieve the automatically handling of goods The keytechnology of intelligent vehicle is similar to the mobilerobot and the difficult and critical points include navigationrouting optimization task scheduling coordination ofmulti-AGV control and information fusion technology Routingoptimization is the focus of this study

The routing optimization of intelligent vehicle is search-ing one optimal or approximate optimal route with a specificperformance (such as shortest distance less time etc) fromstarting point to target point in theenvironment with obsta-cles The route searching is the prerequisite for intelligentvehicle performing various complex tasks so the researchfor effective route planning in a complex environment isnecessary and significant in the field of intelligent warehouseDepending on the degree that environmental information is

Hindawi Publishing CorporationDiscrete Dynamics in Nature and SocietyVolume 2014 Article ID 789754 14 pageshttpdxdoiorg1011552014789754

2 Discrete Dynamics in Nature and Society

known route searching can be divided into two categories(1) global route searching with environmental informationknown (2) local route searching with environmental infor-mation unknown or partially unknown Global route search-ing is to find the optimal or approximate optimal route tomeet certain performance from the starting point to the targetpoint according to the priori model The key problem is theenvironmentmodel building and the route searching strategyLocal route searching means in the unknown or partiallyunknown environment the intelligent vehicle according tothe sensorrsquos information including the location size andshape information of the obstacle gives a satisfied route withno collision

For path planning problem of mobile robot many schol-ars have had extensive research and also gotten some achieve-ment The traditional robot path planning methods such asartificial potential [1] visibility graph [2] graph searchingand grid decoupling method each have the advantages anddisadvantages With the development of intelligent algo-rithms many scholars introduce them into the field ofrobot path planning The intelligent algorithms improve theperformance of the robot path planning to some extent butthey also have their own defects For example genetic algo-rithm is easy to fall into local optimum and has prematureslower convergence and other issues With the increasingof obstacles or encountering complex terrain especially thecomplexity of the intelligent algorithms will greatly increaseand we even cannot find the optimal solution [3]

Tuncer and Yildirim [4] in order to solve the problemof genetic algorithm of premature and slow convergenceproposed a dynamic path planning of mobile robot based onwith improved genetic algorithm Yang and Fu [5] in orderto improve the searching efficiency of genetic algorithmproposed a new mobile robot path planning algorithmcombined with grid method and chaos genetic algorithmThere are some problems in the neural network system suchas networks large-scale common performance and easy tomake a robot into an infinite loop Glasius et al [6] proposeda neural network model based on Hopfield network withdynamically avoiding obstacles The model can avoid localminimumpoint but it is difficult to adapt to the dynamic andhigh speed environment Ant colony algorithm is easy to fallinto local optimal solution and the U-shaped or V-shapedtrap Cai et al [7] proposed a new method combined withthe ant colony algorithm and fuzzy control technologyAlthough this method can solve the robot path planningproblem it is more complex and difficult In order to improveexecution speed and search efficiency Liu [8] proposed animproved algorithm based on ant colony algorithm andgenetic algorithm Liu and Cheng [9] presented visiondetection colony algorithm with elitist strategy to improvethe efficiency Zhou and Hua [10] presented an improved antcolony algorithm using simulated annealing algorithm toimprove the pheromone evaporation coefficient

About the routing optimization in logistics and ware-house scholars also do a lot ofwork and somedo the researchbased on intelligent algorithms

Sun [11] researched the path planning of automatedguided vehicle system He built the map model with graph

theory in the process of AGV path planning and searchedthe shortest path by Dijkstra algorithm Wang and Feng [12]researched the picking path plan for carousel based on antcolony optimization algorithm They gave a mathematicalmodel for hierarchical leveled carousel system with singlepicking station of automatic stereoscopic warehouse andproposed an improved ant colony optimization (ACO) algo-rithm Zeng and Zong [13] researched routing optimizationof ASRS based on simulated annealing genetic algorithmThe simulated annealing algorithm and genetic algorithm arecombined to solve theASRS Pang and Lu [14] researched thepath picking optimization of automated warehouses basedon the ant colony generic algorithm They gave an initialpopulation by the ant colony algorithm and then solved themodel with the genetic algorithms Liu et al [15] researcheddynamic material handling route planning based on real-time operation conditionsThey considered the complex andchangeable material demand environment of the productionsystem and set up a dynamic material transporting routingoptimization model which considered several demandersand multifarious convey angles References [16 17] intro-duced the RFID technology into the path planning Chenet al [16] researched the indoor path planning for seeingrobot eyes based on RFID Guo [17] researched the intelligentnavigation and scheduling of vehicles in warehouses For therequirements of saving time and energy he used bridgingRFID module to take charge of the navigation functionOptimal route was generated by a combinative strategy oftopological-index and 119860lowast algorithm

This paper will introduce RFID technology into large-scale warehousing center and the use of RFID will make theenvironment map updated automatically and timely so therouting optimization problem from starting point to targetshelf will be solved more effectively In the process of routesearching for the ant colony algorithm easy to fall into localoptimum and hard to jumpout theU-type orV-type trap thepaper proposes an evolutionary ant colony algorithm basedon the prior knowledge to effectively find the optimal route

The rest of this paper is organized as follows Our workenvironment model is formulated in Section 2 In Section 3we provide the goal of routing optimization problem andpresent the definitions of ant colony algorithmrsquos parametersThe detailed steps and flow charts are given in Section 3 InSection 4 the simulation results and analysis of four differentalgorithms are provided Finally we conclude our paper inSection 5

2 Modeling the Working Environment forIntelligent Vehicle

Modeling the working environment is the first step for thepath optimization A reasonable description of the workingenvironment can decrease the searching steps in the processof searching the optimal path and reduce the complexity ontime and space In this section we will model the workingenvironment which is mainly the presentations of obstaclesdestination and action space Shelves and goods in large-scale storage center may not only be the action destination

Discrete Dynamics in Nature and Society 3

but also obstacles which make the working environmentcomplicated So to facilitate the following analysis we usegrid method to model the working environment And someassumptions are given as follows

(1) Assume the storage to be rectangular and there aresome static obstacles such as shelves and goodsThe reason for the static assumption is that firstall shelves and immobile goods are static secondalthough the goods can be moved corresponding tothe moving vehicle the moving goods are also staticTherefore all obstacles are considered to be staticHowever the working environment can be changeddynamically after each transport

(2) The intelligent vehicle is viewed as a particle withoutsize

(3) Expand each obstacle into a circumscribed rectangleIf the expansion cannot fill a complete grid then itwill be considered as a grid

(4) Assume the starting point to be fixed and the desti-nation may be different as the changing of the goodsHowever the environment will be updated aftergoods is moved to the destination so the destinationof the new path optimization problem is still static

In the following we will model the working space Let 119862denote the whole storage space including all action space andfinite obstacles Define a rectangular coordinate systemwherethe left upper corner is the origin of the coordinate and theupper border of 119862 is 119909-axis and the left border of 119862 is 119910-axisLet 119909max denote the maximum value of the horizontal axis ofthe point in 119862 and 119910max denote the maximum value of thelongitudinal axis of the point in 119862 so the work space is

119860 = (119909 119910) | 119909 isin [0 119909max] 119910 isin [0 119910max] (1)

Let 119877119888denote the maximum length of each action

step and divide the domain 119862 into the grids with equalitysegmentation and let both lengths of each step in 119909-axisand 119910-axis be 119877

119888 The column number of the grid domain

is denoted by 119873119909 and the row number is denoted by 119873

119910 In

this paper we consider the rectangular 119862 to be a square Let119873119909= 119873119910 So the continuous domain 119860 can give a discrete

space 119860119889defined by

119860119889= (119894 119895) 119894 119895 = 0 1 2 119873

119909 (2)

We set the sequence number for each grid so119860119889also can

be denoted by

119860119889= (119909

119896 119910119896) | 119909119896= fix( 119896

119873119909

) + 1 119910119896= 119896 mod 119873

119909+ 1

119896 = 0 1 1198732

119909minus 1

(3)

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Figure 1 Environment map

In Figure 1 we give a grid description of a working spacewith 100 grids In the grid domain a black grid denotes anobstacle and a white grid denotes an action space

3 Modeling for Routing Optimization ofIntelligence Vehicle

31 Objective Function We consider a working environmentin Figure 1 where the start point is (119909

119904 119910119904) the destination is

(119909119889 119910119889) The routing optimization is to find an optimal route

from all feasible pathsThe feasible path is a path from (119909119904 119910119904)

to (119909119889 119910119889) and can avoid possible obstacles Generally we set

the start point to be (1199091 1199101)

We define the path length by Euclidean distance so thelength of an edge with the points 119901

119894(119909119894 119910119894) and 119901

119894+1(119909119894+1 119910119894+1)

is given as follows

119889 = radic(119909119894+1minus 119909119894)2

+ (119910119894+1minus 119910119894)2

(4)

The path with 119871 grids can be denoted as follows

1199011198941

(1199091198941

1199101198941

)997888rarrsdot sdot sdot997888rarr119901119894119896

(119909119894119896

119910119894119896


(119909119894119871

119910119894119871

)

1198941= 1 119894

119871= 119899

(5)

Therefore the total length119863(119871) of the path is

119863 (119871) =

119871minus1

sum119896=1

radic(119909119894119896+1

minus 119909119894119896

)2

+ (119910119894119896+1

minus 119910119894119896

)2

(6)

In practical operations when making a turn the vehicleneeds to judge the obstacle calculate its size and space extentand relocate the direction which cost a lot of time and energyso we should reduce the number of turns as possible as wecan Therefore the routing optimization problem has two


objectives the least number of turns and the shortest pathlength We consider a weighted sum objective function asfollows

1198651 = (1 +1

radic1 + 119871) times 119863 times 119908

119889+ curve times 119908

119888 (7)

where 119871 is the total number of all grids in a path119863radic1 + 119871 isa correction item and curve is the total number of turns 119908

119889

and 119908119888are the weight and 119908

119889+ 119908119888= 1

To facilitate the observation and the show of experimentresults we use the following new objective function

119865 =100

(1 + (1radic1 + 119871)) times 119863 times 119908119889+ curve times 119908

119888

(8)

In summary the path optimization problem can besummarized as the following model

max 119866 (119871) 119871 = 1 2 119868

st

119866 (119871) = max119875

119865

st

(120579119909119894119896

+ (1 minus 120579) 119909119894119896+1

120579119910119894119896

+ (1 minus 120579) 119910119894119896+1

) notin 119860119874

for any 120579 isin [0 1] 119894119896 119894119896+1isin 119878119886

119901 = (1199011 1199012 119901

119898) 119901119896= (119909119894119896

119910119894119896

)

(1199091198941

1199101198941

) = (1199091 1199101)

(119909119894119871

119910119894119871

) = (119909119889 119910119889)

(9)

where 119868 denotes the total number of feasible grids in theworking environment that is 119868 = 1198732

119909minus 119904 Here we set the

upper-bound of 119871 to be 119868 which is just the reason that thepath including withdraw steps is not optimal

32 Parameters of Ant Colony Algorithm When looking forfood ants release special secretions called pheromones ontheir paths which will evaporate with time The later antswill select one path with the probability that is proportionalto the intensity of pheromones on the path When moreants pass through one path there will be more pheromonesreleased on the path and then this path will be selected byants with higher probabilityThus a kind of positive feedbackmechanism is formed by which ants can eventually find theoptimal route The parameters and strategies of basic modelof ant colony algorithm are as follows

Let119898 be the number of ant colony algorithm

Definition 1 Tabu table is an array of two dimensionswhich records the traversed nodes of each ant tabu

119896records

currently traversed nodes of ant 119896 in each generation Whenant 119896 reaches the target point the route of ant 119896 is just givenby the tabu table tabu

119896

Definition 2 120591119894119895(119905) is the pheromones factor 119905 represents time

and (119894 119895) represents the path from node 119894 to node 119895 (119894 119895 =1 2 119899) 120591

119894119895(119905) represents the retained pheromones of edge

(119894 119895) at time 119905

Definition 3 Heuristic factor 120578119894119895denotes expectation degree

that the antsmove fromnode 119894 to node 119895 andusually is definedas follows

120578119894119895=1

119889119894119895

(10)

where 119889119894119895is the distance between node 119894 and node 119895

Definition 4 Let 119875119896119894119895be the transition probability with which

ant transfers from node 119894 to node 119895 The definition is asfollows

119875119896

119894119895=

[120591119894119895(119905)]120572

[120578119894119895(119905)]120573

sum119904isinallowed

119896

[120591119894119895(119905)]120572

[120578119894119895(119905)]120573

if 119895 isin allowed119896

0 else

(11)

where allowed119896(where 119896 = 1 2 119899) represents the

set of allowed next nodes which can be selected by ant 119896on the current environment 120572 and 120573 denote the degree ofimportance of pheromones on the path and heuristic factor120578119894119895

Definition 5 Δ120591119894119895(119905) is the pheromone increment It repre-

sents the pheromone increment on edge (119894 119895) after time Δ119905The definition is as formula (12) Generally when initializedΔ120591119894119895(0) is always set to zero

Δ120591119894119895(119905) =

119898

sum119896=1

Δ120591119894119895(119905) (12)

where Δ120591119896119894119895(119905) represents the pheromones increment of ant 119896

on edge (119894 119895) after time Δ119905 The definition is as follows

Δ120591119896

119894119895(119905) =

119876

119871119896

ant 119896 pass edge (119894 119895)

0 others(13)

where 119876 is the enhancing coefficient of pheromones whichaffects the speed of convergence to a certain extent 119871

119896

represents the distance of the route which is created by ant119896 in the current iteration

Therefore after the time Δ119905 the pheromones on eachedges can be updated by the following

120591119894119895(119905 + Δ119905) = (1 minus 120588) 120591

119894119895(119905) + Δ120591

119894119895(119905) (14)

where 120588 is the evaporating coefficient of pheromones 1 minus 120588represents the retain factor In order to prevent the unlimitedaccumulation of pheromones set 120588 isin [0 1]

For the first goal of shortest distance the basic idea ofant colony algorithm is to place 119898 ants at the starting pointat the same time and each ant selects one feasible nodewith a certain probability and meanwhile updates the localpheromones The ants select the next available node withthe same strategy until they reach the target point Thusthe path passed by each ant is a feasible solution and thenin accordance with their contribution to the problem they


update global pheromones If the conditions of terminationare met the current optimal solution is output otherwise thenext iteration continues

About the second goal of reducing the turns of route themodeling and related strategies will be described in detail inSection 4

4 Routing Optimization forIntelligent Vehicle Based on EvolutionaryAnt Colony Algorithm

41 Steps of Ant Colony Algorithm The general steps forsolving the routing optimization problem by ant colonyalgorithm are as follows

Step 1 (initialization) The ants are placed at the startingpoint S and S is added to the tabu list tabu

119896 Let the initial

pheromones of each side be a constant 120591119894119895(0) = 120591

0119889 (1205910is a

constant119889 is the distance to the next grid 119889 = 1 orradic2) Herewe redefine the initial pheromones with the distance factorconsidered so it is different from the traditional ant colonyalgorithm 120591

119894119895(0) = 120591 The new definition helps to improve the

convergence Set the current experiment iterations NG = 1the maximum iterations are NGMAX

Step 2 (select the next available node) In the algorithm weselect the next available node 119895 with roulette strategy At anytime 119905 transfer probability 119875119896

119894119895from node 119894 to 119895 is as shown in

formula (11)

Step 3 (pheromones update) After time Δ119905 the pheromonesare updated according to formula (14) and the pheromonesevaporating coefficient is adaptive The pheromones evapo-rating coefficient is very important when the environmentmap is complex If 120588 is too small it is very easy to fall intolocal optimum solution If 120588 is too large it will reduce theconvergence speed of the algorithm So in this paper thepheromones evaporating coefficient is dynamically adjustedaccording to the situation of path length As formula (15) ifthe path length of the path set has distinct difference it willslow convergence speed or otherwise accelerate convergencespeed

120588 (119905) =119863ave minus 119863min119863max minus 119863min

(15)

where 119863max is the length of the longest path 119863ave representsthe average length of all paths and 119863min is the length of theshortest path

Here we also set a limitation for the pheromones evap-orating coefficient The limitation is just to prevent thealgorithm falling into local optimum due to the coefficientbeing too big or too small Here themaximum andminimumvalues are given

Step 4 Set iteration NG = NG+1 If NG gtNGMAX then goto Step 5 otherwise adopt elite ant strategyThe ant with bestfitness value in this iteration is chosen as the elite ant which

is automatically selected into the next iteration and thuscan increase the impact of the optimal route of the previousiteration and improve the convergence of the algorithm Goto Step 2

Step 5 Output the optimal route and the algorithm end

In order to prevent the ants falling into a U-shaped orV-shaped trap fallback strategy is adopted in the algorithmWhen ants fall into the trap if there is no good method todeal with the situation the ants will be in ldquodeadrdquo state that thecurrent feasible node set is empty so the entire algorithmwillbe influenced In the paper when ant 119896 falls into U-shaped orV-shaped trap we let it back to the previous node and thenthe previous node is added to tabu table tabu

119896 If now the

feasible nodes set is still empty do backing until the feasibleset of ant is not empty

The whole algorithm flow chart is as shown in Figure 2

42 Strategy of Routing Optimization As referred to inSection 31 routing optimization of intelligent vehicle hastwo goals one is the shorter distance and the second is thefewer number of turns Inspired by the cultural algorithmwe propose the reducing turns strategy based on the priorknowledge

Themain idea of the cultural algorithm is that in the pop-ulation space individuals have individual experience duringthe evolutionary process and the individual experience willbe passed to the belief space through the function Accept()Individual experience received in belief space will be com-pared and optimized according to certain rules thus forminggroups experience and then update the group experiencewith update() function according to the existing group andindividual experience In belief space after the formationof the group experience the behavior of individuals in thepopulation space will be modified by Influence() functionin order to enable individuals to achieve higher evolutionaryefficiency The basic framework of cultural algorithm [18] isas shown in Figure 3

Considering the second goal we should minimize theturns of the routeThis goal can be achieved by the optimiza-tion operation based on the a priori knowledge on the routewhich is obtained during iterations of ant colony algorithmThe optimization operation is the experience update in beliefspace of cultural colony algorithm In the belief space the twooptimizing operations are based on the a priori knowledgeOne operation is abandoning the roundabout and the otheris reducing turns by parallelogram strategy

(1) Strategy of Abandoning the Roundabout Roundabout willemerge when ants are looking for food and it will influencethe pheromones of the path which is not conducive forrouting optimization and thus will mislead other ants sothe roundabout makes the algorithm have poor convergenceIn order to improve the convergence of the algorithm theoperation of abandoning roundabout must be applied to thecurrent route Set the grid number of one path to be Lncalculate the allowed nodes set for the current node If thenext nodes (except the first next node of the current node)


All ants reach the target point

Reach the max iteration

No

Yes

Yes

No

Yes

No

Start

End

Select the next node by roulette

Initialize parameters

Update pheromones

Select the elite ant into next iteration

Output the optimal route

Ant k fallback one gridAllowedk set is empty

Place m ants on the starting point

Calculate allowedk set

Figure 2 Flow chart of ant colony algorithm

Adjustbelief space

Inheritancepopulation space

Accept() Influence()

Copy andmodify

Performancefunction

Figure 3 Basic framework of cultural algorithm

after current node are in the allowed nodes set you candelete the nodes between the current node and the next nodedirectly from the circuitous path and then the quality of thepath will be improved Figure 4 shows the original circuitouspath For node 32 its allowed node set is (31 33 41 42 43)Except the next node 41 we find node 43 in the next nodesset and also in the allowed nodes set so the path betweennode 43 and node 32 can be deleted The new route afterthe optimization is shown in Figure 5 From Figure 4 andFigure 5 we can see the quality of the route is significantlyimproved after the operation of abandoning roundabout and

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Figure 4 Route before abandoning roundabout

the number of turns is effectively reduced alsoThe flow chartof optimization operation for abandoning the roundabout isshown in Figure 6

(2) Strategy of Reducing Turns by Parallelogram The strategyis to reduce the number of vehicle turns and thus can reduce


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Figure 5 Route after operation of abandoning roundabout

the vehiclersquos walking energy consumption and improve thefitness value of route Select three consecutive nodes theconnection between the first node and the previous nodeon the route forming segment 1 and the connection betweensecond and third node forming segment 2 When segment1 and segment 2 are parallel draw a parallelogram with thethree nodes as the three vertices of the parallelogram andthen we will get two new segments which are not on theoriginal route If the grids passing by the new segments areall free grid then the two original segments on the route willbe deleted the two new segments replace the original and anew route then comes up Obviously the new route has lessturns than the old one The map and the original route areshown in Figure 7 We explain the strategy in detail takingnodes 10 43 and 63 for example Segment 1 between nodes0 and 10 parallels segment 2 between nodes 43 and 63 sodraw up a parallelogramwith nodes 10 43 and 63 as the threevertices of the parallelogram Then two new segments comeup One is segment between nodes 10 and 30 the other isthe one between nodes 30 and 63 The grids passing by thetwo new segments are all free grid so the two old segmentsare substituted by the two new ones Then the new routecomes up and is as shown in Figure 8 From Figure 7 andFigure 8 we can see after the optimization of reducing turnsby parallelogram that the new route has less turns and higherfitness value than the old one The flow chart of optimizationoperation for reducing turns by parallelogram is shown inFigure 9

43 Steps of Evolutionary Ant Colony Algorithm The inte-gration of Sections 41 and 42 is the whole evolutionaryant colony algorithm The algorithm takes the ant colonyas the population space and the optimization for the routewith operation of abandoning roundabout and reducing theturns by parallelogram based on the a priori knowledge asthe group experience updating of belief space The mainsteps of the evolutionary ant colony algorithm for routingoptimization are as follows

(1) In the population space the route set is generated byant colony algorithm and each route with individualexperience is delivered to the belief space

(2) In the belief space all the routes are optimized bystrategies of abandoning roundabout and reducingturns by parallelogram based on the a priori knowl-edge and thus form the groups experience

(3) The optimized routes are delivered back to the popu-lation space to update the pheromones Repeat steps(1)ndash(3) until the end condition of the algorithm issatisfied

The flow chart of evolutionary ant colony algorithm is asshown in Figure 10 Specific operation is as follows

(1) Population Space Detailed operation steps in populationspace are as follows

(1) Build model for working environment of intelligentvehicle by grid method Obtain information of thecurrent environment through RFID technology andthen build the current environment map Determinethe starting point and the destination point

(2) Parameter initialization for ant colony algorithmSet the initial value of iteration initial time initialpheromones tabu list and so forth

(3) According to the ant colony algorithm mentioned inSection 41 select nodes and update pheromones andgenerate corresponding route set for119898 ants

(4) Deliver the route set to the belief space by Accept()function

(5) Receive the updated route set from the belief space byInfluence() function

(6) Global pheromones are updated(7) Judging the termination conditions If the condition

is not satisfied go to step (8) If satisfied output theoptimal route and the intelligent vehicle advancesaccording to the route through the assistance ofRFID During the process of returning starting pointfrom target point the environment map is updatedthrough RFID technology timely and intelligent vehi-cle preparing for the next goods handling

(8) The number of iterations 119905 = 119905 + 1 go to step (3)

(2) Belief Space Detailed operation steps in belief space are asfollows

44 Evolutionary Genetic Algorithm For the problem ofrouting optimization coupledwith the a priori knowledge is avery effectivemethod In order to verify this conclusion applythe a priori knowledge into genetic algorithm Also based onthe framework of cultural algorithm genetic populations arethe population space and in the belief space group experienceis updated based on the a priori knowledge The algorithm iscalled evolutionary genetic algorithmThe routing optimiza-tion for intelligent vehicle is mainly involved in the following


No

Yes

Yes

No

Start

Calculate the grids number Ln of route

End

The nodes on route next T + 1 in allowedT

T == Ln

T = T + 1

T = 1

Select one node P delete the pathbetween T and P recalculate Ln

Obtain the allowedT set

Figure 6 Flow chart of abandoning the roundabout

0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

9

10

0

10

20

30

40

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90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

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55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

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90

1

11

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31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

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93

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14

24

34

44

54

64

74

84

94

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15

25

35

45

55

65

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85

95

6

16

26

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46

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66

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86

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17

27

37

47

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67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

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14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

Figure 7 Original route before reducing turns

points (1) initializing the population giving the originalroute set in the feasible region (2) giving appropriate fitnessfunction combined with the actual working environment ofthe intelligent vehicle (3) according to different situationsof population adaptive genetic algorithm selecting appropri-ate crossover and mutation operator and (4) keeping thediversity of the population in the belief space Flow chart ofevolutionary algorithm is shown in Figure 11 Specific steps ofalgorithm are as follows

(1) Population Space

(1) Initializing the genetic algorithm setting the iterationnumber 119879 = 1

0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

9

10

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

Figure 8 Route after reducing turns by parallelogram

(2) Modeling for working environment of intelligentvehicle by grid method obtaining the feasible routeset and set it as the initial population of geneticalgorithm

(3) According to the fitness function to calculate eachindividualrsquos fitness value do the selection operationfor the populationwith roulette selection adopt elitistkept strategy and generate new populations

(4) Do the single point crossover operation on the adja-cent chromosomes to generate new individuals

(5) Do mutation operation on part of individuals withmutation probability to produce new individuals


No

Yes

Yes

No

Start

Calculate the turns number Tu of route

Draw parallelogram with

End Recalculate the turns number Tu

Yes

No(T minus 1 T) parallel (T + 1 T + 2)

T == Tu

T = T + 1

T T + 1 T + 2 as the three vertices SetT998400 as the new vertex

The grids passing by (T T998400)and (T998400

T + 2) are free

(T minus 1 T) and (T + 1 T + 2) substituted by(T T998400) and (T998400

T + 2)

Set turns T = 1

Figure 9 Flow chart of reducing turns by parallelogram



No

Yes

No

Yes

No

Start

End



Update pheromones



Do operation of reducing turns

Do operation of abandoning roundabout

NoYesInfluence()

Accept()

Belief space

one grid

Yes

Population space

Allowedk set is empty



Get m routes from Tabu table

Get m new routes from belief space

T = m

T = T + 1

Initialize belief space set T = 1

Ant k fallback

Figure 10 Flow chart of evolutionary ant colony algorithm

(6) The new population is delivered to the belief space byAccept() function

(7) Receive the new generation of population by Influ-ence() function of belief space

(8) Judging the conditions for termination 119879 lt 119905max ifthe termination condition is satisfied output the bestindividual

(9) 119879 = 119879 + 1 go to step (3)



Yes

No

Start

End

Generate new population

Generate initial population

Optimize the route get the current best

Do selection operation by roulette and save the elite


Optimized population

Initialize belief space individuals

with later ones delete the poor one according to similarity meanwhile add new one

NoYes

Influence()

Accept()

Belief space

Population space

Do crossover and mutation operation

(m individuals)

T = m

T = T + 1

are sorted set T = 1

The Tth individual compares the similarity

Figure 11 Flow chart of evolutionary genetic algorithm

(2) Belief Space The steps in belief space are as follows thepopulation after selection crossover and mutation of popu-lation space is delivered to belief space the individuals withfitness value less than a certain threshold in the populationdo similarity comparison with each other if the similarityis greater than a certain threshold then the individuals withlower fitness value are deleted and randomly generate a newindividual to join the populationsWhen comparison finishesthe new populations return to population space

5 Simulation

51 Simulation Environment and Parameter Settings In orderto study the efficiency of evolutionary ant colony algorithmfor intelligent vehicle searching optimal route a lot ofsimulation experiments are doneThe hardware environmentof simulation Processor Core (TM) i3-2120 CUP 330GHzRAM 6GB 64-bit operating system and hard disk 500GBOperating system is Windows 8 and Matlab 7100 is theprogramming tool Environment map can be changed as theactual environment change Here we select three maps with20lowast20 grids 50lowast50 grids and 100lowast100 grids All parametersare as shown in Table 1 where 119898 represents the numberof ants 120572 and 120573 represent respectively the importance ofthe pheromones and heuristic factor 120588 represents the globalpheromones evaporation coefficient 120591

0represents the initial

value of pheromones and 119876 represents intensity factor ofpheromones

52 Simulation Results The environment mapI is as shownin Figure 12 The start point is S and the destination point

Table 1 Parameters of evolutionary ant colony algorithm

119898 120572 120573 120588 1205910

119876

20 06 08 03 10 100

0 2 4 6 8 10 12 14 16 18 200

2

4

6

8

10

12

14

16

18

20

G

S

Figure 12 Environment map I

is G We make the comparison with four algorithms theevolutionary ant colony algorithm (EAC) the ant colonygenetic algorithm (AC-GA) in [8] the improved ant colonyalgorithm (SA-AC) in [10] and the evolutionary geneticalgorithm (EGA) There are two algorithms (EAC and EGA)based on experiential knowledge The four algorithms allrun 50 times randomly select one result the optimal fitnessconvergence results are as shown in Figure 13 We can see


015

2

25

3

35

4

The b

est fi

tnes

s

5 10 15 20 25Iteration times

30 35 40 45

EACAC-GA

SA-ACEGA

50

Figure 13 Convergence curves about the optimal fitness on map I

026

28

3

32

34

36

38

4

The b

est fi

tnes

s

5 10 15 20 25Running times

30 35 40 45 50

EACAC-GA

SA-ACEGA

Figure 14 Convergence curves about the optimal fitness running50 times on map I

from Figure 13 EAC algorithm has the highest efficiencyand the best convergence Although EGA also can find theoptimal route its convergence speed is slower than EACalgorithm The AC-GA algorithm and the improved SA-ACalgorithm can hardly find the optimal route and have poorerconvergence than the evolutionary algorithms

The comparison of four algorithms on fitness value of50 times is as shown in Figure 14 We can see that the EACalgorithm can find the optimal route every time and theEGA can find the optimal route with high probability TheAC-GA algorithm and the SA-AC algorithm cannot find theoptimal route yet and their fluctuations are relatively largebut they all can find the approximate optimal route We also

0

10

20

30

40

50

Aver

age r

unni

ng ti

me (

s)

EAC AC‐GAAlgorithms

SA‐AC EGA

Figure 15 Comparison of average running time on map I

0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

G

S

Figure 16 The working environment map II

compare the average running time of four algorithms and theresult is as shown in Figure 15 From Figure 15 we can see thatEAC and EGA run faster than AC-GA and SA-AC EGA isthe fastest and AC-GA is the lowest In summary the EACalgorithm is the most effective one

We do a lot of simulation experiments with 30 differentenvironment maps and have the same conclusion Randomlyselect another twomaps as shown in Figure 16 is 50lowast50mapand Figure 17 is 100lowast100mapThe experimental comparisonresults of map II are as shown in Figures 18 19 and 20 andthe comparison results of map III are as shown in Figures21 22 and 23 The experimental results prove that the EACalgorithm has the highest optimal searching efficiency andbest convergence The EGA has the shortest running timeThe more complex the working environment maps are themore superior the EAC is In summary EAC algorithm is afeasible and an effective algorithm for routing optimizationof automated vehicle


0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80

90

100

G

S

Figure 17 The working environment map III

002

04

06

08

1

12

14

16

18

2

The b

est fi

tnes

s


30 35 40 45 50

EACAC-GA

SA-ACEGA

Figure 18 Convergence curves about the optimal fitness on map II

6 Conclusion

Intelligent vehicle is one of themost crucial parts of the wholelogistics automation and production automation in whichthe routing optimization is one key technology In the paperwe study the route searching problem based on evolutionaryant colony algorithmwithRFID technologyWefirst build theenvironment map and give the target goal When searchingthe optimal route in order to overcome the defect of tradi-tional ant colony algorithm such as easy falling into localoptimum and slow convergence based on the experientialknowledge we propose an evolutionary ant colony algorithm

01

11

12

13

14

15

16

17

18

19

The b

est fi

tnes

s

5 10 15 20 25 30Running times

35 40 45 50

EACAC-GA

SA-ACEGA

Figure 19 Convergence curves about the optimal fitness running50 times on map II

Aver

age r

unni

ng ti

me (

s)

0

100

200

300

400


SA‐AC EGA

Figure 20 Comparison of average running time on map II


0 50

02

04

06

08

1

12

14

The b

est fi

tnes

s

10 15 20 25Iteration times

30 35 40 45 50

EACAC-GA

SA-ACEGA

Figure 21 Convergence curves about the optimal fitness onmap III

The b

est fi

tnes

s

0 504

05

06

07

08

09

1

11

12

13

10 15 20 25Running times

30 35 40 45 50

EACAC-GA

SA-ACEGA

Figure 22 Convergence curves about the optimal fitness running50 times on map III

500

1000

1500

Aver

age r

unni

ng ti

me (

s)

0EAC AC‐GA

AlgorithmsSA‐AC EGA

Figure 23 Comparison of average running time on map III

The new algorithm adopts elite ant strategy ant fallbackstrategy and pheromones evaporation coefficient adaptiveadjustment strategy which is proved feasible and effectiveWhen the groups experience is updated the optimizingoperations of abandoning roundabout and reducing turns byparallelogram based on experiential knowledge are done Alot of experimental results show that the new algorithm ispractical and efficient It is also proved that the algorithm hasa high convergence speed and can find the optimal route withhigher probability Due to the fact that the actual working ismore complex how to use the advanced technology to helpthe vehicle obtain more information timely and dynamicallyavoiding obstacles is still worth researching

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research is supported by the Natural Science Founda-tion of Tianjin research Fund no 14JCYBJC15900 TianjinUniversity Innovation Fund Fund no 2014XRG-0100 andHumanities and Social Sciences Project of Shandong Provin-cial Education Department Fund no J13WG19

References

[1] Z-Z Yu J-H Yan J Zhao Z-F Chen and Y-H Zhu ldquoMobilerobot path planning based on improved artificial potential fieldmethodrdquo Journal of Harbin Institute of Technology vol 43 no 1pp 50ndash55 2011

[2] X Sijun and C Qiying ldquoA visibility graph based path planningalgorithm for mobile robotrdquo Computer Application and Soft-ware vol 3 no 28 pp 220ndash236 2011

[3] F Kuang and Y-N Wang ldquoRobot path planning based onhybrid artificial potential fieldgenetic algorithmrdquo Journal ofSystem Simulation vol 18 no 3 pp 774ndash777 2006

[4] A Tuncer and M Yildirim ldquoDynamic path planning of mobilerobots with improved genetic algorithmrdquo Computers and Elec-trical Engineering vol 38 no 6 pp 1564ndash1572 2012

[5] X-F Yang and J-H Fu ldquoMobile robot path planning based ongrid algorithm and CGArdquo Computer Simulation vol 29 no 7pp 223ndash226 2012

[6] R Glasius A Komoda and S C A M Gielen ldquoA biologicallyinspired neural net for trajectory formation and obstacle avoid-ancerdquo Biological Cybernetics vol 74 no 6 pp 511ndash520 1996

[7] W Cai Q Zhu and J Hu ldquoPath planning based on biphasic antcolony algorithm and fuzzy control in dynamic environmentrdquoin Proceedings of the 2nd International Conference on IntelligentHuman-Machine Systems and Cybernetics (IHMSC rsquo10) vol 1pp 333ndash336 August 2010

[8] C L Liu ldquoImproved ant colony genetic optimization algorithmand its applicationrdquo Journal of Computer Applications vol 33no 11 pp 3111ndash3113 2013

[9] T-F Liu and R-Y Cheng ldquoAnt colony algorithm with elitiststrategy and vision detection for mobile robot path planningrdquoComputer Applications vol 1 no 1 pp 92ndash93 2008


[10] Z-P Zhou and L Hua ldquoImproved colony algorithm for pathplanning under complex environmentrdquo Computer Engineeringand Design vol 32 no 5 pp 1773ndash1776 2011

[11] Q Sun The Research on Path Planning of Automated GuidedVehicle System Zhejiang University Hangzhou China 2012

[12] G Wang and Y-J Feng ldquoPicking path plan for carousel basedon ant colony optimization algorithmrdquo Computer Engineeringvol 36 no 3 pp 221ndash223 2010

[13] M R Zeng and H L Zong ldquoRoute optimization of ASRSbased on simulated annealing genetic algorithmrdquo ManufactureAutomation vol 31 no 4 pp 17ndash19 2009

[14] L Pang and J G Lu ldquoOrder picking optimization of automatedwarehouses based on the ant colony generic algorithmrdquo Com-puter Engineering amp Science vol 34 no 3 pp 148ndash151 2012

[15] M Z Liu J Lu M G Ge Z Q Jiang and J Hu ldquoDynamicmaterial handling route planning based on real-time operationconditionsrdquo Journal of Hefei University of Technology vol 31 no12 pp 1948ndash1952 2008

[16] C Chen J Tang and Z G Jin ldquoIndoor path planning forseeing eyes robot based on RFIDrdquo Journal of Jiangsu Universityof Science and Technology vol 27 no 1 pp 60ndash63 2013

[17] X X Guo Intelligent Navigation and Scheduling of Vehicles inWarehouses Based on RFID Zhejiang University HangzhouChina 2011

[18] J-HGu P-P FanQ-Z Song and E-H Liu ldquoImproved cultureant colony optimization method for solving TSP problemrdquoComputer Engineering and Applications vol 46 no 26 pp 49ndash52 2010

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Differential EquationsInternational Journal of

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Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Algebra

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Stochastic AnalysisInternational Journal of


known route searching can be divided into two categories(1) global route searching with environmental informationknown (2) local route searching with environmental infor-mation unknown or partially unknown Global route search-ing is to find the optimal or approximate optimal route tomeet certain performance from the starting point to the targetpoint according to the priori model The key problem is theenvironmentmodel building and the route searching strategyLocal route searching means in the unknown or partiallyunknown environment the intelligent vehicle according tothe sensorrsquos information including the location size andshape information of the obstacle gives a satisfied route withno collision

For path planning problem of mobile robot many schol-ars have had extensive research and also gotten some achieve-ment The traditional robot path planning methods such asartificial potential [1] visibility graph [2] graph searchingand grid decoupling method each have the advantages anddisadvantages With the development of intelligent algo-rithms many scholars introduce them into the field ofrobot path planning The intelligent algorithms improve theperformance of the robot path planning to some extent butthey also have their own defects For example genetic algo-rithm is easy to fall into local optimum and has prematureslower convergence and other issues With the increasingof obstacles or encountering complex terrain especially thecomplexity of the intelligent algorithms will greatly increaseand we even cannot find the optimal solution [3]

Tuncer and Yildirim [4] in order to solve the problemof genetic algorithm of premature and slow convergenceproposed a dynamic path planning of mobile robot based onwith improved genetic algorithm Yang and Fu [5] in orderto improve the searching efficiency of genetic algorithmproposed a new mobile robot path planning algorithmcombined with grid method and chaos genetic algorithmThere are some problems in the neural network system suchas networks large-scale common performance and easy tomake a robot into an infinite loop Glasius et al [6] proposeda neural network model based on Hopfield network withdynamically avoiding obstacles The model can avoid localminimumpoint but it is difficult to adapt to the dynamic andhigh speed environment Ant colony algorithm is easy to fallinto local optimal solution and the U-shaped or V-shapedtrap Cai et al [7] proposed a new method combined withthe ant colony algorithm and fuzzy control technologyAlthough this method can solve the robot path planningproblem it is more complex and difficult In order to improveexecution speed and search efficiency Liu [8] proposed animproved algorithm based on ant colony algorithm andgenetic algorithm Liu and Cheng [9] presented visiondetection colony algorithm with elitist strategy to improvethe efficiency Zhou and Hua [10] presented an improved antcolony algorithm using simulated annealing algorithm toimprove the pheromone evaporation coefficient

About the routing optimization in logistics and ware-house scholars also do a lot ofwork and somedo the researchbased on intelligent algorithms

Sun [11] researched the path planning of automatedguided vehicle system He built the map model with graph

theory in the process of AGV path planning and searchedthe shortest path by Dijkstra algorithm Wang and Feng [12]researched the picking path plan for carousel based on antcolony optimization algorithm They gave a mathematicalmodel for hierarchical leveled carousel system with singlepicking station of automatic stereoscopic warehouse andproposed an improved ant colony optimization (ACO) algo-rithm Zeng and Zong [13] researched routing optimizationof ASRS based on simulated annealing genetic algorithmThe simulated annealing algorithm and genetic algorithm arecombined to solve theASRS Pang and Lu [14] researched thepath picking optimization of automated warehouses basedon the ant colony generic algorithm They gave an initialpopulation by the ant colony algorithm and then solved themodel with the genetic algorithms Liu et al [15] researcheddynamic material handling route planning based on real-time operation conditionsThey considered the complex andchangeable material demand environment of the productionsystem and set up a dynamic material transporting routingoptimization model which considered several demandersand multifarious convey angles References [16 17] intro-duced the RFID technology into the path planning Chenet al [16] researched the indoor path planning for seeingrobot eyes based on RFID Guo [17] researched the intelligentnavigation and scheduling of vehicles in warehouses For therequirements of saving time and energy he used bridgingRFID module to take charge of the navigation functionOptimal route was generated by a combinative strategy oftopological-index and 119860lowast algorithm

This paper will introduce RFID technology into large-scale warehousing center and the use of RFID will make theenvironment map updated automatically and timely so therouting optimization problem from starting point to targetshelf will be solved more effectively In the process of routesearching for the ant colony algorithm easy to fall into localoptimum and hard to jumpout theU-type orV-type trap thepaper proposes an evolutionary ant colony algorithm basedon the prior knowledge to effectively find the optimal route

The rest of this paper is organized as follows Our workenvironment model is formulated in Section 2 In Section 3we provide the goal of routing optimization problem andpresent the definitions of ant colony algorithmrsquos parametersThe detailed steps and flow charts are given in Section 3 InSection 4 the simulation results and analysis of four differentalgorithms are provided Finally we conclude our paper inSection 5

2 Modeling the Working Environment forIntelligent Vehicle

Modeling the working environment is the first step for thepath optimization A reasonable description of the workingenvironment can decrease the searching steps in the processof searching the optimal path and reduce the complexity ontime and space In this section we will model the workingenvironment which is mainly the presentations of obstaclesdestination and action space Shelves and goods in large-scale storage center may not only be the action destination








119860 = (119909 119910) | 119909 isin [0 119909max] 119910 isin [0 119910max] (1)





119910 In



119860119889= (119894 119895) 119894 119895 = 0 1 2 119873

119909 (2)


be denoted by

119860119889= (119909

119896 119910119896) | 119909119896= fix( 119896

119873119909

) + 1 119910119896= 119896 mod 119873

119909+ 1

119896 = 0 1 1198732

119909minus 1

(3)

0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

9

10

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99











119894(119909119894 119910119894) and 119901

119894+1(119909119894+1 119910119894+1)

is given as follows

119889 = radic(119909119894+1minus 119909119894)2

+ (119910119894+1minus 119910119894)2

(4)


1199011198941

(1199091198941

1199101198941


(119909119894119896

119910119894119896


(119909119894119871

119910119894119871

)

1198941= 1 119894

119871= 119899

(5)


119863 (119871) =

119871minus1

sum119896=1

radic(119909119894119896+1

minus 119909119894119896

)2

+ (119910119894119896+1

minus 119910119894119896

)2

(6)




1198651 = (1 +1


119889+ curve times 119908

119888 (7)


119889


119889+ 119908119888= 1


119865 =100


119888

(8)


max 119866 (119871) 119871 = 1 2 119868

st

119866 (119871) = max119875

119865

st

(120579119909119894119896

+ (1 minus 120579) 119909119894119896+1

120579119910119894119896

+ (1 minus 120579) 119910119894119896+1

) notin 119860119874

for any 120579 isin [0 1] 119894119896 119894119896+1isin 119878119886

119901 = (1199011 1199012 119901

119898) 119901119896= (119909119894119896

119910119894119896

)

(1199091198941

1199101198941

) = (1199091 1199101)

(119909119894119871

119910119894119871

) = (119909119889 119910119889)

(9)







119896records


119896




(119894 119895) at time 119905



120578119894119895=1

119889119894119895

(10)




119875119896

119894119895=

[120591119894119895(119905)]120572

[120578119894119895(119905)]120573


119896

[120591119894119895(119905)]120572

[120578119894119895(119905)]120573


0 else

(11)





Δ120591119894119895(119905) =

119898

sum119896=1

Δ120591119894119895(119905) (12)



Δ120591119896

119894119895(119905) =

119876

119871119896

ant 119896 pass edge (119894 119895)

0 others(13)


119896



120591119894119895(119905 + Δ119905) = (1 minus 120588) 120591

119894119895(119905) + Δ120591

119894119895(119905) (14)











0119889 (1205910is a






formula (11)



(15)







119896 If now the










No

Yes

Yes

No

Yes

No

Start

End



Update pheromones







Adjustbelief space



Copy andmodify

Performancefunction



0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

9

10

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99





0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

9

10

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99




















No

Yes

Yes

No

Start


End


T == Ln

T = T + 1

T = 1




0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

9

10

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99





0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

9

10

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99







No

Yes

Yes

No

Start




Yes


T == Tu

T = T + 1



T + 2) are free


T + 2)

Set turns T = 1




No

Yes

No

Yes

No

Start

End



Update pheromones





NoYesInfluence()

Accept()

Belief space

one grid

Yes

Population space






T = m

T = T + 1


Ant k fallback





(9) 119879 = 119879 + 1 go to step (3)



Yes

No

Start

End









NoYes

Influence()

Accept()

Belief space

Population space


(m individuals)

T = m

T = T + 1





5 Simulation






119898 120572 120573 120588 1205910

119876

20 06 08 03 10 100

0 2 4 6 8 10 12 14 16 18 200

2

4

6

8

10

12

14

16

18

20

G

S




015

2

25

3

35

4

The b

est fi

tnes

s


30 35 40 45

EACAC-GA

SA-ACEGA

50


026

28

3

32

34

36

38

4

The b

est fi

tnes

s


30 35 40 45 50

EACAC-GA

SA-ACEGA




0

10

20

30

40

50

Aver

age r

unni

ng ti

me (

s)


SA‐AC EGA


0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

G

S





0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80

90

100

G

S


002

04

06

08

1

12

14

16

18

2

The b

est fi

tnes

s


30 35 40 45 50

EACAC-GA

SA-ACEGA


6 Conclusion


01

11

12

13

14

15

16

17

18

19

The b

est fi

tnes

s


35 40 45 50

EACAC-GA

SA-ACEGA


Aver

age r

unni

ng ti

me (

s)

0

100

200

300

400


SA‐AC EGA



0 50

02

04

06

08

1

12

14

The b

est fi

tnes

s


30 35 40 45 50

EACAC-GA

SA-ACEGA


The b

est fi

tnes

s

0 504

05

06

07

08

09

1

11

12

13


30 35 40 45 50

EACAC-GA

SA-ACEGA


500

1000

1500

Aver

age r

unni

ng ti

me (

s)

0EAC AC‐GA






Acknowledgments


References



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















119860 = (119909 119910) | 119909 isin [0 119909max] 119910 isin [0 119910max] (1)





119910 In



119860119889= (119894 119895) 119894 119895 = 0 1 2 119873

119909 (2)


be denoted by

119860119889= (119909

119896 119910119896) | 119909119896= fix( 119896

119873119909

) + 1 119910119896= 119896 mod 119873

119909+ 1

119896 = 0 1 1198732

119909minus 1

(3)

0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

9

10

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99











119894(119909119894 119910119894) and 119901

119894+1(119909119894+1 119910119894+1)

is given as follows

119889 = radic(119909119894+1minus 119909119894)2

+ (119910119894+1minus 119910119894)2

(4)


1199011198941

(1199091198941

1199101198941


(119909119894119896

119910119894119896


(119909119894119871

119910119894119871

)

1198941= 1 119894

119871= 119899

(5)


119863 (119871) =

119871minus1

sum119896=1

radic(119909119894119896+1

minus 119909119894119896

)2

+ (119910119894119896+1

minus 119910119894119896

)2

(6)




1198651 = (1 +1


119889+ curve times 119908

119888 (7)


119889


119889+ 119908119888= 1


119865 =100


119888

(8)


max 119866 (119871) 119871 = 1 2 119868

st

119866 (119871) = max119875

119865

st

(120579119909119894119896

+ (1 minus 120579) 119909119894119896+1

120579119910119894119896

+ (1 minus 120579) 119910119894119896+1

) notin 119860119874

for any 120579 isin [0 1] 119894119896 119894119896+1isin 119878119886

119901 = (1199011 1199012 119901

119898) 119901119896= (119909119894119896

119910119894119896

)

(1199091198941

1199101198941

) = (1199091 1199101)

(119909119894119871

119910119894119871

) = (119909119889 119910119889)

(9)







119896records


119896




(119894 119895) at time 119905



120578119894119895=1

119889119894119895

(10)




119875119896

119894119895=

[120591119894119895(119905)]120572

[120578119894119895(119905)]120573


119896

[120591119894119895(119905)]120572

[120578119894119895(119905)]120573


0 else

(11)





Δ120591119894119895(119905) =

119898

sum119896=1

Δ120591119894119895(119905) (12)



Δ120591119896

119894119895(119905) =

119876

119871119896

ant 119896 pass edge (119894 119895)

0 others(13)


119896



120591119894119895(119905 + Δ119905) = (1 minus 120588) 120591

119894119895(119905) + Δ120591

119894119895(119905) (14)











0119889 (1205910is a






formula (11)



(15)







119896 If now the










No

Yes

Yes

No

Yes

No

Start

End



Update pheromones







Adjustbelief space



Copy andmodify

Performancefunction



0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

9

10

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99





0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

9

10

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99




















No

Yes

Yes

No

Start


End


T == Ln

T = T + 1

T = 1




0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

9

10

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99





0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

9

10

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99







No

Yes

Yes

No

Start




Yes


T == Tu

T = T + 1



T + 2) are free


T + 2)

Set turns T = 1




No

Yes

No

Yes

No

Start

End



Update pheromones





NoYesInfluence()

Accept()

Belief space

one grid

Yes

Population space






T = m

T = T + 1


Ant k fallback





(9) 119879 = 119879 + 1 go to step (3)



Yes

No

Start

End









NoYes

Influence()

Accept()

Belief space

Population space


(m individuals)

T = m

T = T + 1





5 Simulation






119898 120572 120573 120588 1205910

119876

20 06 08 03 10 100

0 2 4 6 8 10 12 14 16 18 200

2

4

6

8

10

12

14

16

18

20

G

S




015

2

25

3

35

4

The b

est fi

tnes

s


30 35 40 45

EACAC-GA

SA-ACEGA

50


026

28

3

32

34

36

38

4

The b

est fi

tnes

s


30 35 40 45 50

EACAC-GA

SA-ACEGA




0

10

20

30

40

50

Aver

age r

unni

ng ti

me (

s)


SA‐AC EGA


0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

G

S





0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80

90

100

G

S


002

04

06

08

1

12

14

16

18

2

The b

est fi

tnes

s


30 35 40 45 50

EACAC-GA

SA-ACEGA


6 Conclusion


01

11

12

13

14

15

16

17

18

19

The b

est fi

tnes

s


35 40 45 50

EACAC-GA

SA-ACEGA


Aver

age r

unni

ng ti

me (

s)

0

100

200

300

400


SA‐AC EGA



0 50

02

04

06

08

1

12

14

The b

est fi

tnes

s


30 35 40 45 50

EACAC-GA

SA-ACEGA


The b

est fi

tnes

s

0 504

05

06

07

08

09

1

11

12

13


30 35 40 45 50

EACAC-GA

SA-ACEGA


500

1000

1500

Aver

age r

unni

ng ti

me (

s)

0EAC AC‐GA






Acknowledgments


References



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra











1198651 = (1 +1


119889+ curve times 119908

119888 (7)


119889


119889+ 119908119888= 1


119865 =100


119888

(8)


max 119866 (119871) 119871 = 1 2 119868

st

119866 (119871) = max119875

119865

st

(120579119909119894119896

+ (1 minus 120579) 119909119894119896+1

120579119910119894119896

+ (1 minus 120579) 119910119894119896+1

) notin 119860119874

for any 120579 isin [0 1] 119894119896 119894119896+1isin 119878119886

119901 = (1199011 1199012 119901

119898) 119901119896= (119909119894119896

119910119894119896

)

(1199091198941

1199101198941

) = (1199091 1199101)

(119909119894119871

119910119894119871

) = (119909119889 119910119889)

(9)







119896records


119896




(119894 119895) at time 119905



120578119894119895=1

119889119894119895

(10)




119875119896

119894119895=

[120591119894119895(119905)]120572

[120578119894119895(119905)]120573


119896

[120591119894119895(119905)]120572

[120578119894119895(119905)]120573


0 else

(11)





Δ120591119894119895(119905) =

119898

sum119896=1

Δ120591119894119895(119905) (12)



Δ120591119896

119894119895(119905) =

119876

119871119896

ant 119896 pass edge (119894 119895)

0 others(13)


119896



120591119894119895(119905 + Δ119905) = (1 minus 120588) 120591

119894119895(119905) + Δ120591

119894119895(119905) (14)











0119889 (1205910is a






formula (11)



(15)







119896 If now the










No

Yes

Yes

No

Yes

No

Start

End



Update pheromones







Adjustbelief space



Copy andmodify

Performancefunction



0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

9

10

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99





0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

9

10

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99




















No

Yes

Yes

No

Start


End


T == Ln

T = T + 1

T = 1




0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

9

10

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99





0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

9

10

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99







No

Yes

Yes

No

Start




Yes


T == Tu

T = T + 1



T + 2) are free


T + 2)

Set turns T = 1




No

Yes

No

Yes

No

Start

End



Update pheromones





NoYesInfluence()

Accept()

Belief space

one grid

Yes

Population space






T = m

T = T + 1


Ant k fallback





(9) 119879 = 119879 + 1 go to step (3)



Yes

No

Start

End









NoYes

Influence()

Accept()

Belief space

Population space


(m individuals)

T = m

T = T + 1





5 Simulation






119898 120572 120573 120588 1205910

119876

20 06 08 03 10 100

0 2 4 6 8 10 12 14 16 18 200

2

4

6

8

10

12

14

16

18

20

G

S




015

2

25

3

35

4

The b

est fi

tnes

s


30 35 40 45

EACAC-GA

SA-ACEGA

50


026

28

3

32

34

36

38

4

The b

est fi

tnes

s


30 35 40 45 50

EACAC-GA

SA-ACEGA




0

10

20

30

40

50

Aver

age r

unni

ng ti

me (

s)


SA‐AC EGA


0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

G

S





0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80

90

100

G

S


002

04

06

08

1

12

14

16

18

2

The b

est fi

tnes

s


30 35 40 45 50

EACAC-GA

SA-ACEGA


6 Conclusion


01

11

12

13

14

15

16

17

18

19

The b

est fi

tnes

s


35 40 45 50

EACAC-GA

SA-ACEGA


Aver

age r

unni

ng ti

me (

s)

0

100

200

300

400


SA‐AC EGA



0 50

02

04

06

08

1

12

14

The b

est fi

tnes

s


30 35 40 45 50

EACAC-GA

SA-ACEGA


The b

est fi

tnes

s

0 504

05

06

07

08

09

1

11

12

13


30 35 40 45 50

EACAC-GA

SA-ACEGA


500

1000

1500

Aver

age r

unni

ng ti

me (

s)

0EAC AC‐GA






Acknowledgments


References



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra

















0119889 (1205910is a






formula (11)



(15)







119896 If now the










No

Yes

Yes

No

Yes

No

Start

End



Update pheromones







Adjustbelief space



Copy andmodify

Performancefunction



0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

9

10

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99





0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

9

10

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99




















No

Yes

Yes

No

Start


End


T == Ln

T = T + 1

T = 1




0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

9

10

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99





0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

9

10

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99







No

Yes

Yes

No

Start




Yes


T == Tu

T = T + 1



T + 2) are free


T + 2)

Set turns T = 1




No

Yes

No

Yes

No

Start

End



Update pheromones





NoYesInfluence()

Accept()

Belief space

one grid

Yes

Population space






T = m

T = T + 1


Ant k fallback





(9) 119879 = 119879 + 1 go to step (3)



Yes

No

Start

End









NoYes

Influence()

Accept()

Belief space

Population space


(m individuals)

T = m

T = T + 1





5 Simulation






119898 120572 120573 120588 1205910

119876

20 06 08 03 10 100

0 2 4 6 8 10 12 14 16 18 200

2

4

6

8

10

12

14

16

18

20

G

S




015

2

25

3

35

4

The b

est fi

tnes

s


30 35 40 45

EACAC-GA

SA-ACEGA

50


026

28

3

32

34

36

38

4

The b

est fi

tnes

s


30 35 40 45 50

EACAC-GA

SA-ACEGA




0

10

20

30

40

50

Aver

age r

unni

ng ti

me (

s)


SA‐AC EGA


0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

G

S





0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80

90

100

G

S


002

04

06

08

1

12

14

16

18

2

The b

est fi

tnes

s


30 35 40 45 50

EACAC-GA

SA-ACEGA


6 Conclusion


01

11

12

13

14

15

16

17

18

19

The b

est fi

tnes

s


35 40 45 50

EACAC-GA

SA-ACEGA


Aver

age r

unni

ng ti

me (

s)

0

100

200

300

400


SA‐AC EGA



0 50

02

04

06

08

1

12

14

The b

est fi

tnes

s


30 35 40 45 50

EACAC-GA

SA-ACEGA


The b

est fi

tnes

s

0 504

05

06

07

08

09

1

11

12

13


30 35 40 45 50

EACAC-GA

SA-ACEGA


500

1000

1500

Aver

age r

unni

ng ti

me (

s)

0EAC AC‐GA






Acknowledgments


References



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra












No

Yes

Yes

No

Yes

No

Start

End



Update pheromones







Adjustbelief space



Copy andmodify

Performancefunction



0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

9

10

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99





0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

9

10

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99




















No

Yes

Yes

No

Start


End


T == Ln

T = T + 1

T = 1




0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

9

10

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99





0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

9

10

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99







No

Yes

Yes

No

Start




Yes


T == Tu

T = T + 1



T + 2) are free


T + 2)

Set turns T = 1




No

Yes

No

Yes

No

Start

End



Update pheromones





NoYesInfluence()

Accept()

Belief space

one grid

Yes

Population space






T = m

T = T + 1


Ant k fallback





(9) 119879 = 119879 + 1 go to step (3)



Yes

No

Start

End









NoYes

Influence()

Accept()

Belief space

Population space


(m individuals)

T = m

T = T + 1





5 Simulation






119898 120572 120573 120588 1205910

119876

20 06 08 03 10 100

0 2 4 6 8 10 12 14 16 18 200

2

4

6

8

10

12

14

16

18

20

G

S




015

2

25

3

35

4

The b

est fi

tnes

s


30 35 40 45

EACAC-GA

SA-ACEGA

50


026

28

3

32

34

36

38

4

The b

est fi

tnes

s


30 35 40 45 50

EACAC-GA

SA-ACEGA




0

10

20

30

40

50

Aver

age r

unni

ng ti

me (

s)


SA‐AC EGA


0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

G

S





0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80

90

100

G

S


002

04

06

08

1

12

14

16

18

2

The b

est fi

tnes

s


30 35 40 45 50

EACAC-GA

SA-ACEGA


6 Conclusion


01

11

12

13

14

15

16

17

18

19

The b

est fi

tnes

s


35 40 45 50

EACAC-GA

SA-ACEGA


Aver

age r

unni

ng ti

me (

s)

0

100

200

300

400


SA‐AC EGA



0 50

02

04

06

08

1

12

14

The b

est fi

tnes

s


30 35 40 45 50

EACAC-GA

SA-ACEGA


The b

est fi

tnes

s

0 504

05

06

07

08

09

1

11

12

13


30 35 40 45 50

EACAC-GA

SA-ACEGA


500

1000

1500

Aver

age r

unni

ng ti

me (

s)

0EAC AC‐GA






Acknowledgments


References



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

9

10

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99




















No

Yes

Yes

No

Start


End


T == Ln

T = T + 1

T = 1




0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

9

10

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99





0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

9

10

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99







No

Yes

Yes

No

Start




Yes


T == Tu

T = T + 1



T + 2) are free


T + 2)

Set turns T = 1




No

Yes

No

Yes

No

Start

End



Update pheromones





NoYesInfluence()

Accept()

Belief space

one grid

Yes

Population space






T = m

T = T + 1


Ant k fallback





(9) 119879 = 119879 + 1 go to step (3)



Yes

No

Start

End









NoYes

Influence()

Accept()

Belief space

Population space


(m individuals)

T = m

T = T + 1





5 Simulation






119898 120572 120573 120588 1205910

119876

20 06 08 03 10 100

0 2 4 6 8 10 12 14 16 18 200

2

4

6

8

10

12

14

16

18

20

G

S




015

2

25

3

35

4

The b

est fi

tnes

s


30 35 40 45

EACAC-GA

SA-ACEGA

50


026

28

3

32

34

36

38

4

The b

est fi

tnes

s


30 35 40 45 50

EACAC-GA

SA-ACEGA




0

10

20

30

40

50

Aver

age r

unni

ng ti

me (

s)


SA‐AC EGA


0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

G

S





0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80

90

100

G

S


002

04

06

08

1

12

14

16

18

2

The b

est fi

tnes

s


30 35 40 45 50

EACAC-GA

SA-ACEGA


6 Conclusion


01

11

12

13

14

15

16

17

18

19

The b

est fi

tnes

s


35 40 45 50

EACAC-GA

SA-ACEGA


Aver

age r

unni

ng ti

me (

s)

0

100

200

300

400


SA‐AC EGA



0 50

02

04

06

08

1

12

14

The b

est fi

tnes

s


30 35 40 45 50

EACAC-GA

SA-ACEGA


The b

est fi

tnes

s

0 504

05

06

07

08

09

1

11

12

13


30 35 40 45 50

EACAC-GA

SA-ACEGA


500

1000

1500

Aver

age r

unni

ng ti

me (

s)

0EAC AC‐GA






Acknowledgments


References



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










No

Yes

Yes

No

Start


End


T == Ln

T = T + 1

T = 1




0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

9

10

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99





0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

9

10

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

0

10

20

30

40

50

60

70

80

90

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99







No

Yes

Yes

No

Start




Yes


T == Tu

T = T + 1



T + 2) are free


T + 2)

Set turns T = 1




No

Yes

No

Yes

No

Start

End



Update pheromones





NoYesInfluence()

Accept()

Belief space

one grid

Yes

Population space






T = m

T = T + 1


Ant k fallback





(9) 119879 = 119879 + 1 go to step (3)



Yes

No

Start

End









NoYes

Influence()

Accept()

Belief space

Population space


(m individuals)

T = m

T = T + 1





5 Simulation






119898 120572 120573 120588 1205910

119876

20 06 08 03 10 100

0 2 4 6 8 10 12 14 16 18 200

2

4

6

8

10

12

14

16

18

20

G

S




015

2

25

3

35

4

The b

est fi

tnes

s


30 35 40 45

EACAC-GA

SA-ACEGA

50


026

28

3

32

34

36

38

4

The b

est fi

tnes

s


30 35 40 45 50

EACAC-GA

SA-ACEGA




0

10

20

30

40

50

Aver

age r

unni

ng ti

me (

s)


SA‐AC EGA


0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

G

S





0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80

90

100

G

S


002

04

06

08

1

12

14

16

18

2

The b

est fi

tnes

s


30 35 40 45 50

EACAC-GA

SA-ACEGA


6 Conclusion


01

11

12

13

14

15

16

17

18

19

The b

est fi

tnes

s


35 40 45 50

EACAC-GA

SA-ACEGA


Aver

age r

unni

ng ti

me (

s)

0

100

200

300

400


SA‐AC EGA



0 50

02

04

06

08

1

12

14

The b

est fi

tnes

s


30 35 40 45 50

EACAC-GA

SA-ACEGA


The b

est fi

tnes

s

0 504

05

06

07

08

09

1

11

12

13


30 35 40 45 50

EACAC-GA

SA-ACEGA


500

1000

1500

Aver

age r

unni

ng ti

me (

s)

0EAC AC‐GA






Acknowledgments


References



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










No

Yes

Yes

No

Start




Yes


T == Tu

T = T + 1



T + 2) are free


T + 2)

Set turns T = 1




No

Yes

No

Yes

No

Start

End



Update pheromones





NoYesInfluence()

Accept()

Belief space

one grid

Yes

Population space






T = m

T = T + 1


Ant k fallback





(9) 119879 = 119879 + 1 go to step (3)



Yes

No

Start

End









NoYes

Influence()

Accept()

Belief space

Population space


(m individuals)

T = m

T = T + 1





5 Simulation






119898 120572 120573 120588 1205910

119876

20 06 08 03 10 100

0 2 4 6 8 10 12 14 16 18 200

2

4

6

8

10

12

14

16

18

20

G

S




015

2

25

3

35

4

The b

est fi

tnes

s


30 35 40 45

EACAC-GA

SA-ACEGA

50


026

28

3

32

34

36

38

4

The b

est fi

tnes

s


30 35 40 45 50

EACAC-GA

SA-ACEGA




0

10

20

30

40

50

Aver

age r

unni

ng ti

me (

s)


SA‐AC EGA


0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

G

S





0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80

90

100

G

S


002

04

06

08

1

12

14

16

18

2

The b

est fi

tnes

s


30 35 40 45 50

EACAC-GA

SA-ACEGA


6 Conclusion


01

11

12

13

14

15

16

17

18

19

The b

est fi

tnes

s


35 40 45 50

EACAC-GA

SA-ACEGA


Aver

age r

unni

ng ti

me (

s)

0

100

200

300

400


SA‐AC EGA



0 50

02

04

06

08

1

12

14

The b

est fi

tnes

s


30 35 40 45 50

EACAC-GA

SA-ACEGA


The b

est fi

tnes

s

0 504

05

06

07

08

09

1

11

12

13


30 35 40 45 50

EACAC-GA

SA-ACEGA


500

1000

1500

Aver

age r

unni

ng ti

me (

s)

0EAC AC‐GA






Acknowledgments


References



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra











Yes

No

Start

End









NoYes

Influence()

Accept()

Belief space

Population space


(m individuals)

T = m

T = T + 1





5 Simulation






119898 120572 120573 120588 1205910

119876

20 06 08 03 10 100

0 2 4 6 8 10 12 14 16 18 200

2

4

6

8

10

12

14

16

18

20

G

S




015

2

25

3

35

4

The b

est fi

tnes

s


30 35 40 45

EACAC-GA

SA-ACEGA

50


026

28

3

32

34

36

38

4

The b

est fi

tnes

s


30 35 40 45 50

EACAC-GA

SA-ACEGA




0

10

20

30

40

50

Aver

age r

unni

ng ti

me (

s)


SA‐AC EGA


0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

G

S





0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80

90

100

G

S


002

04

06

08

1

12

14

16

18

2

The b

est fi

tnes

s


30 35 40 45 50

EACAC-GA

SA-ACEGA


6 Conclusion


01

11

12

13

14

15

16

17

18

19

The b

est fi

tnes

s


35 40 45 50

EACAC-GA

SA-ACEGA


Aver

age r

unni

ng ti

me (

s)

0

100

200

300

400


SA‐AC EGA



0 50

02

04

06

08

1

12

14

The b

est fi

tnes

s


30 35 40 45 50

EACAC-GA

SA-ACEGA


The b

est fi

tnes

s

0 504

05

06

07

08

09

1

11

12

13


30 35 40 45 50

EACAC-GA

SA-ACEGA


500

1000

1500

Aver

age r

unni

ng ti

me (

s)

0EAC AC‐GA






Acknowledgments


References



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










015

2

25

3

35

4

The b

est fi

tnes

s


30 35 40 45

EACAC-GA

SA-ACEGA

50


026

28

3

32

34

36

38

4

The b

est fi

tnes

s


30 35 40 45 50

EACAC-GA

SA-ACEGA




0

10

20

30

40

50

Aver

age r

unni

ng ti

me (

s)


SA‐AC EGA


0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

G

S





0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80

90

100

G

S


002

04

06

08

1

12

14

16

18

2

The b

est fi

tnes

s


30 35 40 45 50

EACAC-GA

SA-ACEGA


6 Conclusion


01

11

12

13

14

15

16

17

18

19

The b

est fi

tnes

s


35 40 45 50

EACAC-GA

SA-ACEGA


Aver

age r

unni

ng ti

me (

s)

0

100

200

300

400


SA‐AC EGA



0 50

02

04

06

08

1

12

14

The b

est fi

tnes

s


30 35 40 45 50

EACAC-GA

SA-ACEGA


The b

est fi

tnes

s

0 504

05

06

07

08

09

1

11

12

13


30 35 40 45 50

EACAC-GA

SA-ACEGA


500

1000

1500

Aver

age r

unni

ng ti

me (

s)

0EAC AC‐GA






Acknowledgments


References



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80

90

100

G

S


002

04

06

08

1

12

14

16

18

2

The b

est fi

tnes

s


30 35 40 45 50

EACAC-GA

SA-ACEGA


6 Conclusion


01

11

12

13

14

15

16

17

18

19

The b

est fi

tnes

s


35 40 45 50

EACAC-GA

SA-ACEGA


Aver

age r

unni

ng ti

me (

s)

0

100

200

300

400


SA‐AC EGA



0 50

02

04

06

08

1

12

14

The b

est fi

tnes

s


30 35 40 45 50

EACAC-GA

SA-ACEGA


The b

est fi

tnes

s

0 504

05

06

07

08

09

1

11

12

13


30 35 40 45 50

EACAC-GA

SA-ACEGA


500

1000

1500

Aver

age r

unni

ng ti

me (

s)

0EAC AC‐GA






Acknowledgments


References



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0 50

02

04

06

08

1

12

14

The b

est fi

tnes

s


30 35 40 45 50

EACAC-GA

SA-ACEGA


The b

est fi

tnes

s

0 504

05

06

07

08

09

1

11

12

13


30 35 40 45 50

EACAC-GA

SA-ACEGA


500

1000

1500

Aver

age r

unni

ng ti

me (

s)

0EAC AC‐GA






Acknowledgments


References



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra


























Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









Documents

Research Article Routing Optimization of Intelligent Vehicle in …downloads.hindawi.com/journals/ddns/2014/789754.pdf · 2019-07-31 · colony optimization algorithm. ey gave a mathematical