AHyperheuristicApproachforLocation-RoutingProblemof ...2019/08/26 · 0 +CV)+b, respec-tively. us, FCR per unit distance is ρ˜ ˚M 1 ˜ 0 + ρ ∗ − ˜˚ 0 × M 1 CV. (7) erefore,

Research ArticleA Hyperheuristic Approach for Location-Routing Problem ofCold Chain Logistics considering Fuel Consumption

Zheng Wang1 Longlong Leng 2 Shun Wang2 Gongfa Li 3 and Yanwei Zhao 2

1School of Computer Science and Technology Zhejiang University of Technology Hangzhou 310023 China2Key Laboratory of Special Equipment Manufacturing and Advanced Processing Technology Ministry of EducationZhejiang University of Technology Hangzhou 310023 China3Key Laboratory of Metallurgical Equipment and Control Technology Ministry of EducationWuhan University of Science and Technology Wuhan 430081 China

Correspondence should be addressed to Yanwei Zhao ywzzjuteducn

Received 26 August 2019 Revised 18 November 2019 Accepted 21 November 2019 Published 4 January 2020

Academic Editor Rodolfo E Haber

Copyright copy 2020 Zheng Wang et al is 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

In response to violent market competition and demand for low-carbon economy cold chain logistics companies have to payattention to customer satisfaction and carbon emission for better development In this paper a biobjective mathematical model isestablished for cold chain logistics network in consideration of economic social and environmental benefits in other words thetotal cost and distribution period of cold chain logistics are optimized while the total cost consists of cargo damage costrefrigeration cost of refrigeration equipment transportation cost fuel consumption cost penalty cost of time window andoperation cost of distribution centres One multiobjective hyperheuristic optimization framework is proposed to address thismultiobjective problem In the framework four selection strategies and four acceptance criteria for solution set are proposed toimprove the performance of the multiobjective hyperheuristic framework As known from a comparative study the proposedalgorithm had better overall performance than NSGA-II Furthermore instances of cold chain logistics are modelled and solvedand the resulting Pareto solution set offers diverse options for a decision maker to select an appropriate cold chain logisticsdistribution network in the interest of the logistics company

1 Introduction

Cold chain logistics are developing rapidly with constantimprovement of living standard of the people and increasingdemand for fresh food [1] In order to lower distribution costof cold chain logistics effectively some researchers began tostudy optimization of cold chain logistics distribution net-work [2] However when optimizing cold chain logisticsdistribution network one has to consider economic benefitof logistics distribution distribution-derived carbon emis-sion and other environmental benefits and timeliness of thelogistics network

In a practical cold chain logistics network more than oneobjective may be considered in the system including theminimum total cost the smallest number of vehicles themaximum customer satisfaction the shortest travel pathand the least distribution time Numerous researchers have

studied multiobjective logistics optimization problem Withthe shortest travel path and carbon dioxide emission asoptimization objectives Jemai et al [3] established a vehiclerouting problem (VRP) based on green logistics and solved itby NSGA-II optimization Based on optimization objectivefunctions of the minimum cost and the maximum customersatisfaction Liu et al [4] developed a mathematical modelfor multiobjective location-routing problem (LRP) Molinaet al [5] developed a heterogeneous fleet VRP model withthe minimized cost and emission as objectives Golmo-hammadi et al [6] proposed a mathematical model formultiobjective LRPs with the minimum storage distributioncost and difference in vehicle-traveled distance as optimi-zation objective functions e above literatures are relatedto multiobjective logistics distribution network but multipleperformance metrics of logistics network are not taken intoaccount economic benefit environmental benefit and

HindawiComputational Intelligence and NeuroscienceVolume 2020 Article ID 8395754 17 pageshttpsdoiorg10115520208395754

timeliness Moreover there are a dearth of literatures onLRP-based models for cold chain logistics Wang et al [1]proposed developing a single-objective model in consider-ation of carbon emission for cold chain logistics and solvingit using hybrid genetic algorithm However logistics net-work timeliness has not yet been considered

Hence in this paper properties of cold chain logistics areconsidered from the perspective of LRP-based model notonly economic and environmental benefits but also distri-bution timeliness are taken into account thereby a bio-bjective LRP of cold chain logistics considering fuelconsumption and distribution period is proposed and onemultiobjective hyperheuristic (MOHH) is proposed tomodel and solve this problem erefore main contribu-tions of this paper are described as follows

(i) Problem model with logistics cost and distributionperiod as objective functions a multiobjectivemathematical model for cold chain logistics is de-veloped considering environmental benefit arisingfrom fuel consumption and social benefits likecustomer satisfaction arising from customer timewindow

(ii) Solution algorithm for the above model MOHH isdesigned Based on the framework nature ofhyperheuristics four selection strategies for low-level heuristics (LLHs) and four solution acceptancecriteria are proposed

(iii) Management suggestions and comments based onexperimental results several insights and sugges-tions about logistics distribution are provided frommanagement perspective

2 Methodology

21 Multiobjective Optimization Problem (MOP) One typ-ical MOP normally contains more than 2 conflicting orcontradictory objectives and is also called multicriteriaoptimization problem [7] Without loss of generality oneminimized MOP having D-dimensional decision variablesand m-dimensional subobjectives can be expressed as

minXisinΩ

F(X) f1(X) f2(X) fm(X)( 1113857T

stgi(X) le 0 i 1 2 q

hi(X) 0 i 1 2 p1113896

(1)

where X (x1 x2 x D) isin RD is a D-dimensional de-cision vector and F(X) isin Rm is an m-dimensional objectivevector defining m mapping functions of decision spacetowards objective space RD and Rm are decision space andobjective space respectively gi(X)le 0(i 1 2 q) are qinequality constraints and hi(X) 0 (i 1 2 p) are pequality constraints

On this basis the following related definitions are given [7]

Definition 1 (feasible solution) For one X isinRD if twoclasses of constraints in equation (1) are satisfied then X willbe deemed as a feasible solution

Definition 2 (feasible solution set) A set of all feasible so-lutions is referred to as feasible solution set that is Xf

Definition 3 (Pareto dominant) Suppose thatXA andXB aretwo feasible solutions in the feasible solution set When andonly when the following constraints are satisfied

foralli 1 2 m fi XA( 1113857lefi XB( 1113857

existj 1 2 m fj XA( 1113857ltfj XB( 1113857

⎧⎨

⎩ (2)

where XA dominate XB in other words compared with XBXA is a Pareto dominant which can be expressed asXB≻XA

Definition 4 (Pareto optimal solution) One solutionXlowast isin Xf is referred to as Pareto optimal solution (ornondominated solution) when and only when the followingcondition is satisfied

existX isin Xf X≻Xlowast (3)

Definition 5 (Pareto optimal solution set) As a set of allPareto optimal solutions Pareto optimal solution set isdefined as follows

Plowast ≜ Xlowast |existX isin Xf X≻Xlowast1113966 1113967 (4)

Definition 6 (Pareto front) A curved surface composed ofobjective function values corresponding to all Pareto opti-mal solutions in Pareto optimal solution set Plowast is calledPareto front and denoted as PFlowast

PFlowast ≜ F Xlowast( 1113857 f1 Xlowast( 1113857 f2 Xlowast( 1113857 fm X

lowast( 1113857( 1113857

T|Xlowast isin P

lowast1113966 1113967

(5)

22 Hyperheuristics Metaheuristics (eg grey wolf opti-mization algorithm [8] nature-inspired optimization algo-rithm [9 10] and quantum-behaved particle swarmoptimization [11]) have been widely applied in optimizationproblems However to find solutions of bespoke nature in anew problem-based domain it takes huge efforts andlengthy time to have a good command of effectiveness ofdomain operator combination [12] Moreover it is difficultto select the promising optimal parameters [13] Althoughthe machine learning methods have also been used to solvethe above dilemmas such as obstacle recognition based onmachine learning [14] this paper focuses on the anotherstrategy namely hyperheuristics which are capable ofsolving the above problems effectively Cowling et al [15]defined ldquohyperheuristicrdquo as ldquoheuristics to choose heuristicsrdquofor the first time Later Burke et al [16] expanded itsdefinition (i) heuristic selection and (ii) heuristic genera-tion erefore selection of optional LLHs is generallydecided from indicators of spread or convergence for acandidate solution versus parent solution As known fromthe above literature an LLH can be defined as an operator(crossover or mutation operator) or a metaheuristic (eg

2 Computational Intelligence and Neuroscience

NSGA-II and SPEA2) For a selective heuristic there existsone universal simple framework as shown in Figure 1

e black zone is a domain barrier for isolating high-level heuristics (HLHs) from LLHs e low-level problemdomain contains data information of the real problemLLHs used to search directly for problem space andpopulation information of the problem domain (chro-mosome fitness etc) In high-level control domain thereare two strategies with different objectives operator se-lection strategy and solution acceptance mechanism eselection strategy is used to search for LLH-based spaceand monitor history information of LLH performance soas to select high-quality operators (for isolating any in-formation related to the real problem) while the accep-tance criteria judge whether parent solution Sp should bereplaced depending on quality of children solution (orsolution set) Sc or not and control search direction andconvergence speed of the algorithm where Scu is thecurrent solution In addition between HLHs and LLHsthere are information transmitters used to exchange andtransmit information irrelevant to the problem domainincluding choice information acceptance strategy judg-ment information improvement rate contributed by LLHoperator runtime and frequency and number of con-secutive improvement failures of current solutionMoreover it is to highlight that any decision for high-leveldomain (selection or acceptance strategy) has to be iso-lated from real problem domain (such as encodingcrossover and mutation methods) otherwise hyper-heuristic principles and objectives will be disrupting inother words generality and transplantability of the high-level control strategy are improved in order to apply to anyproblem domain

Although there are plenty of multiobjective algorithms(such as NSGA-II SPEA2 and multiobjective optimizationbased on an improved cross-entropy method [17]) forsolving the practical problems in the real-world applicationsthis paper focuses on the MOHH which has criticalproblems in the following aspects in its design

(1) Design of high-level selection strategy perfor-mance of LLH may exhibit phased feature that isvarying with search progress for example oper-ator performance has inconsistent manifestationsin the early and late phases of search On this basisresearchers have designed different selectionstrategies depending on demand such as choicefunction [18 19] and sliding window-based FRR-MAB [20]

(2) Approach to children solution evaluation for asingle-objective problem it suffices to acquire fitnessimprovement rate (FIR) of children relative toparent But for an MOP objective space is expandedto two or more dimensions so FIR cannot be useddirectly to characterize an approach of replacingparent with children Dominance relationship ofchildren versus parent is utilized [20] Two-stagesorting method is used to evaluate children solutionsand reward corresponding LLHs [18 19]

(3) Solution acceptance mechanism quality of solutionacceptance mechanism has immediate impact onpopulation diversification and intensification thusinfluencing whether an algorithm is able to obtainsatisfactory solutions For single-objective problemsthere are deterministic acceptance mechanisms suchas All Moves (AM) Only Improving (OI) andnoninferior solution acceptance and probabilistic(nondeterministic) acceptance mechanisms such asgreat deluge (GD) delay acceptance simulatedannealing (SA) and Monte Carlo

(4) Domain barrier and information transmitter controlhyperheuristics are aimed at improving algorithmuniversality and transplantability so that the algo-rithm can be applied to real problems in differentdomains So there is crucial information in multi-objective problem domain chromosome fitness inother words chromosome fitness can be used byhigh-level control strategy during multiobjectiveoptimization likewise

erefore design methods are given in this paper for theabove problems in MOHH design respectively so as tosatisfy effectiveness and high performance of solving abiobjective LRP of cold chain logistics considering fuelconsumption and distribution period

23 Mathematical Model of Biobjective LRP of ColdChain Logistics considering Fuel Consumption andDistribution Period

231 Problem Formulation Assumptions and Definitions ofVariables LRP of cold chain logistics studied in this paper isa distribution centre-to-customer supply chain Supposethat the cold chain logistics network is a directed networkcomposed of distribution centres and customer points thatis N NC ND represents a set of all points on the logisticsnetwork whereNC represents a set of customer points it is aweighted directed network where point-to-point distancesare the weights including the distance between a distri-bution centre and a customer and the distance betweencustomers Optimization of a logistics network consists oftwo major aspects reasonable distribution centre selectionand vehicle routing To study instances of cold chain logisticsnetwork reasonably the following assumptions are made

(1) Urban Traffic Status Is Relatively Stable During Distri-bution Period Changes in urban road traffic status are notchaotic in general roads will be congested during morningand evening peak hours in a day if no accident occurscongestion status lasts for about two hours while duringother hours roads will not be so congested and road trafficdoes not vary much

(2) lte Distribution Vehicle Remains in Uniform Speed StateSuppose that urban road congestion status is constant it isvery difficult to predict vehicle speed in LRP and VRP as thespeed varies somewhat with time interval and it is very hardto describe the speed variation model with mathematical

Computational Intelligence and Neuroscience 3

functions therefore in this study of LRP of cold chainlogistics speed of the distribution vehicle is deemeduniform

(3) Other Assumptive Conditions Each distribution centre isequipped with vehicles a distribution vehicle transports coldchain logistics products from each distribution centre tovarious customers and returns to the original distributioncentre e maximum load weight of each vehicle is Q nodemand of one customer exceeds the maximum load weightof each vehicle demand of one customer can be satised byone vehicle only through distribution service and one ve-hicle is able to serve many times If drivers have the samedriving habit and driving skill and each distribution centrehas abundant inventory then cargo shortage will not occur

Notations and variables of the model are dened asfollows candidate distribution centre set ND 1 2 mcustomer set NC 1 2 n available vehicle set K 1 2 φ all-point set N ND cupNC and edge set E (i j)i isinV j isinV ine j(i j) i isin J j isin J ine j transportation dis-tance corresponding to each edge is dij and travel speed is vijcustomer i isinNC has nonnegative cargo allocation demandDiand time window requirement (ETi LTi) while wi is cus-tomer service time vehicle type is the same and the max-imum capacity is CV distribution centre i isinND has anenabling cost of Oi and the maximum capacity of CDi

e following are decision variables xijk is 1 if edge (i j)serves vehicle k otherwise xijk is 0 yj is 1 when distributioncentre j is enabled otherwise yj is 0 zij is 1 when customer i isserved by distribution centre j otherwise zij is 0

e following are additional variables Lijk representsdynamic load of vehicle k on edge (i j) ATik is the time pointat which vehicle k arrives at node i

erefore based on the above model assumptions anddenitions of notations and variables a multiobjectivemathematical model can be given in this paper

232 Model Composition e biobjective model in thispaper is designed to optimize total logistics cost and dis-tribution period the total logistics cost consists of fuelconsumption cost cargo damage cost transportation costrefrigeration cost of refrigerated trucks penalty cost of timewindow and operation cost of distribution centres as de-tailed below

(1) Fuel Consumption Cost According to a report on thewebsite of the government of Japan [21] fuel consumptionof one type of vehicles is directly proportional to load weightIn light of this Xiao et al [22] assumed that a vehicle runs ata constant speed only considered impacts of load weight andtraveled distance on vehicle fuel emission and split vehicleweight into dead weight M0 and load weight M1 then FuelConsumption Rate (FCR) can be calculated using the fol-lowing formula

ρ M1( ) α M0 +M1( ) + b (6)

emaximum load weight that can be borne by a vehicleis dened as CV then FCRs at zero load and full load can beexpressed as ρ0 αM0 + b and ρlowast α(M0 +CV) + b respec-tively us FCR per unit distance is

ρ M1( ) ρ0 + ρlowast minus ρ0( ) timesM1

CV (7)

erefore the fuel consumption generated by vehicle kunder load Lijk is

Solution spacehellip

Pool of LLHs

hellip

LLH1 LLH2 LLH3 LLHn

Dom

ain

barr

ier

Selection strategy

ChooseLLH

ImplementLLH

Scurrent

Acceptance criteria

Accept

Yes

No

Stop

Yes

Return Sbest

No

Update corresponding parametersUpdate scores of LLHs

High-level heuristics

High-level control domainProblem domain

Scurrent Sprev

Problem descriptionConstraintsObjectives of problemInitialize solutionsPool of LLHsTest instances

(i)(ii)(iii)(iv)(v)(vi)

Figure 1 Selective hyperheuristic framework


FCijk ρ0 + ρlowast minus ρ0( 1113857 timesLijk

CV1113888 1113889 times dijxijk (8)

and for this problem mentioned fuel consumption cost isC1 c0 1113944

iisinN1113944jisinN

1113944kisinK

FCijk (9)

where c0 represents unit fuel cost (YuanL)

(2) Cargo Damage Cost of Cold Chain Logistics Based on therationale of previous studies on cold chain logistics productsresearchers incorporated cargo damage cost analysis intodistribution routing optimization of cold chain logisticsnetwork To facilitate the study suppose that cold chainlogistics products in the whole cold chain logistics distri-bution network are stored at a constant temperature in stableenvironment e top consideration is quality degradationof cold chain logistics products over time and according tofood science principles combined with deterioration ratefunction of cold chain logistics products Qi [23] induced amathematical relationship between product quality change∆Q and original quality Q0 as follows

lqm ΔQQ0

times 100 1 minus e1113936iisinN1113936jisinN minus Smiddottijeminus EaRT( )( 11138571113882 1113883 times 100

(10)

where tij dijvij Cargo damage of cold chain logistics isrelated to logistics distribution time only and cargo damagecost is expressed as follows

C2 1113944iisinN

1113944jisinN

1113944kisinK

Lijk 1 minus eminus φ dijvij( 1113857

1113876 1113877

⎧⎪⎨

⎪⎩

⎫⎪⎬

⎪⎭times 100 (11)

Let φ be time sensitivity coefficient its expression is

φ S middot eminus EaRT( ) (12)

(3) Refrigeration Cost of Refrigeration Equipment In thecourse of distribution in cold chain logistics a refriger-ation equipment is not fully closed its external factorssuch as solar radiation will result in a temperature gra-dient between inner and outer surfaces so as to increasethermal load inside the refrigeration equipment eevaporator in the refrigeration equipment will refrigeratethe cargo until overall thermal load is balanced andeventually constant temperature is achieved Fu [24]performed thermal equilibrium analysis by thermalequilibrium method frequently used in energy con-sumption analysis of building system and in cold chainlogistics distribution additional heat of refrigerationequipment arises from such factors as heat exchangebetween internal and external walls of refrigerationequipment heat diffusion of products and equipment incold chain logistics and hot air soaking For the brevity ofstudy only heat load H1 due to high-ratio heat exchangebetween internal and external walls of refrigerationequipment and heat load H2 due to high-ratio heat

exchange upon door opening are considered H1 isexpressed as

H1 R1S T minus T0( 1113857 (13)

where R1 is the thermal conductivity of refrigerationequipment in W(m2middotK) S is the heat transfer area in m2 ofrefrigeration equipment on a refrigerated truck T is thetemperature outside refrigeration equipment in K and T0 isthe product storage temperature of cold chain logistics in KH2 is expressed as follows

H2 R2Sd T minus T0( 1113857 (14)

where R2 is the thermal conductivity of air in W(m2middotK) Sdrepresents the door area of refrigeration equipment in m2and w2 is a parameter of unit refrigeration cost the re-frigeration cost during cold chain logistics network distri-bution can be expressed as

C4 w2 H1 1113944iisinN

1113944jisinN

1113944kisinK

dij

vij

xijk + H2 1113944iisinN

1113944kisinK

wiyik⎛⎝ ⎞⎠ (15)

(4) Transportation Cost When cold chain logistics productsare distributed from a distribution centre to a customertransportation cost will be generated including manage-ment cost of distribution vehicle drivers and transportationstaff toll and vehicle loss cost while unit transportation costper vehicle is assumed to be known and fixed in the logisticssystem Transportation cost of all vehicles is related totransportation distance and calculated using the followingformula

C3 φ 1113944iisinN

1113944jisinN

1113944kisinK

xijkdij (16)

where φ is the cost per traveling distance

(5) Penalty Cost of Time Window As products in cold chainlogistics are perishable the customer demands that thelogistics company distribute cold chain logistics products ina specified time frame To improve logistics service level andcustomer satisfaction penalty cost of time window is in-corporated into cold chain logistics distribution routingobjective function as follows

Pk(i)

α ETi minus ATik( 1113857 ATik ltETi

0 ETi leATik le LTi

β ATik minus LTi( 1113857 LTi ltATik

⎧⎪⎪⎨

⎪⎪⎩(17)

where Pk(i) represents penalty cost of time window that maybe paid when vehicle k is serving customer i ATik representsthe time point at which vehicle k arrives at customer point iα is a penalty coefficient for the case that a distributionvehicle arrives at a customer point at a time earlier than thestart time of time window β is a penalty coefficient for thecase that a distribution vehicle arrives at a customer point ata time later than the start time of time window ETi and LTirepresent the start time and end time of time window


respectively erefore penalty cost of time window can beexpressed as

C5 1113944iisinNC

1113944kisinK

Pk(i) (18)

(6) Operation Cost of Distribution Centres To ensure normaloperation of cold chain logistics network labour costequipment maintenance cost and utilities have to beinvested the above costs altogether constitute operation costof distribution centres in cold chain logistics It is assumedthat daily investment is basically unchanged in practicaloperation thus distribution centres and operation costs areassumed to be fixed known conditions Hence operation costof distribution centres can be expressed as

C6 1113944iisinND

OiYi (19)

233 Location-Routing Optimization Modelling for ColdChain Logistics Based on the above model assumptions anddefinitions of notations and variables a mathematical modelwas developed as follows

minCost C1 + C2 + C3 + C4 + C5 + C6 (20)

minTT maxiisinK

Ti1113864 1113865 (21)

1113944iisinN

xijk 1 forallj isin NC k isin K (22)

1113944iisinN

xihk minus 1113944jisinN

xhjk 0 forallh isin NC k isin K(23)

1113944jisinND

zij 1 foralli isin NC (24)

zij leYj foralli isin NC j isin ND (25)

1113944iisinNC

xik leYk forallk isin ND (26)

xink + zij + 1113944misinND mne j

znm le 2 foralli n isin NC ine n j isin ND

(27)

1113944iisinNC

1113944kisinND

Dizik leCDkYk forallk isin ND(28)

1113944iisinNC

1113944jisinN

Dixijk leCV (29)

ATik ATjk + tij + wjk foralli j isin NC

(30)

ETi leATik le LTi foralli isin NC k isin K (31)

Equations (20) and (21) are objective functions Ob-jective (20) represents minimization of total cost duringoptimization of cold chain logistics LRP including fuelconsumption cost cargo damage cost transportation costrefrigeration cost of refrigerated truck penalty cost of timewindow and operation cost of distribution centre objective(21) represents the shortest vehicle distribution timeConstraint (22) ensures that each customer is served onceconstraint (23) ensures that the vehicle has to leave afterserving a customer constraint (24) indicates that eachcustomer can be assigned to one distribution centre onlyconstraints (25)ndash(27) indicate that the enabled distributioncentre has to serve a customer constraint (28) ensures thattotal demand of customers served by each distributioncentre is not more than capacity of the distribution centreconstraint (29) ensures that total volume of cargoes carriedby each vehicle is not more than its loading capacityconstraint (30) represents temporal connection between twoconsecutive customer points in a vehicle distribution pathand constraint (31) indicates that the time when a vehiclearrives at a customer point may not be out of the permissibletime interval

24 MOHH Conventional methods for solving MOP in-clude weighting method constraint method and hybridmethod In recent years Multiobjective Evolutionary Al-gorithms (MOEAs) as one kind of new methods for solvingMOP have been developed gradually e most frequentlyused MOEAs are Genetic Algorithms (GAs) or multi-objective GAs and representative GAs include VEGAHLGA MOGA NPGA and NSGA [25] In this paperMOHH is proposed for solving cold chain logistics-basedmultiobjective LRP model and distribution routing for coldchain logistics and is compared with Nondominated SortingGenetic Algorithm II (NSGA-II) often used to solve MOPusing elitist strategy [26] NSGA-II employs simple yet ef-ficient nondominated sorting mechanism so as to capturePareto front and Pareto solution set with good distribution

Problem domain and algorithm domain are designedbelowe problem domain involves chromosome encodingand LLHs for optimization while in high-level domain fourhigh-level selection strategies and acceptance mechanismsare designed and finally a multiobjective hyperheuristicframework is given

241 Problem Domain

(1) Chromosome Encoding Direct encoding is used If thereare three distribution centres and 10 customers 0 representsthe distribution centre and 1ndash10 represent customernumbers then a distribution centre can be represented by11ndash13 Customer sequence is generated randomly for ex-ample 9-5-3-2-4-1-6-8-7-10 and sequence location orderrepresents the order of a vehicle arriving at a customerereafter according to principles ldquocustomer demandserved by a vehicle may not exceed load weight of the


vehiclerdquo and ldquocustomer demand served by a distributioncentre may not exceed capacity of the distribution centrerdquodistribution centres are allocated by centroid method henceinitialization path is converted to the following 12-9-5-3-1211-2-4-1-6-11 13-8-7-10-13 e first path represents that avehicle departs from distribution centre no 2 and distributesgoods to customers nos 9 5 and 3 and then returns to theoriginal distribution centre

(2) LLHs LLHs can be classified into mutation heuristicruin-recreate heuristic local search heuristic and crossoverheuristic LLHs are used to manipulate solution space di-rectly as follows

(i) Mutation heuristic

LLH1 2-opt select arbitrarily one path from parentsolution and swap locations of adjacent customerpoints so as to generate a new children solutionLLH2 Or-opt select arbitrarily one path fromparent solution and insert two adjacent customerpoints into other locations so as to generate a newchildren solutionLLH3 interchange select randomly two pathsfrom parent solution and swap locations of anytwo customer points so as to generate a newchildren solutionLLH4 replace select randomly one path and swaplocations of any two customer pointsLLH5 shift select randomly one path from parentsolution while enabling a new distribution centrefor this path so as to generate a new childrensolutionLLH6 interchange select randomly two pathsfrom parent solution and swap their distributioncentres so as to generate a new children solution

(ii) Ruin-recreate heuristic

LLH7 location-based radial ruin select any onecustomer point as ldquoreference customerrdquo andremove other customers at a probability of 1ndash10 according to a rule of approaching ldquoreferencecustomerrdquo in location so as to generate a newchildren solution

(iii) Local search heuristic

LLH8 interchange as in the case of LLH4 but thisoperator returns the improved children solutiononlyLLH9 shift the operation is basically the same asthat of LLH3 except that LLH9 selects a customerpoint according to ldquothe best improvementrdquo cri-terion inserts the customer point into randomlocation of the original path or any other path andreturns an improved children solution onlyLLH10 2-optlowast select randomly two paths fromparent solution choose one location according toldquothe best improvementrdquo criterion swap all cus-tomer points behind the location and return animproved solution only

LLH11 GENI calculate the distance between anytwo customers on different paths in parent solu-tion select the shortest distance as reference dis-tance remove customer points nearest to thereference distance rearrange these customers intoa new path and return an improved childrensolution only

(iv) Crossover heuristic

LLH12 combine select randomly two parentpaths copy one of the parent paths at a probabilityof 25ndash75 to generate a subpath add paths thatoriginate from another parent path and are notcontradictory against this subpath and eventuallyarrange arbitrarily the remaining customer pointsLLH13 longest combine select randomly twoparent paths sort all paths in descending order ofnumber of customer points served add all pathswithout repeated customers to generate a subpathand eventually arrange arbitrarily the remainingcustomer points

242 High-Level Selection Strategies

(1) Simple Random (SR) SR selects randomly LLHs in eachiteration and is usually used as a reference for comparisonwith any other strategy

(2) Tabu Search (TS) TS is to prohibit repeating previousoperation To address a defect that local neighbourhoodsearch algorithm gets readily trapped in local optimal pointsTS algorithm formulates a tabu list to record searched localoptimal points and not to search or search selectively ele-ments in the tabu list in next iteration thereby trap in localoptimum is eliminated and global optimization objective isachieved TS algorithm is an extension of local neigh-bourhood search and a heuristic for global neighbourhoodsearch and gradual optimization

As an HLH strategy for MOHH TS scores performanceof each LLH and thereby selects an operator for currentiteration and updates scores using Reinforcement Learningmechanism in other words if a children solution arisingfrom manipulation of the LLH improves parent solutionthen score of this LLH will be added otherwise it will bededucted

(3) Choice Function (CF) CF selects an LLH based on threedifferent metrics the first metric records previous perfor-mance of each LLH denoted as f1 and LLH performance ofeach LLH can be expressed as

f1 1113944n

ηnminus 1 In LLHj1113872 1113873

Tn LLHj1113872 1113873 (32)

where In(LLHj) and Tn(LLHj) are the improvement value ofeach previously called heuristic and time to call the heuristicrespectively and η is a coefficient ranging from 0 to 1


e second metric attempts to capture connection be-tween LLHs and can be expressed using the followingformula

f2 LLHk LLHj1113872 1113873 1113944n

μnminus 1 In LLHk LLHj1113872 1113873

Tn LLHk LLHj1113872 1113873 (33)

where In(LLHk LLHj) and Tn(LLHk LLHj) represent FIR ofLLHj following LLHk and call time of LLHj following LLHkrespectively Likewise μ is a coefficient ranging from 0 to 1

e third metric is the time period since CF selects thelast LLHj

f3 LLHj1113872 1113873 τ LLHj1113872 1113873 (34)

To rank LLHs a score is given to each LLH

F LLHj1113872 1113873 e times f1 LLHj1113872 1113873 + f times f2 LLHj1113872 1113873 + g times f3 LLHj1113872 1113873

(35)

where e f and g represent weights of three metricsrespectively

(4) Ant-Inspired Selection (AS) [27] Ant colony opti-mization algorithm is a native heuristic of ant behaviour orant population behaviour used to solve hard combinatorialoptimization problem Ant colony algorithm applied inhyperheuristics is able to provide an HLH strategy so as toconstruct good LLH sequence Each ant determines the nextfixed point based on the pheromone in each path (eachvertex represents an LLH) and once the ant arrives at a newvertex it will apply the LLH corresponding to the vertexUnlike the ant colony algorithm in combinatorial optimi-zation problem solving mode an ant colony manipulatesLLHs thus each ant is permitted to visit one point withmultiple times indicating that each heuristic may operatemultiple times in one iteration Details of the design aredescribed in literature [27]

243 High-Level Acceptance Mechanisms Acceptance cri-teria are used to judge whether a children solution canreplace parent solution or not and its performance hasimmediate impact on convergence speed and optimizationaccuracy of a hyperheuristic [28] It is therefore very im-portant to determine superiority or inferiority of a childrensolution to parent solution in design of acceptance criteriae following strategy is used in this paper in a randomlyselected objective function as long as a children solution hasa smaller fitness than parent solution this children solutionwill be regarded to be superior to the parent solution and cango to the next iteration in place of the parent solution isstrategy is also used in the above three selection strategies

(1) All moves (AM) all solutions are accepted regardlessof improvement

(2) Simulated annealing (SA) it is similar to SA algo-rithm Set initial temperature T and cooling coeffi-cient and update annealing temperature TTtimes λafter each iteration Apply an LLH to each iterationaccept an improved solution if any and accept anunimproved solution at a certain probability

expressed as p e∆T where ∆ represents the changeof objective function

(3) Great deluge (GD) [28] set a lower bound (LB)which is an optimal solution in current iterationApply an LLH to each iteration accept an improvedsolution if any and accept an unimproved solutionin presence of the following caseftemplt LB+ (f0 minus LB)times (1 minus iterTmax) where ftemprepresents a children solution f0 represents initialsolution iter represents number of current itera-tions and Tmax represents the maximum number ofiterations

(4) Only improving (OI) accept improved solution onlyand eliminate all inferior solutions

244 MOHH Framework In a LRP model the methodfocuses on designing distribution centres and customergroups and the first job is to address distribution pathbetween customers e process is detailed as follows

Step 1 initialize the population by encoding customersdirectly suppose each chromosome has 10 customerpoints and 3 distribution centres 1ndash10 representcustomer numbers and 0 represents a distributioncentre Distribution centres can be represented by 0(1)-0(3) respectivelyStep 2 initialize parameters of an HLH strategyStep 3 optimize population P

Step 31 select one of two objectives (f1 f2) at an equalprobability randomlyStep 32 select an LLH based on its performanceStep 33 calculate the value of the selected objectivefunction fnStep 34 calculate the value of another objectivefunctionStep 35 update performance metrics of the LLH

Step 4 update Pareto solution set by nondominatedsortingStep 5 evaluate a children solution according to anacceptance mechanism in acceptance criteria and opt toaccept the children solution or notStep 6 update parameters related to HLH strategy andLLH scoreStep 7 judge whether termination condition is satisfiedor not if yes then stop iteration and output optimalsolution otherwise return to step 3Step 8 generate Pareto front

3 Simulation Results and Analysis

31 Parameter Configurations e MOHH was coded inparallel in MATLAB 2015b using a 260GHz Intel Core i5-3230K with 4GB of RAM and running Windows 10

e parameter configurations were set as follows esize of population was set to 100 the maximum number ofiterations was set to 5000 In the choice function three


weights were 05 02 and 03 In the ant-inspired selectionwe followed the default values proposed by Wang et al [27]length of route LP 11 number of ants m 15 factorsε 0001 and σ 1001

32 Performance Metrics To validate performance of theproposed MOHH algorithm the following three metricswere used

(1) Number of Pareto solutions (NPS) this metric isused to determine the number of Pareto solutionsobtained by the algorithm

(2) Spacingmetric (SM) this metric is used to determinedistribution uniformity of Pareto solution set

S 1n

1113944

n

i1d minus di1113872 1113873

2⎡⎣ ⎤⎦12

(36)

where di represents the Euclidean distance fromPareto solution i to the nearest point in real Paretosolution set and d represents mean of all di valuese real Pareto solution set refers to nondominatedsolution set consisting of all Pareto solutions

(3) Diversification metric (DM) this metric is used tomeasure diversity of Pareto solution set

D

1113944

n

i1max x

it minus y

it

11139741113972

(37)

where xit minus yi

t represents the Euclidean distance be-tween nondominated solutions xi

t and yit

33 Experimental Comparison of HLH Strategies To obtainbetter results in solving a biobjective LRP of cold chainlogistics MOHH algorithm was optimized by HLH strategyfirst in other words the best combination of selectionstrategy and acceptance criteria was found by comparingexperimental results One of Solomon reference instanceswas chosen for model solving and as a standard LRPproblem has neither refrigeration cost nor cargo damagecost the total cost calculated in this section excludes re-frigeration cost and cargo damage cost Model solving re-sults of HLH strategies are shown in Table 1

Statistics NPS SM and DM are compared in Table 2 Ascan be found in Tables 1 and 2 AS-GD and TS-SA gave riseto more Pareto solutions than other combinations of HLHstrategies HLH strategy combination TS-SA resulted insmaller SMmetric of nondominated solution set and smaller

Table 1 Experimental results of HLH strategies in solving biobjective LRP

Selection strategy Acceptance criteria NPSDistribution time Total cost

Min Max Min Max

AS

AM 4 11522 12562 139785 166466GD 7 11037 14449 145240 161055OI 5 10452 11388 144198 148493SA 5 10584 11312 142343 160760

CF

AM 4 10853 11242 147482 163772GD 5 10726 12257 149758 163792OI 4 10689 12067 152179 161707SA 6 11133 11492 149411 164242

SR

AM 4 10582 11092 138572 153454GD 3 12764 13230 176301 197800OI 3 10418 11830 134790 145900SA 5 10610 12118 145880 157087

TS

AM 6 10563 11866 141474 146421GD 5 11450 12150 148005 174159OI 6 12222 14375 164531 192463SA 7 10426 11723 133167 133167

Table 2 Comparison of performance metrics of different HLHstrategies for MOHH

Selection strategy Acceptance criteria NPS SM DM

AS

AM 4 1473 978GD 7 2067 1010OI 5 1347 468SA 5 1556 902

CF

AM 4 6294 786GD 5 3930 806OI 4 2921 588SA 6 3030 840

SR

AM 4 4248 815GD 3 3159 765OI 3 291 568SA 5 2696 717

TS

AM 6 589 570GD 5 1341 1053OI 5 2179 1149SA 7 263 1011


spacing indicating that HLH strategy TS-SA results in moreuniform distribution of nondominated solution set ascompared with other HLH strategies in comparison TS-GD TS-OI TS-SA and AS-GD metrics had better DMvalues than other HLH strategy combinations

Figure 2 shows Pareto fronts obtained when selectionstrategies AS CF SR and TS are combined with four dif-ferent acceptance criteria respectively As can be found inthe gure when TS acts as a selection strategy more Paretosolutions were obtained in more uniform distribution andwhen SA acts as acceptance criteria solution metrics NPSSM and DM were superior to other acceptance criteria

In summary when MOHH was applied to biobjectiveLRP optimization the Pareto solution set obtained subject toselection strategy TS and acceptance criteria SA gave rise togood values of various evaluation metrics thus TS-SA as aHLH strategy has better eect of solving biobjective LRPs

34 MOHH Validation Analysis

341 Statistical Analysis of LLH Utilization Two new LLHswere added to improve solving biobjective problems byoptimization utilization data and acceptance rates of LLHswere statistically analysed during algorithm optimizationand performances of HLH strategies and LLHs in

optimization were analysed in order to study the impact ofMOHH algorithm framework on multiobjective optimiza-tion Figure 3 shows the statistical results of LLH utilization

Figure 3 shows that among all LLHs LLH6 had thehighest utilization with a mean utilization of 113 utili-zation of LLH8 reached high values too with a mean uti-lization of 102 whereas mean utilization of LLH7 wasmerely 58 except that LLHs were randomly selected in SRselection strategy LLHs were selected by probability in allthe remaining selection strategies and the probability wasdetermined based on performance of an LLH during al-gorithm iteration it can therefore be inferred that LLH6 andLLH8 have better performance than other LLHs In utili-zation statistics of LLH6 selection strategy TS showed thehighest utilization of LLH6 thus it can be inferred that TSenables better performance of LLH6 a LLH7 utilization ofjust 46 and lower utilization of worse-performance LLHstherefore in solving biobjective LRP selection strategy TS issuperior to three other selection strategies which also val-idates experimental conclusions in this paper

342 Statistical Analysis of Acceptance Rates in LLHsTo study eects of acceptance criteria on solution resultsacceptance rates of LLHs as per four acceptance criteria

1000 1100 1200 1300 1400 1500Delivery duration (min)

14

15

16

17Lo

gisti

cs co

st (Y

uan)

times104

SAOI

GDAM

(a)

Delivery duration (min)

times104

SAOI

GDAM

1050 1100 1150 1200 1250145

15

155

16

165

Logi

stics

cost

(Yua

n)

(b)

times104

SAOI

GDAM

1000 1050 1100 1150 1200 1250 1300 1350Delivery duration (min)

12

14

16

18

2

Logi

stics

cost

(Yua

n)

(c)

times104

SAOI

GDAM

Delivery duration (min)1000 1100 1200 1300 1400 1500

12

14

16

18

2

Logi

stics

cost

(Yua

n)

(d)

Figure 2 Proles of Pareto solution set in four selection strategies Pareto front under (a) AS (b) CF (c) SR and (d) TS


LLH1

LLH2

LLH3

LLH4

LLH5

LLH6

LLH7 LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(a)

LLH1

LLH2

LLH3

LLH4

LLH5

LLH6 LLH7

LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(b)

LLH1

LLH2

LLH3

LLH4

LLH5

LLH6LLH7

LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(c)

LLH1

LLH2

LLH3

LLH4

LLH5

LLH6LLH7

LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(d)

Figure 3 Mean operator utilization data of four selection strategies Usage rate of operators under (a) AS (b) CF (c) SR and (d) TS

10 11 12 13Sequence of operators

0

02

04

06

08

1

Acce

ptan

ce ra

te (

)

1 2 3 4 5 6 7 8 9

(a)

0

02

04

06

08

1

Acce

ptan

ce ra

te (

)


1 2 3 4 5 6 7 8 9

(b)

Figure 4 Continued


using selection strategy TS were statistically analysed (shownin Figure 4)

As can be found in Figure 4 according to acceptancecriterion AM all solutions are accepted so all acceptancerates were 1 as per acceptance criteria GD and SA good-performance LLHs (LLH6 and LLH8) had mean acceptancerates above 09 according to acceptance criterion OI onlyimproved solutions are accepted and higher acceptance ratesof high-quality LLHs were achieved but acceptance rates ofordinary-performance LLHs were lower and readily trappedin local optimum For poor-performance LLH (LLH7) ac-ceptance rates as per acceptance criteria SA and GD were050 and 053 respectively According to acceptance crite-rion SA it is easier to reject poor-performance LLHs andaccept good-performance LLHs therefore acceptance cri-terion SA has more positive impact on improvement of

solutions to a biobjective LRP which validates experimentalconclusions in this paper

35 Experimental Comparison between Algorithms MOHHand NSGA-II To further illustrate eectiveness of MOHHalgorithm in solving biobjective LRPs TS-SA serves as anHLH strategy combination of MOHH for instance solvingas compared with algorithm NSGA-II For the sake offairness NSGA-II adopts the same heuristic that MOHHadopts (Table 3) while multiobjective performance metricswere used to assess the resulting Pareto fronts (Table 4)

In nine instances MOHH had 52 Pareto solutions onaverage while NSGA-II obtained 46 Pareto solutions Interms of performance metrics MOHH was slightly superiorto NSGA-II in NPS and mean SM of MOHH-derived Pareto

Acce

ptan

ce ra

te (

)

0

02

04

06

08

1


1 2 3 4 5 6 7 8 9

(c)

Acce

ptan

ce ra

te (

)

0

02

04

06

08

1


1 2 3 4 5 6 7 8 9

(d)

Figure 4 Operator acceptance rates under (a) AM (b) GD (c) OI and (d) SA

Table 3 Comparison between algorithms MOHH and NSGA-II in solution results

Instance Solution algorithm NPSDistribution time Total cost

Min Max Min Max

R101 MOHH 6 12221 13743 165230 184790NSGA-II 5 20457 23435 174105 182155

R102 MOHH 6 11938 13390 165251 182082NSGA-II 6 21139 22227 168680 174992

R103 MOHH 5 11792 13360 163107 181646NSGA-II 4 21733 22417 169208 189293

R104 MOHH 5 11660 12628 161086 188263NSGA-II 3 21273 21499 195527 199156

R105 MOHH 5 11573 13016 169270 174440NSGA-II 4 21372 22227 177605 184762

R106 MOHH 6 12078 12889 157142 162353NSGA-II 5 22488 26034 170070 173938

R107 MOHH 6 11788 13127 155009 172504NSGA-II 5 21064 21346 153680 160416

R108 MOHH 3 11350 11841 138182 150531NSGA-II 5 21352 24724 156000 160385

R109 MOHH 5 12294 14060 163585 188892NSGA-II 4 20533 23831 153025 159328


solution set was 652 while mean SM of NSGA-II-derivedPareto solution set was 795 therefore MOHH-derivedPareto solution set had smaller mean scheme spacing andmore uniform distribution MOHH-derived Pareto solutionset had a mean DM of 865 while NSGA-II-derived Paretosolution set had a mean DM of 597 therefore MOHH-derived solutions are superior to NSGA-II-derived solutionsin diverse metrics

36 Practical Instances of Cold Chain Logistics It has beenvalidated that MOHH is effective in solving biobjectiveLRPs e cold chain logistics model was solved by MOHHusing selection strategy TS according to acceptance criterion

SA In cold chain logistics network programming there areusually more than one decision objective optimization ofcost alone would fail to meet benefits of the logisticscompany and customers therefore it is essential to performmultiobjective optimization of cold chain logistics

is section focuses on the cold chain logistics of seafoodof a supermarket in Hangzhou City and the subbranches ofthe supermarket have a wide distribution and range ofservices e distribution of subbranches (ie customers) isshown in Figure 5

Aiming at improving competitiveness of cold chainlogistics the supermarket selected five distribution centresin Hangzhou Five distribution centres met the requirementsof the cold chain In this paper 30 subbranches are selected

Table 4 Comparison between MOHH and NSGA-II in performance metrics

Instance Solution algorithm NPS SM DM

R101 MOHH 6 538 1011NSGA-II 5 569 772

R102 MOHH 6 943 909NSGA-II 6 792 600

R103 MOHH 5 227 949NSGA-II 4 763 896

R104 MOHH 5 603 1106NSGA-II 3 812 322

R105 MOHH 5 490 522NSGA-II 4 313 538

R106 MOHH 6 549 635NSGA-II 5 1624 523

R107 MOHH 6 1075 978NSGA-II 5 1118 529

R108 MOHH 3 709 618NSGA-II 5 835 602

R109 MOHH 5 732 1060NSGA-II 4 325 592

Figure 5 Partial distribution map of supermarket in Hangzhou


1 2 3 30 and the distribution centres are represented by31 32 33 34 and 35 e demand and time windows areknown and the distance between each distribution centreand each subbranch is known Each distribution centre isequipped with a dedicated refrigerated truck for distribu-tion e maximum capacity of each vehicle is 5 tons eaverage traveling speed is 40 kmh on urban roads e unitcooling cost w2 is 2 YuanKcal e unit penalty cost α of thesatisfaction time window is 2 Yuanh and the unit penaltycost β is 3 Yuanh later than the customer satisfaction timethe external temperature T is 77K and the temperature T0 inthe refrigerator is 356 K e thermal conductivity R1 of thecompartment is 80 the thermal conductivity R2 is 003 theheat transfer area S of the refrigerated truck is 1725m2 thedoor area Sd is 575m2 the transportation cost per kilometreφ is 4 Yuankm and ρlowastρ0 is 04150155 Lkm diesel price ofZhejiang province is 74 YuanL cargo damage cost c is20 Yuankg time sensitivity coefficient φ is 0005 edistribution information of distribution centres and sub-branches is provided in Tables 5 and 6

Experimentally obtained Pareto solutions are shown inFigure 6 Solving biobjective cold chain logistics LRP byMOHH resulted in a total of 12 Pareto optimal solutionsDistribution time and costs corresponding to Pareto solu-tions were analysed in Table 7 where Cost1 represents pathcost Cost2 represents fuel cost Cost3 represents refrigera-tion cost of the refrigerated truck Cost4 represents cargodamage cost of cold chain logistics Cost5 represents penaltycost of time window and Cost6 represents operation cost ofeach distribution centre

As described in Table 7 all the above 12 distributionschemes are Pareto optimal solutions Pareto No 1 corre-sponds to a solution with the shortest distribution time(42 h) but corresponding total cost reached 221260 YuanPareto No 12 corresponds to a solution with the minimumtotal cost (55220 Yuan) but its distribution time reached75 h

To validate the effect of MOHH in solving instancesLLH utilization during algorithm iteration was statisticallyanalysed as shown in Figure 7 Based on Figure 7 in se-lection strategy TS utilization rates of LLH6 and LLH8 were

Table 5 Information of distribution centres

No Location Capacity Fixed cost31 (120213287 30316118) 50 4032 (120108078 30254743) 40 3533 (120217886 30172352) 70 7034 (120177067 30243263) 55 4035 (120160395 30311877) 60 55

Table 6 Information of subbranches

No Location Demand Servicetime

Timewindows

1 (12021793630296719) 08 03 [00 20]

2 (12020197730263709) 11 03 [10 20]

3 (12012365230290270) 08 03 [00 20]

4 (12021721930206380) 13 03 [30 50]

5 (12019046130341832) 11 03 [30 50]

6 (12016980430282714) 13 03 [30 60]

7 (12004603530263151) 06 03 [20 50]

8 (12019580730185674) 09 03 [30 60]

9 (12023408830197576) 05 03 [40 60]

10 (12027250130334870) 13 03 [20 40]

11 (12012560530313614) 13 03 [30 60]

12 (12010261130300304) 09 03 [20 40]

13 (12028487030150627) 14 03 [10 40]

14 (12018265730264054) 12 03 [00 20]

15 (12016685330269039) 05 03 [20 40]

16 (12020795330249617) 12 03 [30 50]

17 (12028205530169434) 11 03 [10 30]

18 (12015692330280374) 07 03 [30 50]

19 (12017424230196310) 12 03 [00 20]

20 (12017628530219921) 19 03 [20 60]

21 (12009314230340724) 15 03 [30 50]

22 (12023274430209315) 16 03 [05 20]

23 (12017831930283681) 08 03 [10 20]

24 (12020110930208160) 06 03 [10 30]

Table 6 Continued


Timewindows

25 (12019133830355956) 16 03 [30 60]

26 (12018004930252984) 14 03 [05 20]

27 (12016630330309546) 05 03 [10 30]

28 (12023847230358900) 08 03 [30 60]

29 (12017722530249727) 11 03 [05 20]

30 (12022001730315313) 14 03 [10 30]


4 45 5 55 6 65 7 75 8Delivery duration (h)

04

06

08

1

12

14

16

18

2

22

24

Tota

l cos

t (Yu

an)

times104

2 3 4 5 6

7 8 9 10 11 12

1

Figure 6 Pareto front of distribution in cold chain logistics

Table 7 Analysis of cost versus distribution time

No Delivery time (h) Cost1 Cost2 Cost3 Cost4 Cost5 Cost6 Total cost (Yuan)1 42 3040 5169 6243 1092 716 20500 2212602 44 2883 5152 6421 1199 692 8000 956553 45 2531 4126 4462 795 734 8000 926484 49 3029 5411 5921 1259 659 7500 912795 50 3080 5420 5797 1225 646 7500 911686 51 2812 5180 6050 1268 618 7500 909287 54 3502 6352 7701 1517 603 4000 596758 55 2813 5105 6257 1220 647 4000 560429 56 2733 5205 6027 1343 658 4000 5596610 57 2790 5077 6163 1219 694 4000 5594311 62 2785 5015 5991 1184 637 4000 5561212 75 2757 4991 5657 1188 627 4000 55220

LLH1

LLH2

LLH3

LLH4

LLH5

LLH6

LLH7 LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(a)


1 2 3 4 5 6 7 8 90

02

01

04

03

06

05

08

07

09

1

Acce

ptan

ce ra

te (

)

(b)

Figure 7 (a) Usage rate of operators (b) Acceptance rate


the highest (131 and 121 respectively) while utilizationrates of LLH3 and LLH7 were only 51 and 55 re-spectively Moreover according to acceptance criterion SAacceptance rate of LLH6 was more than 09 while acceptancerates of LLH3 and LLH7 were 053 and 052 respectivelyAccording to statistical analysis in Section 33 LLH6 andLLH8 had the best optimization effect while LLH7 had worseperformance In process of solving cold chain logistics in-stances in MOHH LLH6 and LLH8 were still utilized andaccepted at higher rates while LLH7 was utilized and ac-cepted at lower rates it can therefore be concluded thatMOHH has better utilization of good-performance LLHsand better improvement of solution quality

Practicality of MOHHwas validated by instance analysisFor multiobjective LRPs difference in objective preferencewill result in difference in distribution scheme and greatdifferences in distribution centre selection and routingNonetheless multiobjective optimization is capable of bal-ancing between the logistics company and customer de-mand and to meet different demands different distributionschemes can be used to enable balance of interests betweenthe logistics company and customers where possible Fur-thermore with total cost and distribution time as studyobjectives it is in favour of decision maker of the logisticscompany in offering diverse path options

4 Conclusions

In this paper one biobjective mathematical model isestablished for cold chain logistics distribution system and isused to improve economic benefit environmental benefittimeliness and customer satisfaction of the logistics dis-tribution system e first primary objective of the estab-lished multiobjective model is to optimize logisticsdistribution cost consisting of path cost fuel cost refrig-eration cost of the refrigerated truck cargo damage cost ofcold chain logistics penalty cost of time window and op-eration cost of distribution centres while the second primaryobjective is to optimize timeliness of the distribution systemor distribution time To address this problem MOHH al-gorithm was designed for model solving As to HLH strategyfor MOHH the best HLH strategy combination was ob-tained from combinations of four selection strategies andfour acceptance criteria

Based on experimental results TS-SA was the best HLHstrategy Further comparison with solution results of classicmultiobjective solving algorithm NSGA-II validated effec-tiveness of MOHH and finally solving instances of coldchain logistics by MOHH validated practicality of the al-gorithm while the resulting Pareto solution set offers diverseoptions for a decision maker to select an appropriate dis-tribution scheme depending on actual demand

e next study will focus on considering the use of moreactual constraints in cold chain logistics such as heteroge-neous vehicle [29] and simultaneous pickup and delivery[30] so that the problem can be more realistic Higher-performance HLH strategy will be designed to improvesolution quality and stability of the currently proposedMOHH Moreover we will focus on the alternative

frameworks of MOHH like [31 32] and the framework thathas a digital twin to repatriate at runtime [33] In additionconsideration of other carbon emission models will becomeone of the focuses in the next work

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is work was partly supported by the National NaturalScience Foundation of China (no 61572438) and the OpenFund of the Key Laboratory for Metallurgical Equipmentand Control of Ministry of Education in Wuhan Universityof Science and Technology (no 2017B04)

References

[1] S Wang F Tao and Y Shi ldquoOptimization of location-routingproblem for cold chain logistics considering carbon foot-printrdquo International Journal of Environmental Research andPublic Health vol 15 no 1 p 86 2018

[2] Y Zhang G Hua T C E Cheng and J Zhang ldquoCold chaindistribution how to deal with node and arc time windowsrdquoAnnals of Operations Research 2018

[3] J Jemai M Zekri and K Mellouli An NSGA-II Algorithm forthe Green Vehicle Routing Problem Springer Berlin Ger-many 2012

[4] J Liu and V Kachitvichyanukul ldquoA Pareto-based particleswarm optimization algorithm for multi-objective locationrouting problemrdquo International Journal of Industrial Engi-neering lteory Applications and Practice vol 3 no 22pp 314ndash329 2015

[5] J C Molina I Eguia J Racero and F Guerrero ldquoMulti-objective vehicle routing problem with cost and emissionfunctionsrdquo ProcediamdashSocial and Behavioral Sciences vol 160pp 254ndash263 2014

[6] A M Golmohammadi S Amanpour Bonab andA Parishani ldquoA multi-objective location routing problemusing imperialist competitive algorithmrdquo InternationalJournal of Industrial Engineering Computations vol 7 no 3pp 481ndash488 2016

[7] M G Gong G Cheng L C Jiao et al ldquoAdaptive partitioning-based non-dominated individual selection strategy for evo-lutionary multi-objective optimization problemrdquo Journal ofComputer Research and Development vol 4 no 48pp 545ndash557 2011

[8] Z M Gao and J Zhao ldquoAn improved grey wolf optimizationalgorithm with variable weightsrdquo Computational Intelligenceand Neuroscience vol 2019 Article ID 2981282 13 pages2019

[9] F Valdez O Castillo A Jain and D K Jana ldquoNature-in-spired optimization algorithms for neuro-fuzzy models inreal-world control and robotics applicationsrdquo ComputationalIntelligence and Neuroscience vol 2019 Article ID 91284512 pages 2019


[10] R E Precup and R C David Nature-Inspired OptimizationAlgorithms for Fuzzy Controlled Servo Systems Butterworth-Heinemann Elsevier Oxford UK 2019

[11] A arwat and A E Hassanien ldquoQuantum-behaved particleswarm optimization for parameter optimization of supportvector machinerdquo Journal of Classification vol 36 no 3pp 1ndash23 2019

[12] A Strickler J A Prado Lima S R Vergilio and A T R PozoldquoDeriving products for variability test of feature models with ahyper-heuristic approachrdquo Applied Soft Computing vol 49pp 1232ndash1242 2016

[13] I La Fe-Perdomo G Beruvides R Quiza R Haber andM Rivas ldquoAutomatic selection of optimal parameters basedon simple soft-computing methods a case study of micro-milling processesrdquo IEEE Transactions on Industrial Infor-matics vol 15 no 2 pp 800ndash811 2019

[14] F Castano G Beruvides R Haber and A Artuntildeedo ldquoOb-stacle recognition based onmachine learning for on-chip lidarsensors in a cyber-physical systemrdquo Sensors vol 17 no 92017

[15] P Cowling G Kendall and E Soubeiga ldquoA hyper-heuristicapproach to scheduling a sales summitrdquo in Proceedings of theInternational Conference on the Practice and lteory of Au-tomated Timetabling Konstanz Germany August 2000

[16] E K Burke M Gendreau M Hyde et al ldquoHyper-heuristics asurvey of the state of the artrdquo Journal of the OperationalResearch Society vol 12 no 64 pp 1695ndash1724 2013

[17] G Beruvides R Quiza and R E Haber ldquoMulti-objectiveoptimization based on an improved cross-entropy method acase study of a micro-scale manufacturing processrdquo Infor-mation Sciences vol 334-335 pp 161ndash173 2016

[18] M Maashi E O ash and G Kendall ldquoA multi-objectivehyper-heuristic based on choice functionrdquo Expert Systemswith Applications vol 41 no 9 pp 4475ndash4493 2014

[19] M Maashi G Kendall and E O nda ldquoChoice function basedhyper-heuristics for multi-objective optimizationrdquo AppliedSoft Computing vol 28 pp 312ndash326 2015

[20] G Guizzo G Fritsche S Vergilio et al A Hyper-Heuristic fortheMulti-Objective Integration and Test Order Problem ACMNew York NY USA 2015

[21] Website of the Government of Japan Factors Contributing toFuel Consumption and Carbon Dioxide Emission of PassengerCars 2010

[22] Y Xiao Q Zhao I Kaku and Y Xu ldquoDevelopment of a fuelconsumption optimization model for the capacitated vehiclerouting problemrdquo Computers amp Operations Research vol 39no 7 pp 1419ndash1431 2012

[23] J T Qi ldquoStudy on distribution vehicle routing problem ofcold chain logistics for urban agricultural productsrdquo Journalof Zhejiang Sci-Tech University 2016 in Chinese

[24] J Fu ldquoStudy on distribution routing optimization of urbancold chain logisticsrdquo Journal of Dalian University of Tech-nology 2016 in Chinese

[25] Y Gao ldquoStudy and application of non-dominated sortinggenetic algorithm (NSGA)rdquo Journal of Zhejiang University2006 in Chinese

[26] K Deb A Pratap S Agarwal and T Meyarivan ldquoA fast andelitist multiobjective genetic algorithm NSGA-IIrdquo IEEETransactions on Evolutionary Computation vol 6 no 2pp 182ndash197 2002

[27] S Wang Y W Zhao L L Leng et al ldquoAnt colony-basedselection hyper-heuristic for low-carbon location-routingrdquoComputer Integrated Manufacturing System pp 1ndash27 Inpress

[28] Y W Zhao L L Leng S Wang et al ldquoSolving heterogeneousfleet low-carbon location-routing problem by evolutionaryhyper-heuristicrdquo Control and Decision pp 1ndash15 In press

[29] L L Leng Y W Zhao Z Wang H Wang and J ZhangldquoShared mechanism-based self-adaptive hyperheuristic forregional low-carbon location-routing problem with timewindowsrdquo Mathematical Problems in Engineering vol 2018Article ID 8987402 21 pages 2018

[30] Y W Zhao L L Leng and C M Zhang ldquoA novel frameworkof hyper-heuristic approach and its application in location-routing problem with simultaneous pickup and deliveryrdquoOperational Research 2019

[31] L Leng Y Zhao Z Wang J Zhang W Wang and C ZhangldquoA novel hyper-heuristic for the biobjective regional low-carbon location-routing problem with multiple constraintsrdquoSustainability vol 11 no 6 p 1596 2019

[32] L Leng Y Zhao J Zhang and C Zhang ldquoAn effective ap-proach for the multiobjective regional low-carbon location-routing problemrdquo International Journal of EnvironmentalResearch and Public Health vol 16 no 11 p 2064 2019

[33] R H Guerra R Quiza A Villalonga J Arenas andF Castano ldquoDigital twin-based optimization for ultrapreci-sion motion systems with backlash and frictionrdquo IEEE Accessvol 7 pp 93462ndash93472 2019


Computer Games Technology

International Journal of

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Advances in

FuzzySystems


Volume 2018


ReconfigurableComputing



Applied Computational Intelligence and Soft Computing

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Hindawiwwwhindawicom Volumethinsp2018


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wwwhindawicom Volume 2018

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Multimedia


Biomedical Imaging



Engineering Mathematics


RoboticsJournal of



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Mathematical Problems in Engineering

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

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Human-ComputerInteraction

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Submit your manuscripts atwwwhindawicom

timeliness Moreover there are a dearth of literatures onLRP-based models for cold chain logistics Wang et al [1]proposed developing a single-objective model in consider-ation of carbon emission for cold chain logistics and solvingit using hybrid genetic algorithm However logistics net-work timeliness has not yet been considered

Hence in this paper properties of cold chain logistics areconsidered from the perspective of LRP-based model notonly economic and environmental benefits but also distri-bution timeliness are taken into account thereby a bio-bjective LRP of cold chain logistics considering fuelconsumption and distribution period is proposed and onemultiobjective hyperheuristic (MOHH) is proposed tomodel and solve this problem erefore main contribu-tions of this paper are described as follows

(i) Problem model with logistics cost and distributionperiod as objective functions a multiobjectivemathematical model for cold chain logistics is de-veloped considering environmental benefit arisingfrom fuel consumption and social benefits likecustomer satisfaction arising from customer timewindow

(ii) Solution algorithm for the above model MOHH isdesigned Based on the framework nature ofhyperheuristics four selection strategies for low-level heuristics (LLHs) and four solution acceptancecriteria are proposed

(iii) Management suggestions and comments based onexperimental results several insights and sugges-tions about logistics distribution are provided frommanagement perspective

2 Methodology

21 Multiobjective Optimization Problem (MOP) One typ-ical MOP normally contains more than 2 conflicting orcontradictory objectives and is also called multicriteriaoptimization problem [7] Without loss of generality oneminimized MOP having D-dimensional decision variablesand m-dimensional subobjectives can be expressed as

minXisinΩ

F(X) f1(X) f2(X) fm(X)( 1113857T

stgi(X) le 0 i 1 2 q

hi(X) 0 i 1 2 p1113896

(1)

where X (x1 x2 x D) isin RD is a D-dimensional de-cision vector and F(X) isin Rm is an m-dimensional objectivevector defining m mapping functions of decision spacetowards objective space RD and Rm are decision space andobjective space respectively gi(X)le 0(i 1 2 q) are qinequality constraints and hi(X) 0 (i 1 2 p) are pequality constraints

On this basis the following related definitions are given [7]

Definition 1 (feasible solution) For one X isinRD if twoclasses of constraints in equation (1) are satisfied then X willbe deemed as a feasible solution

Definition 2 (feasible solution set) A set of all feasible so-lutions is referred to as feasible solution set that is Xf

Definition 3 (Pareto dominant) Suppose thatXA andXB aretwo feasible solutions in the feasible solution set When andonly when the following constraints are satisfied

foralli 1 2 m fi XA( 1113857lefi XB( 1113857

existj 1 2 m fj XA( 1113857ltfj XB( 1113857

⎧⎨

⎩ (2)

where XA dominate XB in other words compared with XBXA is a Pareto dominant which can be expressed asXB≻XA

Definition 4 (Pareto optimal solution) One solutionXlowast isin Xf is referred to as Pareto optimal solution (ornondominated solution) when and only when the followingcondition is satisfied

existX isin Xf X≻Xlowast (3)

Definition 5 (Pareto optimal solution set) As a set of allPareto optimal solutions Pareto optimal solution set isdefined as follows

Plowast ≜ Xlowast |existX isin Xf X≻Xlowast1113966 1113967 (4)

Definition 6 (Pareto front) A curved surface composed ofobjective function values corresponding to all Pareto opti-mal solutions in Pareto optimal solution set Plowast is calledPareto front and denoted as PFlowast

PFlowast ≜ F Xlowast( 1113857 f1 Xlowast( 1113857 f2 Xlowast( 1113857 fm X

lowast( 1113857( 1113857

T|Xlowast isin P

lowast1113966 1113967

(5)

22 Hyperheuristics Metaheuristics (eg grey wolf opti-mization algorithm [8] nature-inspired optimization algo-rithm [9 10] and quantum-behaved particle swarmoptimization [11]) have been widely applied in optimizationproblems However to find solutions of bespoke nature in anew problem-based domain it takes huge efforts andlengthy time to have a good command of effectiveness ofdomain operator combination [12] Moreover it is difficultto select the promising optimal parameters [13] Althoughthe machine learning methods have also been used to solvethe above dilemmas such as obstacle recognition based onmachine learning [14] this paper focuses on the anotherstrategy namely hyperheuristics which are capable ofsolving the above problems effectively Cowling et al [15]defined ldquohyperheuristicrdquo as ldquoheuristics to choose heuristicsrdquofor the first time Later Burke et al [16] expanded itsdefinition (i) heuristic selection and (ii) heuristic genera-tion erefore selection of optional LLHs is generallydecided from indicators of spread or convergence for acandidate solution versus parent solution As known fromthe above literature an LLH can be defined as an operator(crossover or mutation operator) or a metaheuristic (eg























ρ M1( ) α M0 +M1( ) + b (6)



CV (7)



Pool of LLHs

hellip

LLH1 LLH2 LLH3 LLHn

Dom

ain

barr

ier

Selection strategy

ChooseLLH

ImplementLLH

Scurrent

Acceptance criteria

Accept

Yes

No

Stop

Yes

Return Sbest

No




Scurrent Sprev








iisinN1113944jisinN

1113944kisinK

FCijk (9)



lqm ΔQQ0


(10)


C2 1113944iisinN

1113944jisinN

1113944kisinK


1113876 1113877

⎧⎪⎨

⎪⎩

⎫⎪⎬

⎪⎭times 100 (11)





H1 R1S T minus T0( 1113857 (13)


H2 R2Sd T minus T0( 1113857 (14)



1113944jisinN

1113944kisinK

dij

vij


1113944kisinK

wiyik⎛⎝ ⎞⎠ (15)


C3 φ 1113944iisinN

1113944jisinN

1113944kisinK

xijkdij (16)



Pk(i)


0 ETi leATik le LTi


⎧⎪⎪⎨

⎪⎪⎩(17)




C5 1113944iisinNC

1113944kisinK

Pk(i) (18)


C6 1113944iisinND

OiYi (19)


minCost C1 + C2 + C3 + C4 + C5 + C6 (20)

minTT maxiisinK

Ti1113864 1113865 (21)

1113944iisinN


1113944iisinN



1113944jisinND



1113944iisinNC




(27)

1113944iisinNC

1113944kisinND


1113944iisinNC

1113944jisinN

Dixijk leCV (29)


(30)





241 Problem Domain



















f1 1113944n


Tn LLHj1113872 1113873 (32)




f2 LLHk LLHj1113872 1113873 1113944n


Tn LLHk LLHj1113872 1113873 (33)



f3 LLHj1113872 1113873 τ LLHj1113872 1113873 (34)



(35)





















S 1n

1113944

n

i1d minus di1113872 1113873

2⎡⎣ ⎤⎦12

(36)



D

1113944

n

i1max x

it minus y

it

11139741113972

(37)

where xit minus yi


t and yit





Min Max Min Max

AS

AM 4 11522 12562 139785 166466GD 7 11037 14449 145240 161055OI 5 10452 11388 144198 148493SA 5 10584 11312 142343 160760

CF

AM 4 10853 11242 147482 163772GD 5 10726 12257 149758 163792OI 4 10689 12067 152179 161707SA 6 11133 11492 149411 164242

SR

AM 4 10582 11092 138572 153454GD 3 12764 13230 176301 197800OI 3 10418 11830 134790 145900SA 5 10610 12118 145880 157087

TS

AM 6 10563 11866 141474 146421GD 5 11450 12150 148005 174159OI 6 12222 14375 164531 192463SA 7 10426 11723 133167 133167



AS

AM 4 1473 978GD 7 2067 1010OI 5 1347 468SA 5 1556 902

CF

AM 4 6294 786GD 5 3930 806OI 4 2921 588SA 6 3030 840

SR

AM 4 4248 815GD 3 3159 765OI 3 291 568SA 5 2696 717

TS

AM 6 589 570GD 5 1341 1053OI 5 2179 1149SA 7 263 1011











14

15

16

17Lo

gisti

cs co

st (Y

uan)

times104

SAOI

GDAM

(a)


times104

SAOI

GDAM

1050 1100 1150 1200 1250145

15

155

16

165

Logi

stics

cost

(Yua

n)

(b)

times104

SAOI

GDAM


12

14

16

18

2

Logi

stics

cost

(Yua

n)

(c)

times104

SAOI

GDAM


12

14

16

18

2

Logi

stics

cost

(Yua

n)

(d)



LLH1

LLH2

LLH3

LLH4

LLH5

LLH6

LLH7 LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(a)

LLH1

LLH2

LLH3

LLH4

LLH5

LLH6 LLH7

LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(b)

LLH1

LLH2

LLH3

LLH4

LLH5

LLH6LLH7

LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(c)

LLH1

LLH2

LLH3

LLH4

LLH5

LLH6LLH7

LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(d)



0

02

04

06

08

1

Acce

ptan

ce ra

te (

)

1 2 3 4 5 6 7 8 9

(a)

0

02

04

06

08

1

Acce

ptan

ce ra

te (

)


1 2 3 4 5 6 7 8 9

(b)

Figure 4 Continued







Acce

ptan

ce ra

te (

)

0

02

04

06

08

1


1 2 3 4 5 6 7 8 9

(c)

Acce

ptan

ce ra

te (

)

0

02

04

06

08

1


1 2 3 4 5 6 7 8 9

(d)




Min Max Min Max

R101 MOHH 6 12221 13743 165230 184790NSGA-II 5 20457 23435 174105 182155

R102 MOHH 6 11938 13390 165251 182082NSGA-II 6 21139 22227 168680 174992

R103 MOHH 5 11792 13360 163107 181646NSGA-II 4 21733 22417 169208 189293

R104 MOHH 5 11660 12628 161086 188263NSGA-II 3 21273 21499 195527 199156

R105 MOHH 5 11573 13016 169270 174440NSGA-II 4 21372 22227 177605 184762

R106 MOHH 6 12078 12889 157142 162353NSGA-II 5 22488 26034 170070 173938

R107 MOHH 6 11788 13127 155009 172504NSGA-II 5 21064 21346 153680 160416

R108 MOHH 3 11350 11841 138182 150531NSGA-II 5 21352 24724 156000 160385

R109 MOHH 5 12294 14060 163585 188892NSGA-II 4 20533 23831 153025 159328









R101 MOHH 6 538 1011NSGA-II 5 569 772

R102 MOHH 6 943 909NSGA-II 6 792 600

R103 MOHH 5 227 949NSGA-II 4 763 896

R104 MOHH 5 603 1106NSGA-II 3 812 322

R105 MOHH 5 490 522NSGA-II 4 313 538

R106 MOHH 6 549 635NSGA-II 5 1624 523

R107 MOHH 6 1075 978NSGA-II 5 1118 529

R108 MOHH 3 709 618NSGA-II 5 835 602

R109 MOHH 5 732 1060NSGA-II 4 325 592











Timewindows

1 (12021793630296719) 08 03 [00 20]

2 (12020197730263709) 11 03 [10 20]

3 (12012365230290270) 08 03 [00 20]

4 (12021721930206380) 13 03 [30 50]

5 (12019046130341832) 11 03 [30 50]

6 (12016980430282714) 13 03 [30 60]

7 (12004603530263151) 06 03 [20 50]

8 (12019580730185674) 09 03 [30 60]

9 (12023408830197576) 05 03 [40 60]

10 (12027250130334870) 13 03 [20 40]

11 (12012560530313614) 13 03 [30 60]

12 (12010261130300304) 09 03 [20 40]

13 (12028487030150627) 14 03 [10 40]

14 (12018265730264054) 12 03 [00 20]

15 (12016685330269039) 05 03 [20 40]

16 (12020795330249617) 12 03 [30 50]

17 (12028205530169434) 11 03 [10 30]

18 (12015692330280374) 07 03 [30 50]

19 (12017424230196310) 12 03 [00 20]

20 (12017628530219921) 19 03 [20 60]

21 (12009314230340724) 15 03 [30 50]

22 (12023274430209315) 16 03 [05 20]

23 (12017831930283681) 08 03 [10 20]

24 (12020110930208160) 06 03 [10 30]

Table 6 Continued


Timewindows

25 (12019133830355956) 16 03 [30 60]

26 (12018004930252984) 14 03 [05 20]

27 (12016630330309546) 05 03 [10 30]

28 (12023847230358900) 08 03 [30 60]

29 (12017722530249727) 11 03 [05 20]

30 (12022001730315313) 14 03 [10 30]



04

06

08

1

12

14

16

18

2

22

24

Tota

l cos

t (Yu

an)

times104

2 3 4 5 6

7 8 9 10 11 12

1




LLH1

LLH2

LLH3

LLH4

LLH5

LLH6

LLH7 LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(a)


1 2 3 4 5 6 7 8 90

02

01

04

03

06

05

08

07

09

1

Acce

ptan

ce ra

te (

)

(b)





4 Conclusions





Data Availability




Acknowledgments


References









































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in

























ρ M1( ) α M0 +M1( ) + b (6)



CV (7)



Pool of LLHs

hellip

LLH1 LLH2 LLH3 LLHn

Dom

ain

barr

ier

Selection strategy

ChooseLLH

ImplementLLH

Scurrent

Acceptance criteria

Accept

Yes

No

Stop

Yes

Return Sbest

No




Scurrent Sprev








iisinN1113944jisinN

1113944kisinK

FCijk (9)



lqm ΔQQ0


(10)


C2 1113944iisinN

1113944jisinN

1113944kisinK


1113876 1113877

⎧⎪⎨

⎪⎩

⎫⎪⎬

⎪⎭times 100 (11)





H1 R1S T minus T0( 1113857 (13)


H2 R2Sd T minus T0( 1113857 (14)



1113944jisinN

1113944kisinK

dij

vij


1113944kisinK

wiyik⎛⎝ ⎞⎠ (15)


C3 φ 1113944iisinN

1113944jisinN

1113944kisinK

xijkdij (16)



Pk(i)


0 ETi leATik le LTi


⎧⎪⎪⎨

⎪⎪⎩(17)




C5 1113944iisinNC

1113944kisinK

Pk(i) (18)


C6 1113944iisinND

OiYi (19)


minCost C1 + C2 + C3 + C4 + C5 + C6 (20)

minTT maxiisinK

Ti1113864 1113865 (21)

1113944iisinN


1113944iisinN



1113944jisinND



1113944iisinNC




(27)

1113944iisinNC

1113944kisinND


1113944iisinNC

1113944jisinN

Dixijk leCV (29)


(30)





241 Problem Domain



















f1 1113944n


Tn LLHj1113872 1113873 (32)




f2 LLHk LLHj1113872 1113873 1113944n


Tn LLHk LLHj1113872 1113873 (33)



f3 LLHj1113872 1113873 τ LLHj1113872 1113873 (34)



(35)





















S 1n

1113944

n

i1d minus di1113872 1113873

2⎡⎣ ⎤⎦12

(36)



D

1113944

n

i1max x

it minus y

it

11139741113972

(37)

where xit minus yi


t and yit





Min Max Min Max

AS

AM 4 11522 12562 139785 166466GD 7 11037 14449 145240 161055OI 5 10452 11388 144198 148493SA 5 10584 11312 142343 160760

CF

AM 4 10853 11242 147482 163772GD 5 10726 12257 149758 163792OI 4 10689 12067 152179 161707SA 6 11133 11492 149411 164242

SR

AM 4 10582 11092 138572 153454GD 3 12764 13230 176301 197800OI 3 10418 11830 134790 145900SA 5 10610 12118 145880 157087

TS

AM 6 10563 11866 141474 146421GD 5 11450 12150 148005 174159OI 6 12222 14375 164531 192463SA 7 10426 11723 133167 133167



AS

AM 4 1473 978GD 7 2067 1010OI 5 1347 468SA 5 1556 902

CF

AM 4 6294 786GD 5 3930 806OI 4 2921 588SA 6 3030 840

SR

AM 4 4248 815GD 3 3159 765OI 3 291 568SA 5 2696 717

TS

AM 6 589 570GD 5 1341 1053OI 5 2179 1149SA 7 263 1011











14

15

16

17Lo

gisti

cs co

st (Y

uan)

times104

SAOI

GDAM

(a)


times104

SAOI

GDAM

1050 1100 1150 1200 1250145

15

155

16

165

Logi

stics

cost

(Yua

n)

(b)

times104

SAOI

GDAM


12

14

16

18

2

Logi

stics

cost

(Yua

n)

(c)

times104

SAOI

GDAM


12

14

16

18

2

Logi

stics

cost

(Yua

n)

(d)



LLH1

LLH2

LLH3

LLH4

LLH5

LLH6

LLH7 LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(a)

LLH1

LLH2

LLH3

LLH4

LLH5

LLH6 LLH7

LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(b)

LLH1

LLH2

LLH3

LLH4

LLH5

LLH6LLH7

LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(c)

LLH1

LLH2

LLH3

LLH4

LLH5

LLH6LLH7

LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(d)



0

02

04

06

08

1

Acce

ptan

ce ra

te (

)

1 2 3 4 5 6 7 8 9

(a)

0

02

04

06

08

1

Acce

ptan

ce ra

te (

)


1 2 3 4 5 6 7 8 9

(b)

Figure 4 Continued







Acce

ptan

ce ra

te (

)

0

02

04

06

08

1


1 2 3 4 5 6 7 8 9

(c)

Acce

ptan

ce ra

te (

)

0

02

04

06

08

1


1 2 3 4 5 6 7 8 9

(d)




Min Max Min Max

R101 MOHH 6 12221 13743 165230 184790NSGA-II 5 20457 23435 174105 182155

R102 MOHH 6 11938 13390 165251 182082NSGA-II 6 21139 22227 168680 174992

R103 MOHH 5 11792 13360 163107 181646NSGA-II 4 21733 22417 169208 189293

R104 MOHH 5 11660 12628 161086 188263NSGA-II 3 21273 21499 195527 199156

R105 MOHH 5 11573 13016 169270 174440NSGA-II 4 21372 22227 177605 184762

R106 MOHH 6 12078 12889 157142 162353NSGA-II 5 22488 26034 170070 173938

R107 MOHH 6 11788 13127 155009 172504NSGA-II 5 21064 21346 153680 160416

R108 MOHH 3 11350 11841 138182 150531NSGA-II 5 21352 24724 156000 160385

R109 MOHH 5 12294 14060 163585 188892NSGA-II 4 20533 23831 153025 159328









R101 MOHH 6 538 1011NSGA-II 5 569 772

R102 MOHH 6 943 909NSGA-II 6 792 600

R103 MOHH 5 227 949NSGA-II 4 763 896

R104 MOHH 5 603 1106NSGA-II 3 812 322

R105 MOHH 5 490 522NSGA-II 4 313 538

R106 MOHH 6 549 635NSGA-II 5 1624 523

R107 MOHH 6 1075 978NSGA-II 5 1118 529

R108 MOHH 3 709 618NSGA-II 5 835 602

R109 MOHH 5 732 1060NSGA-II 4 325 592











Timewindows

1 (12021793630296719) 08 03 [00 20]

2 (12020197730263709) 11 03 [10 20]

3 (12012365230290270) 08 03 [00 20]

4 (12021721930206380) 13 03 [30 50]

5 (12019046130341832) 11 03 [30 50]

6 (12016980430282714) 13 03 [30 60]

7 (12004603530263151) 06 03 [20 50]

8 (12019580730185674) 09 03 [30 60]

9 (12023408830197576) 05 03 [40 60]

10 (12027250130334870) 13 03 [20 40]

11 (12012560530313614) 13 03 [30 60]

12 (12010261130300304) 09 03 [20 40]

13 (12028487030150627) 14 03 [10 40]

14 (12018265730264054) 12 03 [00 20]

15 (12016685330269039) 05 03 [20 40]

16 (12020795330249617) 12 03 [30 50]

17 (12028205530169434) 11 03 [10 30]

18 (12015692330280374) 07 03 [30 50]

19 (12017424230196310) 12 03 [00 20]

20 (12017628530219921) 19 03 [20 60]

21 (12009314230340724) 15 03 [30 50]

22 (12023274430209315) 16 03 [05 20]

23 (12017831930283681) 08 03 [10 20]

24 (12020110930208160) 06 03 [10 30]

Table 6 Continued


Timewindows

25 (12019133830355956) 16 03 [30 60]

26 (12018004930252984) 14 03 [05 20]

27 (12016630330309546) 05 03 [10 30]

28 (12023847230358900) 08 03 [30 60]

29 (12017722530249727) 11 03 [05 20]

30 (12022001730315313) 14 03 [10 30]



04

06

08

1

12

14

16

18

2

22

24

Tota

l cos

t (Yu

an)

times104

2 3 4 5 6

7 8 9 10 11 12

1




LLH1

LLH2

LLH3

LLH4

LLH5

LLH6

LLH7 LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(a)


1 2 3 4 5 6 7 8 90

02

01

04

03

06

05

08

07

09

1

Acce

ptan

ce ra

te (

)

(b)





4 Conclusions





Data Availability




Acknowledgments


References









































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in












ρ M1( ) α M0 +M1( ) + b (6)



CV (7)



Pool of LLHs

hellip

LLH1 LLH2 LLH3 LLHn

Dom

ain

barr

ier

Selection strategy

ChooseLLH

ImplementLLH

Scurrent

Acceptance criteria

Accept

Yes

No

Stop

Yes

Return Sbest

No




Scurrent Sprev








iisinN1113944jisinN

1113944kisinK

FCijk (9)



lqm ΔQQ0


(10)


C2 1113944iisinN

1113944jisinN

1113944kisinK


1113876 1113877

⎧⎪⎨

⎪⎩

⎫⎪⎬

⎪⎭times 100 (11)





H1 R1S T minus T0( 1113857 (13)


H2 R2Sd T minus T0( 1113857 (14)



1113944jisinN

1113944kisinK

dij

vij


1113944kisinK

wiyik⎛⎝ ⎞⎠ (15)


C3 φ 1113944iisinN

1113944jisinN

1113944kisinK

xijkdij (16)



Pk(i)


0 ETi leATik le LTi


⎧⎪⎪⎨

⎪⎪⎩(17)




C5 1113944iisinNC

1113944kisinK

Pk(i) (18)


C6 1113944iisinND

OiYi (19)


minCost C1 + C2 + C3 + C4 + C5 + C6 (20)

minTT maxiisinK

Ti1113864 1113865 (21)

1113944iisinN


1113944iisinN



1113944jisinND



1113944iisinNC




(27)

1113944iisinNC

1113944kisinND


1113944iisinNC

1113944jisinN

Dixijk leCV (29)


(30)





241 Problem Domain



















f1 1113944n


Tn LLHj1113872 1113873 (32)




f2 LLHk LLHj1113872 1113873 1113944n


Tn LLHk LLHj1113872 1113873 (33)



f3 LLHj1113872 1113873 τ LLHj1113872 1113873 (34)



(35)





















S 1n

1113944

n

i1d minus di1113872 1113873

2⎡⎣ ⎤⎦12

(36)



D

1113944

n

i1max x

it minus y

it

11139741113972

(37)

where xit minus yi


t and yit





Min Max Min Max

AS

AM 4 11522 12562 139785 166466GD 7 11037 14449 145240 161055OI 5 10452 11388 144198 148493SA 5 10584 11312 142343 160760

CF

AM 4 10853 11242 147482 163772GD 5 10726 12257 149758 163792OI 4 10689 12067 152179 161707SA 6 11133 11492 149411 164242

SR

AM 4 10582 11092 138572 153454GD 3 12764 13230 176301 197800OI 3 10418 11830 134790 145900SA 5 10610 12118 145880 157087

TS

AM 6 10563 11866 141474 146421GD 5 11450 12150 148005 174159OI 6 12222 14375 164531 192463SA 7 10426 11723 133167 133167



AS

AM 4 1473 978GD 7 2067 1010OI 5 1347 468SA 5 1556 902

CF

AM 4 6294 786GD 5 3930 806OI 4 2921 588SA 6 3030 840

SR

AM 4 4248 815GD 3 3159 765OI 3 291 568SA 5 2696 717

TS

AM 6 589 570GD 5 1341 1053OI 5 2179 1149SA 7 263 1011











14

15

16

17Lo

gisti

cs co

st (Y

uan)

times104

SAOI

GDAM

(a)


times104

SAOI

GDAM

1050 1100 1150 1200 1250145

15

155

16

165

Logi

stics

cost

(Yua

n)

(b)

times104

SAOI

GDAM


12

14

16

18

2

Logi

stics

cost

(Yua

n)

(c)

times104

SAOI

GDAM


12

14

16

18

2

Logi

stics

cost

(Yua

n)

(d)



LLH1

LLH2

LLH3

LLH4

LLH5

LLH6

LLH7 LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(a)

LLH1

LLH2

LLH3

LLH4

LLH5

LLH6 LLH7

LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(b)

LLH1

LLH2

LLH3

LLH4

LLH5

LLH6LLH7

LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(c)

LLH1

LLH2

LLH3

LLH4

LLH5

LLH6LLH7

LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(d)



0

02

04

06

08

1

Acce

ptan

ce ra

te (

)

1 2 3 4 5 6 7 8 9

(a)

0

02

04

06

08

1

Acce

ptan

ce ra

te (

)


1 2 3 4 5 6 7 8 9

(b)

Figure 4 Continued







Acce

ptan

ce ra

te (

)

0

02

04

06

08

1


1 2 3 4 5 6 7 8 9

(c)

Acce

ptan

ce ra

te (

)

0

02

04

06

08

1


1 2 3 4 5 6 7 8 9

(d)




Min Max Min Max

R101 MOHH 6 12221 13743 165230 184790NSGA-II 5 20457 23435 174105 182155

R102 MOHH 6 11938 13390 165251 182082NSGA-II 6 21139 22227 168680 174992

R103 MOHH 5 11792 13360 163107 181646NSGA-II 4 21733 22417 169208 189293

R104 MOHH 5 11660 12628 161086 188263NSGA-II 3 21273 21499 195527 199156

R105 MOHH 5 11573 13016 169270 174440NSGA-II 4 21372 22227 177605 184762

R106 MOHH 6 12078 12889 157142 162353NSGA-II 5 22488 26034 170070 173938

R107 MOHH 6 11788 13127 155009 172504NSGA-II 5 21064 21346 153680 160416

R108 MOHH 3 11350 11841 138182 150531NSGA-II 5 21352 24724 156000 160385

R109 MOHH 5 12294 14060 163585 188892NSGA-II 4 20533 23831 153025 159328









R101 MOHH 6 538 1011NSGA-II 5 569 772

R102 MOHH 6 943 909NSGA-II 6 792 600

R103 MOHH 5 227 949NSGA-II 4 763 896

R104 MOHH 5 603 1106NSGA-II 3 812 322

R105 MOHH 5 490 522NSGA-II 4 313 538

R106 MOHH 6 549 635NSGA-II 5 1624 523

R107 MOHH 6 1075 978NSGA-II 5 1118 529

R108 MOHH 3 709 618NSGA-II 5 835 602

R109 MOHH 5 732 1060NSGA-II 4 325 592











Timewindows

1 (12021793630296719) 08 03 [00 20]

2 (12020197730263709) 11 03 [10 20]

3 (12012365230290270) 08 03 [00 20]

4 (12021721930206380) 13 03 [30 50]

5 (12019046130341832) 11 03 [30 50]

6 (12016980430282714) 13 03 [30 60]

7 (12004603530263151) 06 03 [20 50]

8 (12019580730185674) 09 03 [30 60]

9 (12023408830197576) 05 03 [40 60]

10 (12027250130334870) 13 03 [20 40]

11 (12012560530313614) 13 03 [30 60]

12 (12010261130300304) 09 03 [20 40]

13 (12028487030150627) 14 03 [10 40]

14 (12018265730264054) 12 03 [00 20]

15 (12016685330269039) 05 03 [20 40]

16 (12020795330249617) 12 03 [30 50]

17 (12028205530169434) 11 03 [10 30]

18 (12015692330280374) 07 03 [30 50]

19 (12017424230196310) 12 03 [00 20]

20 (12017628530219921) 19 03 [20 60]

21 (12009314230340724) 15 03 [30 50]

22 (12023274430209315) 16 03 [05 20]

23 (12017831930283681) 08 03 [10 20]

24 (12020110930208160) 06 03 [10 30]

Table 6 Continued


Timewindows

25 (12019133830355956) 16 03 [30 60]

26 (12018004930252984) 14 03 [05 20]

27 (12016630330309546) 05 03 [10 30]

28 (12023847230358900) 08 03 [30 60]

29 (12017722530249727) 11 03 [05 20]

30 (12022001730315313) 14 03 [10 30]



04

06

08

1

12

14

16

18

2

22

24

Tota

l cos

t (Yu

an)

times104

2 3 4 5 6

7 8 9 10 11 12

1




LLH1

LLH2

LLH3

LLH4

LLH5

LLH6

LLH7 LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(a)


1 2 3 4 5 6 7 8 90

02

01

04

03

06

05

08

07

09

1

Acce

ptan

ce ra

te (

)

(b)





4 Conclusions





Data Availability




Acknowledgments


References









































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in







iisinN1113944jisinN

1113944kisinK

FCijk (9)



lqm ΔQQ0


(10)


C2 1113944iisinN

1113944jisinN

1113944kisinK


1113876 1113877

⎧⎪⎨

⎪⎩

⎫⎪⎬

⎪⎭times 100 (11)





H1 R1S T minus T0( 1113857 (13)


H2 R2Sd T minus T0( 1113857 (14)



1113944jisinN

1113944kisinK

dij

vij


1113944kisinK

wiyik⎛⎝ ⎞⎠ (15)


C3 φ 1113944iisinN

1113944jisinN

1113944kisinK

xijkdij (16)



Pk(i)


0 ETi leATik le LTi


⎧⎪⎪⎨

⎪⎪⎩(17)




C5 1113944iisinNC

1113944kisinK

Pk(i) (18)


C6 1113944iisinND

OiYi (19)


minCost C1 + C2 + C3 + C4 + C5 + C6 (20)

minTT maxiisinK

Ti1113864 1113865 (21)

1113944iisinN


1113944iisinN



1113944jisinND



1113944iisinNC




(27)

1113944iisinNC

1113944kisinND


1113944iisinNC

1113944jisinN

Dixijk leCV (29)


(30)





241 Problem Domain



















f1 1113944n


Tn LLHj1113872 1113873 (32)




f2 LLHk LLHj1113872 1113873 1113944n


Tn LLHk LLHj1113872 1113873 (33)



f3 LLHj1113872 1113873 τ LLHj1113872 1113873 (34)



(35)





















S 1n

1113944

n

i1d minus di1113872 1113873

2⎡⎣ ⎤⎦12

(36)



D

1113944

n

i1max x

it minus y

it

11139741113972

(37)

where xit minus yi


t and yit





Min Max Min Max

AS

AM 4 11522 12562 139785 166466GD 7 11037 14449 145240 161055OI 5 10452 11388 144198 148493SA 5 10584 11312 142343 160760

CF

AM 4 10853 11242 147482 163772GD 5 10726 12257 149758 163792OI 4 10689 12067 152179 161707SA 6 11133 11492 149411 164242

SR

AM 4 10582 11092 138572 153454GD 3 12764 13230 176301 197800OI 3 10418 11830 134790 145900SA 5 10610 12118 145880 157087

TS

AM 6 10563 11866 141474 146421GD 5 11450 12150 148005 174159OI 6 12222 14375 164531 192463SA 7 10426 11723 133167 133167



AS

AM 4 1473 978GD 7 2067 1010OI 5 1347 468SA 5 1556 902

CF

AM 4 6294 786GD 5 3930 806OI 4 2921 588SA 6 3030 840

SR

AM 4 4248 815GD 3 3159 765OI 3 291 568SA 5 2696 717

TS

AM 6 589 570GD 5 1341 1053OI 5 2179 1149SA 7 263 1011











14

15

16

17Lo

gisti

cs co

st (Y

uan)

times104

SAOI

GDAM

(a)


times104

SAOI

GDAM

1050 1100 1150 1200 1250145

15

155

16

165

Logi

stics

cost

(Yua

n)

(b)

times104

SAOI

GDAM


12

14

16

18

2

Logi

stics

cost

(Yua

n)

(c)

times104

SAOI

GDAM


12

14

16

18

2

Logi

stics

cost

(Yua

n)

(d)



LLH1

LLH2

LLH3

LLH4

LLH5

LLH6

LLH7 LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(a)

LLH1

LLH2

LLH3

LLH4

LLH5

LLH6 LLH7

LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(b)

LLH1

LLH2

LLH3

LLH4

LLH5

LLH6LLH7

LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(c)

LLH1

LLH2

LLH3

LLH4

LLH5

LLH6LLH7

LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(d)



0

02

04

06

08

1

Acce

ptan

ce ra

te (

)

1 2 3 4 5 6 7 8 9

(a)

0

02

04

06

08

1

Acce

ptan

ce ra

te (

)


1 2 3 4 5 6 7 8 9

(b)

Figure 4 Continued







Acce

ptan

ce ra

te (

)

0

02

04

06

08

1


1 2 3 4 5 6 7 8 9

(c)

Acce

ptan

ce ra

te (

)

0

02

04

06

08

1


1 2 3 4 5 6 7 8 9

(d)




Min Max Min Max

R101 MOHH 6 12221 13743 165230 184790NSGA-II 5 20457 23435 174105 182155

R102 MOHH 6 11938 13390 165251 182082NSGA-II 6 21139 22227 168680 174992

R103 MOHH 5 11792 13360 163107 181646NSGA-II 4 21733 22417 169208 189293

R104 MOHH 5 11660 12628 161086 188263NSGA-II 3 21273 21499 195527 199156

R105 MOHH 5 11573 13016 169270 174440NSGA-II 4 21372 22227 177605 184762

R106 MOHH 6 12078 12889 157142 162353NSGA-II 5 22488 26034 170070 173938

R107 MOHH 6 11788 13127 155009 172504NSGA-II 5 21064 21346 153680 160416

R108 MOHH 3 11350 11841 138182 150531NSGA-II 5 21352 24724 156000 160385

R109 MOHH 5 12294 14060 163585 188892NSGA-II 4 20533 23831 153025 159328









R101 MOHH 6 538 1011NSGA-II 5 569 772

R102 MOHH 6 943 909NSGA-II 6 792 600

R103 MOHH 5 227 949NSGA-II 4 763 896

R104 MOHH 5 603 1106NSGA-II 3 812 322

R105 MOHH 5 490 522NSGA-II 4 313 538

R106 MOHH 6 549 635NSGA-II 5 1624 523

R107 MOHH 6 1075 978NSGA-II 5 1118 529

R108 MOHH 3 709 618NSGA-II 5 835 602

R109 MOHH 5 732 1060NSGA-II 4 325 592











Timewindows

1 (12021793630296719) 08 03 [00 20]

2 (12020197730263709) 11 03 [10 20]

3 (12012365230290270) 08 03 [00 20]

4 (12021721930206380) 13 03 [30 50]

5 (12019046130341832) 11 03 [30 50]

6 (12016980430282714) 13 03 [30 60]

7 (12004603530263151) 06 03 [20 50]

8 (12019580730185674) 09 03 [30 60]

9 (12023408830197576) 05 03 [40 60]

10 (12027250130334870) 13 03 [20 40]

11 (12012560530313614) 13 03 [30 60]

12 (12010261130300304) 09 03 [20 40]

13 (12028487030150627) 14 03 [10 40]

14 (12018265730264054) 12 03 [00 20]

15 (12016685330269039) 05 03 [20 40]

16 (12020795330249617) 12 03 [30 50]

17 (12028205530169434) 11 03 [10 30]

18 (12015692330280374) 07 03 [30 50]

19 (12017424230196310) 12 03 [00 20]

20 (12017628530219921) 19 03 [20 60]

21 (12009314230340724) 15 03 [30 50]

22 (12023274430209315) 16 03 [05 20]

23 (12017831930283681) 08 03 [10 20]

24 (12020110930208160) 06 03 [10 30]

Table 6 Continued


Timewindows

25 (12019133830355956) 16 03 [30 60]

26 (12018004930252984) 14 03 [05 20]

27 (12016630330309546) 05 03 [10 30]

28 (12023847230358900) 08 03 [30 60]

29 (12017722530249727) 11 03 [05 20]

30 (12022001730315313) 14 03 [10 30]



04

06

08

1

12

14

16

18

2

22

24

Tota

l cos

t (Yu

an)

times104

2 3 4 5 6

7 8 9 10 11 12

1




LLH1

LLH2

LLH3

LLH4

LLH5

LLH6

LLH7 LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(a)


1 2 3 4 5 6 7 8 90

02

01

04

03

06

05

08

07

09

1

Acce

ptan

ce ra

te (

)

(b)





4 Conclusions





Data Availability




Acknowledgments


References









































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in





C5 1113944iisinNC

1113944kisinK

Pk(i) (18)


C6 1113944iisinND

OiYi (19)


minCost C1 + C2 + C3 + C4 + C5 + C6 (20)

minTT maxiisinK

Ti1113864 1113865 (21)

1113944iisinN


1113944iisinN



1113944jisinND



1113944iisinNC




(27)

1113944iisinNC

1113944kisinND


1113944iisinNC

1113944jisinN

Dixijk leCV (29)


(30)





241 Problem Domain



















f1 1113944n


Tn LLHj1113872 1113873 (32)




f2 LLHk LLHj1113872 1113873 1113944n


Tn LLHk LLHj1113872 1113873 (33)



f3 LLHj1113872 1113873 τ LLHj1113872 1113873 (34)



(35)





















S 1n

1113944

n

i1d minus di1113872 1113873

2⎡⎣ ⎤⎦12

(36)



D

1113944

n

i1max x

it minus y

it

11139741113972

(37)

where xit minus yi


t and yit





Min Max Min Max

AS

AM 4 11522 12562 139785 166466GD 7 11037 14449 145240 161055OI 5 10452 11388 144198 148493SA 5 10584 11312 142343 160760

CF

AM 4 10853 11242 147482 163772GD 5 10726 12257 149758 163792OI 4 10689 12067 152179 161707SA 6 11133 11492 149411 164242

SR

AM 4 10582 11092 138572 153454GD 3 12764 13230 176301 197800OI 3 10418 11830 134790 145900SA 5 10610 12118 145880 157087

TS

AM 6 10563 11866 141474 146421GD 5 11450 12150 148005 174159OI 6 12222 14375 164531 192463SA 7 10426 11723 133167 133167



AS

AM 4 1473 978GD 7 2067 1010OI 5 1347 468SA 5 1556 902

CF

AM 4 6294 786GD 5 3930 806OI 4 2921 588SA 6 3030 840

SR

AM 4 4248 815GD 3 3159 765OI 3 291 568SA 5 2696 717

TS

AM 6 589 570GD 5 1341 1053OI 5 2179 1149SA 7 263 1011











14

15

16

17Lo

gisti

cs co

st (Y

uan)

times104

SAOI

GDAM

(a)


times104

SAOI

GDAM

1050 1100 1150 1200 1250145

15

155

16

165

Logi

stics

cost

(Yua

n)

(b)

times104

SAOI

GDAM


12

14

16

18

2

Logi

stics

cost

(Yua

n)

(c)

times104

SAOI

GDAM


12

14

16

18

2

Logi

stics

cost

(Yua

n)

(d)



LLH1

LLH2

LLH3

LLH4

LLH5

LLH6

LLH7 LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(a)

LLH1

LLH2

LLH3

LLH4

LLH5

LLH6 LLH7

LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(b)

LLH1

LLH2

LLH3

LLH4

LLH5

LLH6LLH7

LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(c)

LLH1

LLH2

LLH3

LLH4

LLH5

LLH6LLH7

LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(d)



0

02

04

06

08

1

Acce

ptan

ce ra

te (

)

1 2 3 4 5 6 7 8 9

(a)

0

02

04

06

08

1

Acce

ptan

ce ra

te (

)


1 2 3 4 5 6 7 8 9

(b)

Figure 4 Continued







Acce

ptan

ce ra

te (

)

0

02

04

06

08

1


1 2 3 4 5 6 7 8 9

(c)

Acce

ptan

ce ra

te (

)

0

02

04

06

08

1


1 2 3 4 5 6 7 8 9

(d)




Min Max Min Max

R101 MOHH 6 12221 13743 165230 184790NSGA-II 5 20457 23435 174105 182155

R102 MOHH 6 11938 13390 165251 182082NSGA-II 6 21139 22227 168680 174992

R103 MOHH 5 11792 13360 163107 181646NSGA-II 4 21733 22417 169208 189293

R104 MOHH 5 11660 12628 161086 188263NSGA-II 3 21273 21499 195527 199156

R105 MOHH 5 11573 13016 169270 174440NSGA-II 4 21372 22227 177605 184762

R106 MOHH 6 12078 12889 157142 162353NSGA-II 5 22488 26034 170070 173938

R107 MOHH 6 11788 13127 155009 172504NSGA-II 5 21064 21346 153680 160416

R108 MOHH 3 11350 11841 138182 150531NSGA-II 5 21352 24724 156000 160385

R109 MOHH 5 12294 14060 163585 188892NSGA-II 4 20533 23831 153025 159328









R101 MOHH 6 538 1011NSGA-II 5 569 772

R102 MOHH 6 943 909NSGA-II 6 792 600

R103 MOHH 5 227 949NSGA-II 4 763 896

R104 MOHH 5 603 1106NSGA-II 3 812 322

R105 MOHH 5 490 522NSGA-II 4 313 538

R106 MOHH 6 549 635NSGA-II 5 1624 523

R107 MOHH 6 1075 978NSGA-II 5 1118 529

R108 MOHH 3 709 618NSGA-II 5 835 602

R109 MOHH 5 732 1060NSGA-II 4 325 592











Timewindows

1 (12021793630296719) 08 03 [00 20]

2 (12020197730263709) 11 03 [10 20]

3 (12012365230290270) 08 03 [00 20]

4 (12021721930206380) 13 03 [30 50]

5 (12019046130341832) 11 03 [30 50]

6 (12016980430282714) 13 03 [30 60]

7 (12004603530263151) 06 03 [20 50]

8 (12019580730185674) 09 03 [30 60]

9 (12023408830197576) 05 03 [40 60]

10 (12027250130334870) 13 03 [20 40]

11 (12012560530313614) 13 03 [30 60]

12 (12010261130300304) 09 03 [20 40]

13 (12028487030150627) 14 03 [10 40]

14 (12018265730264054) 12 03 [00 20]

15 (12016685330269039) 05 03 [20 40]

16 (12020795330249617) 12 03 [30 50]

17 (12028205530169434) 11 03 [10 30]

18 (12015692330280374) 07 03 [30 50]

19 (12017424230196310) 12 03 [00 20]

20 (12017628530219921) 19 03 [20 60]

21 (12009314230340724) 15 03 [30 50]

22 (12023274430209315) 16 03 [05 20]

23 (12017831930283681) 08 03 [10 20]

24 (12020110930208160) 06 03 [10 30]

Table 6 Continued


Timewindows

25 (12019133830355956) 16 03 [30 60]

26 (12018004930252984) 14 03 [05 20]

27 (12016630330309546) 05 03 [10 30]

28 (12023847230358900) 08 03 [30 60]

29 (12017722530249727) 11 03 [05 20]

30 (12022001730315313) 14 03 [10 30]



04

06

08

1

12

14

16

18

2

22

24

Tota

l cos

t (Yu

an)

times104

2 3 4 5 6

7 8 9 10 11 12

1




LLH1

LLH2

LLH3

LLH4

LLH5

LLH6

LLH7 LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(a)


1 2 3 4 5 6 7 8 90

02

01

04

03

06

05

08

07

09

1

Acce

ptan

ce ra

te (

)

(b)





4 Conclusions





Data Availability




Acknowledgments


References









































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in




















f1 1113944n


Tn LLHj1113872 1113873 (32)




f2 LLHk LLHj1113872 1113873 1113944n


Tn LLHk LLHj1113872 1113873 (33)



f3 LLHj1113872 1113873 τ LLHj1113872 1113873 (34)



(35)





















S 1n

1113944

n

i1d minus di1113872 1113873

2⎡⎣ ⎤⎦12

(36)



D

1113944

n

i1max x

it minus y

it

11139741113972

(37)

where xit minus yi


t and yit





Min Max Min Max

AS

AM 4 11522 12562 139785 166466GD 7 11037 14449 145240 161055OI 5 10452 11388 144198 148493SA 5 10584 11312 142343 160760

CF

AM 4 10853 11242 147482 163772GD 5 10726 12257 149758 163792OI 4 10689 12067 152179 161707SA 6 11133 11492 149411 164242

SR

AM 4 10582 11092 138572 153454GD 3 12764 13230 176301 197800OI 3 10418 11830 134790 145900SA 5 10610 12118 145880 157087

TS

AM 6 10563 11866 141474 146421GD 5 11450 12150 148005 174159OI 6 12222 14375 164531 192463SA 7 10426 11723 133167 133167



AS

AM 4 1473 978GD 7 2067 1010OI 5 1347 468SA 5 1556 902

CF

AM 4 6294 786GD 5 3930 806OI 4 2921 588SA 6 3030 840

SR

AM 4 4248 815GD 3 3159 765OI 3 291 568SA 5 2696 717

TS

AM 6 589 570GD 5 1341 1053OI 5 2179 1149SA 7 263 1011











14

15

16

17Lo

gisti

cs co

st (Y

uan)

times104

SAOI

GDAM

(a)


times104

SAOI

GDAM

1050 1100 1150 1200 1250145

15

155

16

165

Logi

stics

cost

(Yua

n)

(b)

times104

SAOI

GDAM


12

14

16

18

2

Logi

stics

cost

(Yua

n)

(c)

times104

SAOI

GDAM


12

14

16

18

2

Logi

stics

cost

(Yua

n)

(d)



LLH1

LLH2

LLH3

LLH4

LLH5

LLH6

LLH7 LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(a)

LLH1

LLH2

LLH3

LLH4

LLH5

LLH6 LLH7

LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(b)

LLH1

LLH2

LLH3

LLH4

LLH5

LLH6LLH7

LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(c)

LLH1

LLH2

LLH3

LLH4

LLH5

LLH6LLH7

LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(d)



0

02

04

06

08

1

Acce

ptan

ce ra

te (

)

1 2 3 4 5 6 7 8 9

(a)

0

02

04

06

08

1

Acce

ptan

ce ra

te (

)


1 2 3 4 5 6 7 8 9

(b)

Figure 4 Continued







Acce

ptan

ce ra

te (

)

0

02

04

06

08

1


1 2 3 4 5 6 7 8 9

(c)

Acce

ptan

ce ra

te (

)

0

02

04

06

08

1


1 2 3 4 5 6 7 8 9

(d)




Min Max Min Max

R101 MOHH 6 12221 13743 165230 184790NSGA-II 5 20457 23435 174105 182155

R102 MOHH 6 11938 13390 165251 182082NSGA-II 6 21139 22227 168680 174992

R103 MOHH 5 11792 13360 163107 181646NSGA-II 4 21733 22417 169208 189293

R104 MOHH 5 11660 12628 161086 188263NSGA-II 3 21273 21499 195527 199156

R105 MOHH 5 11573 13016 169270 174440NSGA-II 4 21372 22227 177605 184762

R106 MOHH 6 12078 12889 157142 162353NSGA-II 5 22488 26034 170070 173938

R107 MOHH 6 11788 13127 155009 172504NSGA-II 5 21064 21346 153680 160416

R108 MOHH 3 11350 11841 138182 150531NSGA-II 5 21352 24724 156000 160385

R109 MOHH 5 12294 14060 163585 188892NSGA-II 4 20533 23831 153025 159328









R101 MOHH 6 538 1011NSGA-II 5 569 772

R102 MOHH 6 943 909NSGA-II 6 792 600

R103 MOHH 5 227 949NSGA-II 4 763 896

R104 MOHH 5 603 1106NSGA-II 3 812 322

R105 MOHH 5 490 522NSGA-II 4 313 538

R106 MOHH 6 549 635NSGA-II 5 1624 523

R107 MOHH 6 1075 978NSGA-II 5 1118 529

R108 MOHH 3 709 618NSGA-II 5 835 602

R109 MOHH 5 732 1060NSGA-II 4 325 592











Timewindows

1 (12021793630296719) 08 03 [00 20]

2 (12020197730263709) 11 03 [10 20]

3 (12012365230290270) 08 03 [00 20]

4 (12021721930206380) 13 03 [30 50]

5 (12019046130341832) 11 03 [30 50]

6 (12016980430282714) 13 03 [30 60]

7 (12004603530263151) 06 03 [20 50]

8 (12019580730185674) 09 03 [30 60]

9 (12023408830197576) 05 03 [40 60]

10 (12027250130334870) 13 03 [20 40]

11 (12012560530313614) 13 03 [30 60]

12 (12010261130300304) 09 03 [20 40]

13 (12028487030150627) 14 03 [10 40]

14 (12018265730264054) 12 03 [00 20]

15 (12016685330269039) 05 03 [20 40]

16 (12020795330249617) 12 03 [30 50]

17 (12028205530169434) 11 03 [10 30]

18 (12015692330280374) 07 03 [30 50]

19 (12017424230196310) 12 03 [00 20]

20 (12017628530219921) 19 03 [20 60]

21 (12009314230340724) 15 03 [30 50]

22 (12023274430209315) 16 03 [05 20]

23 (12017831930283681) 08 03 [10 20]

24 (12020110930208160) 06 03 [10 30]

Table 6 Continued


Timewindows

25 (12019133830355956) 16 03 [30 60]

26 (12018004930252984) 14 03 [05 20]

27 (12016630330309546) 05 03 [10 30]

28 (12023847230358900) 08 03 [30 60]

29 (12017722530249727) 11 03 [05 20]

30 (12022001730315313) 14 03 [10 30]



04

06

08

1

12

14

16

18

2

22

24

Tota

l cos

t (Yu

an)

times104

2 3 4 5 6

7 8 9 10 11 12

1




LLH1

LLH2

LLH3

LLH4

LLH5

LLH6

LLH7 LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(a)


1 2 3 4 5 6 7 8 90

02

01

04

03

06

05

08

07

09

1

Acce

ptan

ce ra

te (

)

(b)





4 Conclusions





Data Availability




Acknowledgments


References









































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in





f2 LLHk LLHj1113872 1113873 1113944n


Tn LLHk LLHj1113872 1113873 (33)



f3 LLHj1113872 1113873 τ LLHj1113872 1113873 (34)



(35)





















S 1n

1113944

n

i1d minus di1113872 1113873

2⎡⎣ ⎤⎦12

(36)



D

1113944

n

i1max x

it minus y

it

11139741113972

(37)

where xit minus yi


t and yit





Min Max Min Max

AS

AM 4 11522 12562 139785 166466GD 7 11037 14449 145240 161055OI 5 10452 11388 144198 148493SA 5 10584 11312 142343 160760

CF

AM 4 10853 11242 147482 163772GD 5 10726 12257 149758 163792OI 4 10689 12067 152179 161707SA 6 11133 11492 149411 164242

SR

AM 4 10582 11092 138572 153454GD 3 12764 13230 176301 197800OI 3 10418 11830 134790 145900SA 5 10610 12118 145880 157087

TS

AM 6 10563 11866 141474 146421GD 5 11450 12150 148005 174159OI 6 12222 14375 164531 192463SA 7 10426 11723 133167 133167



AS

AM 4 1473 978GD 7 2067 1010OI 5 1347 468SA 5 1556 902

CF

AM 4 6294 786GD 5 3930 806OI 4 2921 588SA 6 3030 840

SR

AM 4 4248 815GD 3 3159 765OI 3 291 568SA 5 2696 717

TS

AM 6 589 570GD 5 1341 1053OI 5 2179 1149SA 7 263 1011











14

15

16

17Lo

gisti

cs co

st (Y

uan)

times104

SAOI

GDAM

(a)


times104

SAOI

GDAM

1050 1100 1150 1200 1250145

15

155

16

165

Logi

stics

cost

(Yua

n)

(b)

times104

SAOI

GDAM


12

14

16

18

2

Logi

stics

cost

(Yua

n)

(c)

times104

SAOI

GDAM


12

14

16

18

2

Logi

stics

cost

(Yua

n)

(d)



LLH1

LLH2

LLH3

LLH4

LLH5

LLH6

LLH7 LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(a)

LLH1

LLH2

LLH3

LLH4

LLH5

LLH6 LLH7

LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(b)

LLH1

LLH2

LLH3

LLH4

LLH5

LLH6LLH7

LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(c)

LLH1

LLH2

LLH3

LLH4

LLH5

LLH6LLH7

LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(d)



0

02

04

06

08

1

Acce

ptan

ce ra

te (

)

1 2 3 4 5 6 7 8 9

(a)

0

02

04

06

08

1

Acce

ptan

ce ra

te (

)


1 2 3 4 5 6 7 8 9

(b)

Figure 4 Continued







Acce

ptan

ce ra

te (

)

0

02

04

06

08

1


1 2 3 4 5 6 7 8 9

(c)

Acce

ptan

ce ra

te (

)

0

02

04

06

08

1


1 2 3 4 5 6 7 8 9

(d)




Min Max Min Max

R101 MOHH 6 12221 13743 165230 184790NSGA-II 5 20457 23435 174105 182155

R102 MOHH 6 11938 13390 165251 182082NSGA-II 6 21139 22227 168680 174992

R103 MOHH 5 11792 13360 163107 181646NSGA-II 4 21733 22417 169208 189293

R104 MOHH 5 11660 12628 161086 188263NSGA-II 3 21273 21499 195527 199156

R105 MOHH 5 11573 13016 169270 174440NSGA-II 4 21372 22227 177605 184762

R106 MOHH 6 12078 12889 157142 162353NSGA-II 5 22488 26034 170070 173938

R107 MOHH 6 11788 13127 155009 172504NSGA-II 5 21064 21346 153680 160416

R108 MOHH 3 11350 11841 138182 150531NSGA-II 5 21352 24724 156000 160385

R109 MOHH 5 12294 14060 163585 188892NSGA-II 4 20533 23831 153025 159328









R101 MOHH 6 538 1011NSGA-II 5 569 772

R102 MOHH 6 943 909NSGA-II 6 792 600

R103 MOHH 5 227 949NSGA-II 4 763 896

R104 MOHH 5 603 1106NSGA-II 3 812 322

R105 MOHH 5 490 522NSGA-II 4 313 538

R106 MOHH 6 549 635NSGA-II 5 1624 523

R107 MOHH 6 1075 978NSGA-II 5 1118 529

R108 MOHH 3 709 618NSGA-II 5 835 602

R109 MOHH 5 732 1060NSGA-II 4 325 592











Timewindows

1 (12021793630296719) 08 03 [00 20]

2 (12020197730263709) 11 03 [10 20]

3 (12012365230290270) 08 03 [00 20]

4 (12021721930206380) 13 03 [30 50]

5 (12019046130341832) 11 03 [30 50]

6 (12016980430282714) 13 03 [30 60]

7 (12004603530263151) 06 03 [20 50]

8 (12019580730185674) 09 03 [30 60]

9 (12023408830197576) 05 03 [40 60]

10 (12027250130334870) 13 03 [20 40]

11 (12012560530313614) 13 03 [30 60]

12 (12010261130300304) 09 03 [20 40]

13 (12028487030150627) 14 03 [10 40]

14 (12018265730264054) 12 03 [00 20]

15 (12016685330269039) 05 03 [20 40]

16 (12020795330249617) 12 03 [30 50]

17 (12028205530169434) 11 03 [10 30]

18 (12015692330280374) 07 03 [30 50]

19 (12017424230196310) 12 03 [00 20]

20 (12017628530219921) 19 03 [20 60]

21 (12009314230340724) 15 03 [30 50]

22 (12023274430209315) 16 03 [05 20]

23 (12017831930283681) 08 03 [10 20]

24 (12020110930208160) 06 03 [10 30]

Table 6 Continued


Timewindows

25 (12019133830355956) 16 03 [30 60]

26 (12018004930252984) 14 03 [05 20]

27 (12016630330309546) 05 03 [10 30]

28 (12023847230358900) 08 03 [30 60]

29 (12017722530249727) 11 03 [05 20]

30 (12022001730315313) 14 03 [10 30]



04

06

08

1

12

14

16

18

2

22

24

Tota

l cos

t (Yu

an)

times104

2 3 4 5 6

7 8 9 10 11 12

1




LLH1

LLH2

LLH3

LLH4

LLH5

LLH6

LLH7 LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(a)


1 2 3 4 5 6 7 8 90

02

01

04

03

06

05

08

07

09

1

Acce

ptan

ce ra

te (

)

(b)





4 Conclusions





Data Availability




Acknowledgments


References









































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in








S 1n

1113944

n

i1d minus di1113872 1113873

2⎡⎣ ⎤⎦12

(36)



D

1113944

n

i1max x

it minus y

it

11139741113972

(37)

where xit minus yi


t and yit





Min Max Min Max

AS

AM 4 11522 12562 139785 166466GD 7 11037 14449 145240 161055OI 5 10452 11388 144198 148493SA 5 10584 11312 142343 160760

CF

AM 4 10853 11242 147482 163772GD 5 10726 12257 149758 163792OI 4 10689 12067 152179 161707SA 6 11133 11492 149411 164242

SR

AM 4 10582 11092 138572 153454GD 3 12764 13230 176301 197800OI 3 10418 11830 134790 145900SA 5 10610 12118 145880 157087

TS

AM 6 10563 11866 141474 146421GD 5 11450 12150 148005 174159OI 6 12222 14375 164531 192463SA 7 10426 11723 133167 133167



AS

AM 4 1473 978GD 7 2067 1010OI 5 1347 468SA 5 1556 902

CF

AM 4 6294 786GD 5 3930 806OI 4 2921 588SA 6 3030 840

SR

AM 4 4248 815GD 3 3159 765OI 3 291 568SA 5 2696 717

TS

AM 6 589 570GD 5 1341 1053OI 5 2179 1149SA 7 263 1011











14

15

16

17Lo

gisti

cs co

st (Y

uan)

times104

SAOI

GDAM

(a)


times104

SAOI

GDAM

1050 1100 1150 1200 1250145

15

155

16

165

Logi

stics

cost

(Yua

n)

(b)

times104

SAOI

GDAM


12

14

16

18

2

Logi

stics

cost

(Yua

n)

(c)

times104

SAOI

GDAM


12

14

16

18

2

Logi

stics

cost

(Yua

n)

(d)



LLH1

LLH2

LLH3

LLH4

LLH5

LLH6

LLH7 LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(a)

LLH1

LLH2

LLH3

LLH4

LLH5

LLH6 LLH7

LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(b)

LLH1

LLH2

LLH3

LLH4

LLH5

LLH6LLH7

LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(c)

LLH1

LLH2

LLH3

LLH4

LLH5

LLH6LLH7

LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(d)



0

02

04

06

08

1

Acce

ptan

ce ra

te (

)

1 2 3 4 5 6 7 8 9

(a)

0

02

04

06

08

1

Acce

ptan

ce ra

te (

)


1 2 3 4 5 6 7 8 9

(b)

Figure 4 Continued







Acce

ptan

ce ra

te (

)

0

02

04

06

08

1


1 2 3 4 5 6 7 8 9

(c)

Acce

ptan

ce ra

te (

)

0

02

04

06

08

1


1 2 3 4 5 6 7 8 9

(d)




Min Max Min Max

R101 MOHH 6 12221 13743 165230 184790NSGA-II 5 20457 23435 174105 182155

R102 MOHH 6 11938 13390 165251 182082NSGA-II 6 21139 22227 168680 174992

R103 MOHH 5 11792 13360 163107 181646NSGA-II 4 21733 22417 169208 189293

R104 MOHH 5 11660 12628 161086 188263NSGA-II 3 21273 21499 195527 199156

R105 MOHH 5 11573 13016 169270 174440NSGA-II 4 21372 22227 177605 184762

R106 MOHH 6 12078 12889 157142 162353NSGA-II 5 22488 26034 170070 173938

R107 MOHH 6 11788 13127 155009 172504NSGA-II 5 21064 21346 153680 160416

R108 MOHH 3 11350 11841 138182 150531NSGA-II 5 21352 24724 156000 160385

R109 MOHH 5 12294 14060 163585 188892NSGA-II 4 20533 23831 153025 159328









R101 MOHH 6 538 1011NSGA-II 5 569 772

R102 MOHH 6 943 909NSGA-II 6 792 600

R103 MOHH 5 227 949NSGA-II 4 763 896

R104 MOHH 5 603 1106NSGA-II 3 812 322

R105 MOHH 5 490 522NSGA-II 4 313 538

R106 MOHH 6 549 635NSGA-II 5 1624 523

R107 MOHH 6 1075 978NSGA-II 5 1118 529

R108 MOHH 3 709 618NSGA-II 5 835 602

R109 MOHH 5 732 1060NSGA-II 4 325 592











Timewindows

1 (12021793630296719) 08 03 [00 20]

2 (12020197730263709) 11 03 [10 20]

3 (12012365230290270) 08 03 [00 20]

4 (12021721930206380) 13 03 [30 50]

5 (12019046130341832) 11 03 [30 50]

6 (12016980430282714) 13 03 [30 60]

7 (12004603530263151) 06 03 [20 50]

8 (12019580730185674) 09 03 [30 60]

9 (12023408830197576) 05 03 [40 60]

10 (12027250130334870) 13 03 [20 40]

11 (12012560530313614) 13 03 [30 60]

12 (12010261130300304) 09 03 [20 40]

13 (12028487030150627) 14 03 [10 40]

14 (12018265730264054) 12 03 [00 20]

15 (12016685330269039) 05 03 [20 40]

16 (12020795330249617) 12 03 [30 50]

17 (12028205530169434) 11 03 [10 30]

18 (12015692330280374) 07 03 [30 50]

19 (12017424230196310) 12 03 [00 20]

20 (12017628530219921) 19 03 [20 60]

21 (12009314230340724) 15 03 [30 50]

22 (12023274430209315) 16 03 [05 20]

23 (12017831930283681) 08 03 [10 20]

24 (12020110930208160) 06 03 [10 30]

Table 6 Continued


Timewindows

25 (12019133830355956) 16 03 [30 60]

26 (12018004930252984) 14 03 [05 20]

27 (12016630330309546) 05 03 [10 30]

28 (12023847230358900) 08 03 [30 60]

29 (12017722530249727) 11 03 [05 20]

30 (12022001730315313) 14 03 [10 30]



04

06

08

1

12

14

16

18

2

22

24

Tota

l cos

t (Yu

an)

times104

2 3 4 5 6

7 8 9 10 11 12

1




LLH1

LLH2

LLH3

LLH4

LLH5

LLH6

LLH7 LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(a)


1 2 3 4 5 6 7 8 90

02

01

04

03

06

05

08

07

09

1

Acce

ptan

ce ra

te (

)

(b)





4 Conclusions





Data Availability




Acknowledgments


References









































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in













14

15

16

17Lo

gisti

cs co

st (Y

uan)

times104

SAOI

GDAM

(a)


times104

SAOI

GDAM

1050 1100 1150 1200 1250145

15

155

16

165

Logi

stics

cost

(Yua

n)

(b)

times104

SAOI

GDAM


12

14

16

18

2

Logi

stics

cost

(Yua

n)

(c)

times104

SAOI

GDAM


12

14

16

18

2

Logi

stics

cost

(Yua

n)

(d)



LLH1

LLH2

LLH3

LLH4

LLH5

LLH6

LLH7 LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(a)

LLH1

LLH2

LLH3

LLH4

LLH5

LLH6 LLH7

LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(b)

LLH1

LLH2

LLH3

LLH4

LLH5

LLH6LLH7

LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(c)

LLH1

LLH2

LLH3

LLH4

LLH5

LLH6LLH7

LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(d)



0

02

04

06

08

1

Acce

ptan

ce ra

te (

)

1 2 3 4 5 6 7 8 9

(a)

0

02

04

06

08

1

Acce

ptan

ce ra

te (

)


1 2 3 4 5 6 7 8 9

(b)

Figure 4 Continued







Acce

ptan

ce ra

te (

)

0

02

04

06

08

1


1 2 3 4 5 6 7 8 9

(c)

Acce

ptan

ce ra

te (

)

0

02

04

06

08

1


1 2 3 4 5 6 7 8 9

(d)




Min Max Min Max

R101 MOHH 6 12221 13743 165230 184790NSGA-II 5 20457 23435 174105 182155

R102 MOHH 6 11938 13390 165251 182082NSGA-II 6 21139 22227 168680 174992

R103 MOHH 5 11792 13360 163107 181646NSGA-II 4 21733 22417 169208 189293

R104 MOHH 5 11660 12628 161086 188263NSGA-II 3 21273 21499 195527 199156

R105 MOHH 5 11573 13016 169270 174440NSGA-II 4 21372 22227 177605 184762

R106 MOHH 6 12078 12889 157142 162353NSGA-II 5 22488 26034 170070 173938

R107 MOHH 6 11788 13127 155009 172504NSGA-II 5 21064 21346 153680 160416

R108 MOHH 3 11350 11841 138182 150531NSGA-II 5 21352 24724 156000 160385

R109 MOHH 5 12294 14060 163585 188892NSGA-II 4 20533 23831 153025 159328









R101 MOHH 6 538 1011NSGA-II 5 569 772

R102 MOHH 6 943 909NSGA-II 6 792 600

R103 MOHH 5 227 949NSGA-II 4 763 896

R104 MOHH 5 603 1106NSGA-II 3 812 322

R105 MOHH 5 490 522NSGA-II 4 313 538

R106 MOHH 6 549 635NSGA-II 5 1624 523

R107 MOHH 6 1075 978NSGA-II 5 1118 529

R108 MOHH 3 709 618NSGA-II 5 835 602

R109 MOHH 5 732 1060NSGA-II 4 325 592











Timewindows

1 (12021793630296719) 08 03 [00 20]

2 (12020197730263709) 11 03 [10 20]

3 (12012365230290270) 08 03 [00 20]

4 (12021721930206380) 13 03 [30 50]

5 (12019046130341832) 11 03 [30 50]

6 (12016980430282714) 13 03 [30 60]

7 (12004603530263151) 06 03 [20 50]

8 (12019580730185674) 09 03 [30 60]

9 (12023408830197576) 05 03 [40 60]

10 (12027250130334870) 13 03 [20 40]

11 (12012560530313614) 13 03 [30 60]

12 (12010261130300304) 09 03 [20 40]

13 (12028487030150627) 14 03 [10 40]

14 (12018265730264054) 12 03 [00 20]

15 (12016685330269039) 05 03 [20 40]

16 (12020795330249617) 12 03 [30 50]

17 (12028205530169434) 11 03 [10 30]

18 (12015692330280374) 07 03 [30 50]

19 (12017424230196310) 12 03 [00 20]

20 (12017628530219921) 19 03 [20 60]

21 (12009314230340724) 15 03 [30 50]

22 (12023274430209315) 16 03 [05 20]

23 (12017831930283681) 08 03 [10 20]

24 (12020110930208160) 06 03 [10 30]

Table 6 Continued


Timewindows

25 (12019133830355956) 16 03 [30 60]

26 (12018004930252984) 14 03 [05 20]

27 (12016630330309546) 05 03 [10 30]

28 (12023847230358900) 08 03 [30 60]

29 (12017722530249727) 11 03 [05 20]

30 (12022001730315313) 14 03 [10 30]



04

06

08

1

12

14

16

18

2

22

24

Tota

l cos

t (Yu

an)

times104

2 3 4 5 6

7 8 9 10 11 12

1




LLH1

LLH2

LLH3

LLH4

LLH5

LLH6

LLH7 LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(a)


1 2 3 4 5 6 7 8 90

02

01

04

03

06

05

08

07

09

1

Acce

ptan

ce ra

te (

)

(b)





4 Conclusions





Data Availability




Acknowledgments


References









































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in




LLH1

LLH2

LLH3

LLH4

LLH5

LLH6

LLH7 LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(a)

LLH1

LLH2

LLH3

LLH4

LLH5

LLH6 LLH7

LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(b)

LLH1

LLH2

LLH3

LLH4

LLH5

LLH6LLH7

LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(c)

LLH1

LLH2

LLH3

LLH4

LLH5

LLH6LLH7

LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(d)



0

02

04

06

08

1

Acce

ptan

ce ra

te (

)

1 2 3 4 5 6 7 8 9

(a)

0

02

04

06

08

1

Acce

ptan

ce ra

te (

)


1 2 3 4 5 6 7 8 9

(b)

Figure 4 Continued







Acce

ptan

ce ra

te (

)

0

02

04

06

08

1


1 2 3 4 5 6 7 8 9

(c)

Acce

ptan

ce ra

te (

)

0

02

04

06

08

1


1 2 3 4 5 6 7 8 9

(d)




Min Max Min Max

R101 MOHH 6 12221 13743 165230 184790NSGA-II 5 20457 23435 174105 182155

R102 MOHH 6 11938 13390 165251 182082NSGA-II 6 21139 22227 168680 174992

R103 MOHH 5 11792 13360 163107 181646NSGA-II 4 21733 22417 169208 189293

R104 MOHH 5 11660 12628 161086 188263NSGA-II 3 21273 21499 195527 199156

R105 MOHH 5 11573 13016 169270 174440NSGA-II 4 21372 22227 177605 184762

R106 MOHH 6 12078 12889 157142 162353NSGA-II 5 22488 26034 170070 173938

R107 MOHH 6 11788 13127 155009 172504NSGA-II 5 21064 21346 153680 160416

R108 MOHH 3 11350 11841 138182 150531NSGA-II 5 21352 24724 156000 160385

R109 MOHH 5 12294 14060 163585 188892NSGA-II 4 20533 23831 153025 159328









R101 MOHH 6 538 1011NSGA-II 5 569 772

R102 MOHH 6 943 909NSGA-II 6 792 600

R103 MOHH 5 227 949NSGA-II 4 763 896

R104 MOHH 5 603 1106NSGA-II 3 812 322

R105 MOHH 5 490 522NSGA-II 4 313 538

R106 MOHH 6 549 635NSGA-II 5 1624 523

R107 MOHH 6 1075 978NSGA-II 5 1118 529

R108 MOHH 3 709 618NSGA-II 5 835 602

R109 MOHH 5 732 1060NSGA-II 4 325 592











Timewindows

1 (12021793630296719) 08 03 [00 20]

2 (12020197730263709) 11 03 [10 20]

3 (12012365230290270) 08 03 [00 20]

4 (12021721930206380) 13 03 [30 50]

5 (12019046130341832) 11 03 [30 50]

6 (12016980430282714) 13 03 [30 60]

7 (12004603530263151) 06 03 [20 50]

8 (12019580730185674) 09 03 [30 60]

9 (12023408830197576) 05 03 [40 60]

10 (12027250130334870) 13 03 [20 40]

11 (12012560530313614) 13 03 [30 60]

12 (12010261130300304) 09 03 [20 40]

13 (12028487030150627) 14 03 [10 40]

14 (12018265730264054) 12 03 [00 20]

15 (12016685330269039) 05 03 [20 40]

16 (12020795330249617) 12 03 [30 50]

17 (12028205530169434) 11 03 [10 30]

18 (12015692330280374) 07 03 [30 50]

19 (12017424230196310) 12 03 [00 20]

20 (12017628530219921) 19 03 [20 60]

21 (12009314230340724) 15 03 [30 50]

22 (12023274430209315) 16 03 [05 20]

23 (12017831930283681) 08 03 [10 20]

24 (12020110930208160) 06 03 [10 30]

Table 6 Continued


Timewindows

25 (12019133830355956) 16 03 [30 60]

26 (12018004930252984) 14 03 [05 20]

27 (12016630330309546) 05 03 [10 30]

28 (12023847230358900) 08 03 [30 60]

29 (12017722530249727) 11 03 [05 20]

30 (12022001730315313) 14 03 [10 30]



04

06

08

1

12

14

16

18

2

22

24

Tota

l cos

t (Yu

an)

times104

2 3 4 5 6

7 8 9 10 11 12

1




LLH1

LLH2

LLH3

LLH4

LLH5

LLH6

LLH7 LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(a)


1 2 3 4 5 6 7 8 90

02

01

04

03

06

05

08

07

09

1

Acce

ptan

ce ra

te (

)

(b)





4 Conclusions





Data Availability




Acknowledgments


References









































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in









Acce

ptan

ce ra

te (

)

0

02

04

06

08

1


1 2 3 4 5 6 7 8 9

(c)

Acce

ptan

ce ra

te (

)

0

02

04

06

08

1


1 2 3 4 5 6 7 8 9

(d)




Min Max Min Max

R101 MOHH 6 12221 13743 165230 184790NSGA-II 5 20457 23435 174105 182155

R102 MOHH 6 11938 13390 165251 182082NSGA-II 6 21139 22227 168680 174992

R103 MOHH 5 11792 13360 163107 181646NSGA-II 4 21733 22417 169208 189293

R104 MOHH 5 11660 12628 161086 188263NSGA-II 3 21273 21499 195527 199156

R105 MOHH 5 11573 13016 169270 174440NSGA-II 4 21372 22227 177605 184762

R106 MOHH 6 12078 12889 157142 162353NSGA-II 5 22488 26034 170070 173938

R107 MOHH 6 11788 13127 155009 172504NSGA-II 5 21064 21346 153680 160416

R108 MOHH 3 11350 11841 138182 150531NSGA-II 5 21352 24724 156000 160385

R109 MOHH 5 12294 14060 163585 188892NSGA-II 4 20533 23831 153025 159328









R101 MOHH 6 538 1011NSGA-II 5 569 772

R102 MOHH 6 943 909NSGA-II 6 792 600

R103 MOHH 5 227 949NSGA-II 4 763 896

R104 MOHH 5 603 1106NSGA-II 3 812 322

R105 MOHH 5 490 522NSGA-II 4 313 538

R106 MOHH 6 549 635NSGA-II 5 1624 523

R107 MOHH 6 1075 978NSGA-II 5 1118 529

R108 MOHH 3 709 618NSGA-II 5 835 602

R109 MOHH 5 732 1060NSGA-II 4 325 592











Timewindows

1 (12021793630296719) 08 03 [00 20]

2 (12020197730263709) 11 03 [10 20]

3 (12012365230290270) 08 03 [00 20]

4 (12021721930206380) 13 03 [30 50]

5 (12019046130341832) 11 03 [30 50]

6 (12016980430282714) 13 03 [30 60]

7 (12004603530263151) 06 03 [20 50]

8 (12019580730185674) 09 03 [30 60]

9 (12023408830197576) 05 03 [40 60]

10 (12027250130334870) 13 03 [20 40]

11 (12012560530313614) 13 03 [30 60]

12 (12010261130300304) 09 03 [20 40]

13 (12028487030150627) 14 03 [10 40]

14 (12018265730264054) 12 03 [00 20]

15 (12016685330269039) 05 03 [20 40]

16 (12020795330249617) 12 03 [30 50]

17 (12028205530169434) 11 03 [10 30]

18 (12015692330280374) 07 03 [30 50]

19 (12017424230196310) 12 03 [00 20]

20 (12017628530219921) 19 03 [20 60]

21 (12009314230340724) 15 03 [30 50]

22 (12023274430209315) 16 03 [05 20]

23 (12017831930283681) 08 03 [10 20]

24 (12020110930208160) 06 03 [10 30]

Table 6 Continued


Timewindows

25 (12019133830355956) 16 03 [30 60]

26 (12018004930252984) 14 03 [05 20]

27 (12016630330309546) 05 03 [10 30]

28 (12023847230358900) 08 03 [30 60]

29 (12017722530249727) 11 03 [05 20]

30 (12022001730315313) 14 03 [10 30]



04

06

08

1

12

14

16

18

2

22

24

Tota

l cos

t (Yu

an)

times104

2 3 4 5 6

7 8 9 10 11 12

1




LLH1

LLH2

LLH3

LLH4

LLH5

LLH6

LLH7 LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(a)


1 2 3 4 5 6 7 8 90

02

01

04

03

06

05

08

07

09

1

Acce

ptan

ce ra

te (

)

(b)





4 Conclusions





Data Availability




Acknowledgments


References









































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in











R101 MOHH 6 538 1011NSGA-II 5 569 772

R102 MOHH 6 943 909NSGA-II 6 792 600

R103 MOHH 5 227 949NSGA-II 4 763 896

R104 MOHH 5 603 1106NSGA-II 3 812 322

R105 MOHH 5 490 522NSGA-II 4 313 538

R106 MOHH 6 549 635NSGA-II 5 1624 523

R107 MOHH 6 1075 978NSGA-II 5 1118 529

R108 MOHH 3 709 618NSGA-II 5 835 602

R109 MOHH 5 732 1060NSGA-II 4 325 592











Timewindows

1 (12021793630296719) 08 03 [00 20]

2 (12020197730263709) 11 03 [10 20]

3 (12012365230290270) 08 03 [00 20]

4 (12021721930206380) 13 03 [30 50]

5 (12019046130341832) 11 03 [30 50]

6 (12016980430282714) 13 03 [30 60]

7 (12004603530263151) 06 03 [20 50]

8 (12019580730185674) 09 03 [30 60]

9 (12023408830197576) 05 03 [40 60]

10 (12027250130334870) 13 03 [20 40]

11 (12012560530313614) 13 03 [30 60]

12 (12010261130300304) 09 03 [20 40]

13 (12028487030150627) 14 03 [10 40]

14 (12018265730264054) 12 03 [00 20]

15 (12016685330269039) 05 03 [20 40]

16 (12020795330249617) 12 03 [30 50]

17 (12028205530169434) 11 03 [10 30]

18 (12015692330280374) 07 03 [30 50]

19 (12017424230196310) 12 03 [00 20]

20 (12017628530219921) 19 03 [20 60]

21 (12009314230340724) 15 03 [30 50]

22 (12023274430209315) 16 03 [05 20]

23 (12017831930283681) 08 03 [10 20]

24 (12020110930208160) 06 03 [10 30]

Table 6 Continued


Timewindows

25 (12019133830355956) 16 03 [30 60]

26 (12018004930252984) 14 03 [05 20]

27 (12016630330309546) 05 03 [10 30]

28 (12023847230358900) 08 03 [30 60]

29 (12017722530249727) 11 03 [05 20]

30 (12022001730315313) 14 03 [10 30]



04

06

08

1

12

14

16

18

2

22

24

Tota

l cos

t (Yu

an)

times104

2 3 4 5 6

7 8 9 10 11 12

1




LLH1

LLH2

LLH3

LLH4

LLH5

LLH6

LLH7 LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(a)


1 2 3 4 5 6 7 8 90

02

01

04

03

06

05

08

07

09

1

Acce

ptan

ce ra

te (

)

(b)





4 Conclusions





Data Availability




Acknowledgments


References









































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in












Timewindows

1 (12021793630296719) 08 03 [00 20]

2 (12020197730263709) 11 03 [10 20]

3 (12012365230290270) 08 03 [00 20]

4 (12021721930206380) 13 03 [30 50]

5 (12019046130341832) 11 03 [30 50]

6 (12016980430282714) 13 03 [30 60]

7 (12004603530263151) 06 03 [20 50]

8 (12019580730185674) 09 03 [30 60]

9 (12023408830197576) 05 03 [40 60]

10 (12027250130334870) 13 03 [20 40]

11 (12012560530313614) 13 03 [30 60]

12 (12010261130300304) 09 03 [20 40]

13 (12028487030150627) 14 03 [10 40]

14 (12018265730264054) 12 03 [00 20]

15 (12016685330269039) 05 03 [20 40]

16 (12020795330249617) 12 03 [30 50]

17 (12028205530169434) 11 03 [10 30]

18 (12015692330280374) 07 03 [30 50]

19 (12017424230196310) 12 03 [00 20]

20 (12017628530219921) 19 03 [20 60]

21 (12009314230340724) 15 03 [30 50]

22 (12023274430209315) 16 03 [05 20]

23 (12017831930283681) 08 03 [10 20]

24 (12020110930208160) 06 03 [10 30]

Table 6 Continued


Timewindows

25 (12019133830355956) 16 03 [30 60]

26 (12018004930252984) 14 03 [05 20]

27 (12016630330309546) 05 03 [10 30]

28 (12023847230358900) 08 03 [30 60]

29 (12017722530249727) 11 03 [05 20]

30 (12022001730315313) 14 03 [10 30]



04

06

08

1

12

14

16

18

2

22

24

Tota

l cos

t (Yu

an)

times104

2 3 4 5 6

7 8 9 10 11 12

1




LLH1

LLH2

LLH3

LLH4

LLH5

LLH6

LLH7 LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(a)


1 2 3 4 5 6 7 8 90

02

01

04

03

06

05

08

07

09

1

Acce

ptan

ce ra

te (

)

(b)





4 Conclusions





Data Availability




Acknowledgments


References









































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in





04

06

08

1

12

14

16

18

2

22

24

Tota

l cos

t (Yu

an)

times104

2 3 4 5 6

7 8 9 10 11 12

1




LLH1

LLH2

LLH3

LLH4

LLH5

LLH6

LLH7 LLH8

LLH9

LLH10

LLH11

LLH12

LLH13

(a)


1 2 3 4 5 6 7 8 90

02

01

04

03

06

05

08

07

09

1

Acce

ptan

ce ra

te (

)

(b)





4 Conclusions





Data Availability




Acknowledgments


References









































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in






4 Conclusions





Data Availability




Acknowledgments


References









































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in


































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in









Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in




Documents

AHyperheuristicApproachforLocation-RoutingProblemof ...2019/08/26 · 0 +CV)+b, respec-tively. us, FCR per unit distance is ρ˜ ˚M 1 ˜ 0 + ρ ∗ − ˜˚ 0 × M 1 CV. (7) erefore,