Adaptive Autotuning Mathematical Approaches for Integrated...

Research ArticleAdaptive Autotuning Mathematical Approaches for IntegratedOptimization of Automated Container Terminal

Meisu Zhong 1 Yongsheng Yang 1 Yamin Zhou1 and Octavian Postolache 2

1Institute of Logistics Science amp Engineering Shanghai Maritime University Shanghai 201306 China2Instituto de TelecomunicacotildeesISCTE-IUL Lisboa Portugal

Correspondence should be addressed to Yongsheng Yang yangys_smu126com

Received 18 June 2019 Revised 16 September 2019 Accepted 16 October 2019 Published 27 November 2019

Academic Editor Marco Mussetta

Copyright copy 2019 Meisu Zhong 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

With the development of automated container terminals (ACTs) reducing the loading and unloading time of operation andimproving the working efficiency and service level have become the key point Taking into account the actual operation mode ofloading and unloading in ACTs a mixed integer programming model is adopted in this study to minimize the loading andunloading time of ships which can optimize the integrated scheduling of the gantry cranes (QCs) automated guided vehicles(AGVs) and automated rail-mounted gantries (ARMGs) in automated terminals Various basic metaheuristic and improvedhybrid algorithms were developed to optimize the model proving the effectiveness of themodel to obtain an optimized schedulingscheme by numerical experiments and comparing the different performances of algorithmse results show that the hybrid GA-PSO algorithm with adaptive autotuning approaches by fuzzy control is superior to other algorithms in terms of solution time andquality which can effectively solve the problem of integrated scheduling of automated container terminals to improve efficiency

1 Introduction

As the global economic growth accelerates the demand ofcontainer transportation expands progressively e auto-mated terminal plays an important role in the global supplychain However energy consumption and carbon emissionincrease sharply and how to reduce the energy and costs andhow to improve the efficiency have been the goal of ports [1 2]In the fierce competition between ports the automated op-eration mode can not only reduce labor costs but also improvethe service level whichwill attractmore customers tomeet theport requirements of large scale and high efficiency So theautomated container terminals devote themselves to short-ening the working time and advancing the economic effi-ciency which have become the key to sustainable developmentof ports However due to the high cost of equipment inautomated terminals it is hard to increase the number ofcommon used equipment to improve the efficiency [3] such asquay cranes (QCs) automatic guided vehicles (AGVs) andyard cranes (YCs) erefore the reasonable scheme of in-tegrated scheduling of three kinds of equipment for loading

and unloading container operations has become the key toimproving efficiency of automated terminals

Over the past decade automated terminals have becomethe development trend of ports in China for exampleXiamen Port has been gradually developed in practice op-eration Shanghai Yangshan Deep Water Port and QingdaoPort have been finished and put into operation at presentand many ports are under transformation or construction ofautomated terminals And specifically in Xiamen Port QCsuse double trolley to replace single trolley for operationAGVs have been used instead of trucks for horizontaltransportation and automated rail-mounted gantries(ARMGs) have almost displaced tyre cranes in yards ereasonable scheduling scheme can make full use of re-sources reduce the berth time of ships and the waiting timeof equipment and improve the efficiency of loading andunloading in ports erefore it is of great significance tostudy the integrated scheduling of QCs AGVs and ARMGsto improve the efficiency and help to save energy in ports

Our contribution is two-fold First most of the researchabout automated terminals is about single or two parts of

HindawiMathematical Problems in EngineeringVolume 2019 Article ID 7641670 14 pageshttpsdoiorg10115520197641670

equipment is paper considers the actual situation ofloading and unloading operation modes putting forward amethod to realize the integrated scheduling of QCs AGVsand ARMGs with the objective to minimize overall oper-ation timeis well-thought-out model is more reliable andrealistic and has better schedule optimization

e second is that most of the research studies of op-timization algorithms in solving this kind of problem usebasic metaheuristic algorithms We perform extensive nu-merical experiments to clearly compare the accurate algo-rithm (branch and bound) the basic metaheuristicalgorithms (genetic algorithm particle swarm optimizationand bat algorithm) and the improved metaheuristic algo-rithm (hybrid GA-PSO algorithm and hybrid BAT-GA) tobetter illustrate this problem obtaining optimum solutionsin short time And this result shows that the hybrid GA-PSOalgorithm with a fuzzy logic controller for adaptive auto-tuning is effective and shows significant improvementcompared with other methods

is paper is organized as follows Section 2 reviews therelevant literature In Section 3 the integrated schedulingproblem is formulated as a mixed integer programming(MIP) model Several algorithms are proposed in Section 4Numerical experiments based on simulation optimizationare conducted to examine effectiveness of the proposedmethod and the performance of different algorithms inSection 5 Finally some conclusions of this research aredrawn in Section 6

2 Literature Review

Automated terminal system is very complex involving mul-tiple subsystemsere are numerous studies on the schedulingand optimization of automated terminals such as the sched-uling of a single equipment separately [4ndash7] the collaborativescheduling between two handling equipment [8ndash12] and theintegrated scheduling between three handling equipment[13ndash16] Because automated terminals are a complex integratedsystem the research of single- or two-equipment scheduling isnot significant for the improvement of operation efficiency ofautomated terminals which also does not accord with theactual situation of automated terminals

21 Accurate Algorithms of Automated Terminals For ac-curate algorithms of container terminals most of the researchstudies focused on branch and bound algorithm (BampB) anddata envelopment analysis (DEA) For example Pjevcevicet al [17] studied the collaborative scheduling of QCs andAGVs in automated terminals used the DEA method toanalyze the operation efficiency of unloading containers andfinally obtained the reasonable scheduling scheme Jiang andJin [18] researched the integrated scheduling problem of QCsAGVs and YCs with the goal of minimizing cost of QCs bythe BampB method to solve the built mixed integer pro-gramming model through numerical experiments showingthat this method can improve the efficiency of terminalsere are also some comparisons of accurate algorithms andother algorithms Alsoufi et al [4] based on the scheduling

problem of QCs used the CPLEX to evaluate and compare theBampBmethod with the genetic algorithm from small- to large-scale examples but the results showed that the genetic al-gorithm had better performance

As mentioned above the accurate algorithm can get theexact solution but when the scale is relatively large it showslack of feasibility due to the influence of computation timeand complex logic relation in program [19ndash21] So moreworks chose to use metaheuristic algorithms

22 Basic Metaheuristic Algorithm of Automated TerminalsFor basic metaheuristic algorithms of container terminalsmost of the literature mainly used genetic algorithm (GA)particle swarm optimization (PSO) and simulated annealing(SA) which are usually based on the perception or expe-rience to construct algorithms For example Moghaddamet al [22] proposed a mixed integer programming model ofQC scheduling and it was hard to obtain the optimal so-lution through optimization software in reasonable time butthe GA solved this problem and showed the certain supe-riority Lu and Le [23] solved the collaborative schedulingmodel of AGVs and YCs by using PSO algorithm and theresults showed that this method could obtain the optimizedsolution Combining berth allocation with the QC sched-uling problem Salhi et al [24] compared the results of GAwith those of the exact CPLEX and showed the rationality ofusing the GA to find the optimal solution However inrecent years there has been much research on the com-parison of different algorithms of automated terminalsHomayouni et al [14] researched the integrated schedulingof container terminals adopting the GA and comparing itwith the SA and the result indicated that with the increase inthe number of containers the solving efficiency of the GA isobviously better than the SA Tominimize the delay time andenergy consumption of ships He et al [25] used the GA andPSO algorithm to effectively solve this problem and dis-cussed the solving ability of different algorithms

Although the basic metaheuristic algorithms may notobtain the exact solution it can obtain the suboptimal so-lution and the complexity of computing time is relativelylow and comparatively its applicability and stability arebetter than those of the accurate algorithm [26ndash28] How-ever taking more factors into consideration in automatedterminals the model is more complex and the basic met-aheuristic algorithm has shown up the disadvantages such aslonger computing time and slow convergence speed [29 30]

23 Improved Metaheuristic Algorithm of AutomatedTerminals For the application of improved metaheuristicalgorithms to container terminals many attempts have beenmade to improve different algorithms For example to solvethe ship scheduling problem Wang et al [31] used the im-proved discrete chaotic PSO algorithm and the simulationoptimization results showed that this method was suitable forthis problem Kaveshgar et al [32] proposed that the extendedGA designed to solve the scheduling problem of QCs can findthe optimal solution of a large-scale example in a shorter timeAccording to the working efficiency of QC scheduling

2 Mathematical Problems in Engineering

preparation time andmakespan Legato et al [33] establishedthe mixed integer programming model with the modiedBampB method through numerical experiments obtaining thehigh quality of scheduling solution A genetic couplingheuristic algorithm by Gu et al [34] was designed to solve theproblem of cooperative scheduling of yards in terminals andthe performance of the model and proposed algorithm wasconrmed with reference to numerous cases Shu et al [35]studied the scheduling of automatic stacker cranes in auto-mated terminals established a mathematical model andproposed an improved multiobjective genetic algorithmwhich satised the requirements of time sensitivity in de-cision improving the intelligence degree of container ter-minals Li et al [36] with theminimum shipping distance andtime as a target has set up a cooperative scheduling model ofberths and QCs based on the improved PSO algorithm to testthe performance of the model by numerical experiments Inorder to improve the eciency of the berth and horizontaltransportation Dkhil et al [13] combined the multiobjectiveoptimization model with Pareto promotion using themodied adaptive tabu search algorithm to nd the eciencyindex De et al [37] considering the scheduling and pathplanning in terminals proposed a mixed integer nonlinearprogramming model by using an eective search algorithmand comparing it with PSO and genetic algorithms illus-trated the superiority of the proposed algorithm

On the whole improved metaheuristic algorithms areobviously better than metaheuristic algorithms in conver-gence speed and accuracy [38ndash41] which is mainly problem-oriented and shows improvement according to the structureand characteristics of the problem So a majority of studiesstill selected the improved metaheuristic algorithms to solvethis kind of problem in recent years

3 Model Formulation

Automated container terminals have many parts and thispaper mainly studies the seaside operation area the hori-zontal transport and the storage yard which are correlatedand constrained mutually e seaside operation area isequipped with the QCs for loading and unloading con-tainers AGVs are used in horizontal transportation whichcan move containers from the QC to the yard the storageyard is equipped with ARMGs e yard has two ARMGsand AGV-mates in front of each block Figure 1 shows thelayout of a typical automated container terminal

e main operational process of the loading andunloading of this problem is as follows (1) e AGV re-ceived the unloading order (loading order) to transport thecontainer from the QC to the assigned block (to transportthe container from the AGV-mate to the assigned QC)Firstly the main trolley of QC unloads the container fromthe ship to the transfer platform of QC and then the portaltrolley unloads the containers from the transfer platform tothe AGV as shown in Figure 2 (2) e AGV transports thecontainer to the AGV-mate in front of the specied blockwhich obeys the operation scheduling rules the AGV canprovide service to any QCs and blocks and the path oftransportation has been set (3) e front ARMG puts the

container from AGV-mate to the staging area in the blockand the back ARMG puts the container to the speciedlocation of yard or the external truck and then the AGVwilldo the next task e loading process is the opposite

31 Assumptions is paper assumes the following condi-tions for this scheduling problem of container terminals

(1) e main trolley of QC loads the container to thetransfer platform or unloads the container from thetransfer platform to the ship and its running time isrelated to the position of the container in shipswhich is subjected to uniform distribution

(2) e portal trolley loads the container to AGV orunloads the container from the transfer platform toAGV and its running time is xed without regard tothe capacity of transfer platform and the number ofAGV-mates

(3) e QC and the ARMG can only load and unloadone container at a time AGVs can only transportone container at a time

(4) e time for a crane (including both QCs andARMGs) to releasepick up a container onfrom theAGVblock is negligible the time for the transfer ofcontainer from the AGV-mate to the storage yard is axed value and the time for the transfer of containersfrom the storage yard to the specied location of yardor the external truck satises uniform distribution

(5) In order to reduce the empty-loading ratio andimprove the utilization of AGVs the AGV completesa loading task and then to perform an unloading taskor after performing an unloading task to complete aloading task

32 Model Parameter(1) Parameter set

U set of import containersL set of export containers

Yard crane

Quay crane

Ship

AGV guide path

AGV-mate

Storage yard

Figure 1 Layout of automated container terminal

Mathematical Problems in Engineering 3

N set of containers N UcupLV set of AGVsQ set of QCsB set of blocksS set of dummy starting point of QCsF set of dummy nishing point of QCsOs Os Qcup SO O Os cupOFOF OF QcupF

(2) Symbolic parameters

T1 is the time of unloading the container by theportal trolley to the apron under the QC It is alsoknown as the time of discharge of the container inthe apron to the transfer platformT2 is the time recorded when the rst ARMG putsthe container on the storage areaM is a very large positive numberdik is the time when the QC k uses the main trolleyto handle the ith container from the ship to thetransfer platform It is also known as the time whenthe QC k puts the ith container from the transferplatform to the shipti is the time taken by AGV to transport the ithcontainerzik is the time when the second ARMG puts the ithcontainer from the storage area to the end positionafter the QC k handling of the ith container

(3) Decision variablesNot 0-1 variables

fik is the time when the QC k has nished the ithcontainergik is the time when the QC k starts to handle theith container i isin Nk

pik is the time when the QC k uses the portal trolleyto get the ith container from AGV or the ithcontainer to be put on the AGVzik is the time when the QC k unloads the ithcontainer on AGV-mate or loads the ith containerfrom AGV-mate

0-1 variables

xikjl is the AGV which just handling the ith con-tainer of the QC k is scheduled to handle the jthcontainer of QC l i isin U j isin L or i isin L j isin Uαikc is the AGV c to handle the ith container of QCk αikc 1 otherwise αikc 0θikb is the ith container of QC k located in block bθikb 1 otherwise θikb 0

33Model emathematical programming model is set upby the above parameters to minimize the loading andunloading time of the ship this integrated problem can beformulated as follows

min max Fk minus Sk( ) (1)

e objective of this model is to minimize the timedierence between nish of the last task and start of the rsttask which represents the loading and unloading time of theship

Subject to constraints

Fk maxkisinOF

fik foralli isin Nk (2)

Sk minkisinOS

uik foralli isin Nk (3)

Constraint (2) means that it selects the last time from theset of all containers task as the the completing time of the

1Discharging

Loading2

Maintrolley

Portaltrolley

Figure 2 Operating modes of loading and unloading


last task e constraint expressed in (3) ensures that theearliest time is considered from a time set of all containers asthe starting time of the first task

1113944lisinOF

1113944jisinL

xikjl 1 foralli isin U k isin OS(4)

1113944kisinOS

1113944iisinU

xikjl 1 forallj isin L l isin OF(5)

1113944cisinV

αikc 1 foralli isin Nk k isin OS (6)

1113944iisinNk

αikc 1 forallc isin V k isin OF (7)

1113944bisinB

θikb 1 foralli isin Nk k isin OS (8)

1113944iisinNk

θikb 1 forallb isin B k isin OS (9)

Constraint expressed in (4) ensures that the same AGVis used to complete the loading task of the QC after it hasfinished the unloading task Constraint (5) implies thatafter the QC finishes a loading task the same AGV is usedto complete the unloading task of the QC Constraint (4)and Constraint (5) confirm the completion of the loadingand unloading processes Constraint (6) indicates thateach loading and unloading task can only be performed byone AGV Constraint (7) implies that every AGV onlyperforms one task at a time Constraint (8) means that theARMG transports a container to be stacked in the assignedblock of the storage yard Constraint (9) expresses thateach ARMG in block can only load and unload onecontainer at a time

gik + dik + T1 lepik foralli isin U k isin O (10)

pik + 1113944cisinV

tiαikc le zik foralli isin U k isin O (11)

zik + T2 + 1113944bisinB

hikθikb lefik foralli isin U k isin O (12)

Constraints (10) to (12) represent the correspondingrelationship of time between a ship starting and finishing aloading task Constraint (10) represents the time when theAGV begins to transport the container from the QC basedon the time that the portal trolley of the QC takes to handlethe container Constraint (11) means the relationship of thetime when the AGV starts to transport the container to theAGV-mate Constraint (12) signifies the relationship be-tween the time the container transportation is finished bythe ARMG and the time the container is transported to theAGV-mate

zik + 1113944cisinV

tiαikc le zjl + M 1 minus xikjl1113872 1113873

foralli isin U j isin L k isin OS l isin OF

(13)

Constraint (13) gives the relationship between the timewhen the same AGV finishes an unloading task and thenstarts the next loading task

gjl + 1113944bisinB

hjlθjlb + T2 le zjl forallj isin L l isin O (14)

zjl + 1113944cisinV

tjαjlc lepjl forallj isin L l isin O (15)

pjl + T1 + djl lefjl forallj isin L l isin OF (16)

Constraints (14) to (16) express the relationship betweenthe time when the container is initially loaded from the blockand the completion of loading at each time of shipmentConstraint (14) represents the time when the ARMG in theback of block obtains the container which is less than thetime needed for the AGV to obtain the container from theAGV-mate Constraint (15) means that the starting time ofAGV from the block does not exceed the time of the AGVarriving at the QC Constraint (16) implies the time taken bythe portal trolley in QC to obtain the container from theAGV which is no more than the time when the loading taskis finished

pjl + 1113944cisinV

tjαjlc lepik + M 1 minus xjlik1113872 1113873


(17)

Constraint (17) represents the time relation between thecompletion of a loading task by the AGV and start of thenext unloading task

g(i+1)k minus gik dik + d(i+1)k foralli isin U k isin O (18)

g(i+1)k minus gik hik + h(i+1)k foralli isin L k isin O (19)

dik gt 0 gik ge 0 hik gt 0 pik gt 0 fik gt 0 zik gt 0

foralli isin Nk k isin O

(20)

ti ge 0 foralli isin Nk (21)

Constraint (18) explains the time relation of the maintrolley of QC when it starts to unload two consecutivecontainers Constraint (19) represents the time relationshipof the ARMG in the back of block when it loads twoconsecutive containers Constraint (20) represents the rangeof time parameters Constraint (21) expresses the range oftime parameters about the AGVsrsquo transportation

4 Proposed Algorithm

41 Hybrid GA-PSO (HGA-PSO) Algorithm with Fuzzy LogicController to Adaptive Autotuning e genetic algorithm(GA) and particle swarm optimization (PSO) are two well-known metaheuristic methods of optimization [42 43] eGA takes all the individuals in the population as the researchobject which is a method to search the optimal solution by


simulating the biological evolution process in nature esolving problem of a population is according to the evolutionby natural selection (probability optimization) each sub-sequent generation evolved better approximation With theaid of crossover and mutation of genetic operators gener-ating the new population of solution and then to selectindividual by the fitness value the selected individual will bemore adaptable to the environmente best individual afterdecoding can be used as the approximate optimal solution ofthe problem

PSO is a parallel algorithm which is inspired by bi-ological population characteristics and has strong robust-ness simulating the random searching process of birds forhunting and extending it to multidimensional space Allparticles by evaluating their fitness function to determine thecurrent location with the speed of particles to adjust thedistance and direction of their flights and every particle hasthe memory function and can remember the best searchingsite

e flight speed of the particle can be dynamically ad-justed by the flight experience of the particle and its com-panions PSO can flexibly update the position of the particlein real-time by using equations (22) and (23) which showsits superiority [44] Compared with the GA which is easierto implement the PSO does not require alteration of manyparameters e fitness of particle can be calculated as

vk(t + 1) vk(t) + b1r1 hbestk minus xk(t)1113872 1113873 + b2r2 gbest minus xk(t)( 1113857

(22)

xk(t + 1) xk(t) + vk(t + 1) (23)

where vk(t) is the velocity of particle at the tth iteration b1and b2 are the acceleration constants and r1 and r2 isin [0 1]which follows the uniform random distribution

GA is an algorithm showing stability and applicabilityand its remarkable performance has been proved in manyresearch studies [45] However the metaheuristic GAcannot guarantee the optimal solution in all cases due to theuncertain parameters Yun and Gen [46] researched theadaptive autotuning strategy by changing the average fitnessof GA taking advantage of the mathematical optimizationmethod which can adaptively update crossover and mu-tation rates during the genetic search processes to achievethe fuzzy logic control in the parent and their offspring Ifthis approach is applied in this problem the average fitnessat generation t can be set as follows

Δfavg(t) fPs(t) minus fOs

(t) 1Ps

1113944

Ps

k1fk(t) minus

1Os

1113944

Os

k1fk(t)

(24)

where Ps and Os are the population size and offspring sizethat satisfy the constraints respectively and f(t) is theadaptability function representing the individual fitness

We proposed that this hybrid GA-PSO is an improvedmetaheuristic algorithm It not only combines the PSOparameters with GA operators but also uses the fuzzy logiccontroller with the initialization of parameters and

particles which through the adaptive auto tuning strategycan constantly adjust in the iteration process of populatione overall procedure of this method is illustrated inFigure 3 to obtain a better solution to this problem especific reasons of using this improved hybrid GA-PSOalgorithm are as follows (a) it has more adaptability andcompatibility and it accords with the characteristics andstructure of this model in container terminals and is suitedfor dealing with many parameters and relative complexlogic relations (b) it makes use of advantages of differentmetaheuristic algorithms (PSO and GA) and has betterglobal searching ability especially in solving process (c) itcan improve the diversity of the population and the abilityof continuous optimization On the whole it can promise abetter performance in solving the actual problem comparedwith the other algorithms [47ndash49]

As discussed above we consider the integrated sched-uling of QCs AGVs and ARMGs in container terminals thetask encoding procedure of this is as follows (1) applying thesmallest position value (SPV) rule [48 50] (2) assigning thetasksrsquo codes to the related particles (3) identifying the op-eration sequence in each task is paper uses integerencoding assuming that there are 2 QCs each QC having 4loading containers and 4 unloading containers and 4 AGVsto transport containers e QCs and blocks have beenmatched but the chromosomes are relatively long andmultiple-point crossover and swapping mutation are usedas shown in Figure 4 We select multiple crossing points onchromosomes randomly and exchange the subsequencebetween the parent and the offspring After the crossover toeffectively improve the chromosomes the genes in chro-mosomes are needed to be checked and repaired by theswapping mutation

e final encoded solution should estimate the objectivefunction which minimizes the loading and unloading timeof the ship as given in equations (2) to (21) Equation (1) isused to evaluate the total fitness values of this problem

42 Hybrid BAT-GA (HBAT-GA) Bat algorithm (BAT) isused to simulate the random search of bats using the sonar todetect prey and avoid obstacle in nature the process ofoptimization and searching is also themovement and prey ofthe individual bat in populations Taking advantage ofecholocation technology of bats using different pulse fre-quencies and loudness the BAT solved the problem byevaluating the value of fitness function to judge the locationIt has the advantage of distributed and fast convergence butis still a new swarm intelligence algorithm due to the in-stability of convergence and imprecise calculation in solvingproblems [51 52] e hybrid BAT-GA is a method whichutilizes the crossover mutation and selection of GA toincrease the diversity of population and the ability of globalsearch Inspired from diverse metaheuristic algorithmsvarious improved kinds of BAT were designed and used tosolve many optimization problems successfully [53]

In BAT each bat is defined by its position Xi velocity Vipulse frequency Fi pulse loudness Ai and pulse emission rateRi to search the space each bat updates the following equations


Fi Fmin + Fmax minus Fmin( )β β isin [0 1]

Vt+1i Vti + Xti minus Xi( )Fi

Xt+1i Xt

i + Vt+1i

Xnewi Xold

i + εAi ε isin [minus 1 1]

At+1i αAti 0lt αlt 1

Rt+1i R0i minus exp(minus σt) σ gt 0

(25)

Figure 5 shows the whole pseudo code of hybrid BAT-GAe process should be repeated until reaching the maximumpopulatione gene with global optimumwill be returned asthe best tness once meeting the optimal stopping criteria

5 Computational Experiments and Discussion

To achieve the integrated scheduling of QCs AGVs andARMG we used the commercial software AIMMS 311 forsmall-sized problems which obtained branch and bound(BampB) algorithm in CPLEX Due to the increase in thenumber of containers it was dicult to obtain optimal so-lutions erefore we adopted the metaheuristic algorithmto obtain approximate optimal solution for large-sizedproblems We also provided the comparison results between

the metaheuristic algorithm and AIMMS to verify the ef-fectiveness of the metaheuristic algorithm in small-sizedproblems We implemented the various heuristic and im-proved heuristic algorithms in MATLAB 2018a on a com-puter with an Intel (R) Core (Tm) CPU340 i7-6700GHzand 4GB RAM running theWindows 10 operation system Inorder to reduce the deviation caused by the randomness of theheuristic algorithm every problemwas solved 20 times wherethe average computation time (CPU time) and best tnessvalue (BFV) were used as the nal results

51 Initial Setting

(1) e number of loading and unloading containersvaried from 1 to 1000 where 4sim100 was considered asthe small-sized problem and 100sim1000 as the large-sized problem We also considered the number ofblocks and ARMGs in the ranges 2sim8 and 4sim16 whilethe number of considered AGVs varied from 8 to 24

(2) In this work we obtained the port operation valuesfrom the Xiamen Automated Container terminal eprocessing time of the main trolley that placed thecontainer onto the transfer platform followed theuniform distribution U (20 40) s e processing timeof the portal trolley that placed the container onto theAGV from the transfer platform was xed at 20 s andthe processing time of the ARMG localized in the frontof the yard which obtained the container from theAGV-mate and then unloaded it in the storage area wasxed at 25 se processing time of ARMG localized inthe back of yard that moved the container from thestorage area to the assigned truck followed the uniformdistribution U (20 30) s e path of horizontaltransportation is set in advance All of these valuescorrespond with a real-time situation of the terminal

(3) e GA parameters were set based on preliminarytests including a crossover rate (Pc) of 09 mutationrate (Pm) of 01 population size (Ps) of 50 andmaximum generation (Mg) of 500 e PSO pa-rameters included alternate rate (Pa) [08 2 2] andprecious rate (Pr) 005e BATparameters includedα of 095 σ of 09 pulse loudness Ai isin[0 1] andpulse emission rate Ri isin[0 05]

52 Results for Small-Sized Problems irteen small-sizedexperiments were performed where the number of con-tainers varied from 4 to 100 Table 1 shows that for the small-sized problems the GA achieves approximately BFV com-pared to the BampB in terms of speed where the CPU time ofthe former algorithm ranged from 346 to 1266 s and that ofBampB ranges from 1237 s to 1153482 s e BampB cannot beapplied for experiments with more than 40 containerswhich increases the computation time exponentially eresults also conrm that BampB cannot solve the large-sizedproblems within a reasonable time frame In addition weobserve that the dierence of BFV between the GA and theBampB is small where the maximum gap rate of BFV is 420

procedure hybrid GA-PSO for the integrated scheduling in ACTsinput problem data PSO parameters (f(x) b1 b2 maxIter) GA parameters

output the best solution


begin

intialize (vk xk) for each particle k P(t) = [xk(t)] populationevaluate xk (t) by decoding routine and keep the best solutionwhile t le maxIter do

for each particle xk in swarm doupdate velocity vk(t + 1) and position xk(t + 1) by (22) and (23)find the local best position of the particle hbestk

find the global best position for the particle gbestk

evaluate xk(t + 1) by encoding routine

if f(xk(t + 1)) lt f(hbestk) then

update hbestk = xk(t + 1)

end

end

end

(Ps Mg Pm Pc) and Pc(t ndash 1) Pm(t ndash 1) ∆favg(t ndash 1) ∆favg (t) ε γ

gbest = argminf(hbestk f (gbest))

creat offspring C(t) from xk(t + 1) by multi-point crossover routinecreat offspring C(t) from xk(t + 1) by insertion mutation routinecheck and repair all offspring C(t) for feasible solutionimprove offspring C(t) by hill-climb method routineevaluate C(t) by decoding routine and update the best solution bycomparing with gbestselect P(t + 1) from P(t) and C(t) by routine wheel selection routinetune parameter by the fuzzy logic controller to adaptive auto tuning by (24)

if ε le ∆favg(t ndash 1) le γ and ε le ∆favg(t) le γ

if ndashγ le ∆favg(t ndash 1) le ndashε and ndashγ le ∆favg(t) le ndashε

if ndashε le ∆favg(t ndash 1) le ε and ndashε le ∆favg(t) le ε

then increase Pm and Pc for next generation

then decrease Pm and Pc for next generation

then rapidly increase Pm and Pc for next generation

t o iteration number

+ 1t t

Figure 3 Procedure for hybrid GA-PSO and the fuzzy logiccontroller for adaptive autotuning


e GA can obtain the optimal tness value for the rst twocases e BFV exhibits the same growth trend as thenumber of containers increases as shown in Table 1

53 Results for Large-Sized Problems As the CPU time in-creases it becomes more dicult to use the BampB method to

solve the large-sized optimization problems GA can gen-erate an optimal solution in small-sized problems within areasonable time frame so we used some metaheuristic al-gorithms (PSOBAT) to solve the large-sized problems aboutthe automated terminals We considered a number ofcontainers in an interval of 150ndash1000 with 8ndash24 AGVs 2ndash8QCs and 2ndash8 blocks to perform simulations Table 2

procedure Hybrid BAT-GA for the integrated scheduling in ACTsinput Problem data BAT parameters [position X(i) velocity V(i) pluse rates R(i) pluse loudnessA(i) emission rate R(i)] and GA parameters (Ps Mg Pm Pc)output the best solution (fitness value)f


begin

initialize [X(i) V(i)] for each bat i f populationdefine the pulse frequency F(i) at X(i)calculate the fitness of each initial position F(i) at X(i) by (25)while (i lt maximum number of iterations) and (optimal solution not found) do

for each bat X(i) in population dogenerate the new solution by adjusting the F(i) and V(i) and adapting velocity V(i)r by (26)and (27)find and evaiuate a new soluton f lowastif (rand gt R(i)) then

generate a local solution around the selected best solutionend if

end forsend the local best to genetic populationfor each genetic in population do

generate a global best solution f lowastlowast by crossover rate Pc and mutation rate Pm

if (boundary lt f lowastlowast) thengenerate a random solution with in the boundary

end ifrank the chromosome to determine the best solution

end for

end whileevaluate fitness and met the criteria rule

end

i i + 1

i i + 1

t o

Figure 5 Procedure for hybrid BAT-GA

Parent 1 1 5 2 7 6 8 3 1 2 3 44 1 2 3 4 5 2 8 4 1 3 7 6

Parent 2

Unloading AGV number Loading

8 3 7 5 1 2 4 1 3 2 46 1 4 2 3 6 1 5 3 7 2 8 4

Offspring 1 4 2 7 5 1 8 3 1 2 4 36 1 3 4 2 8 4 5 3 7 2 8 4

Offspring 2 8 3 2 7 6 5 1 3 2 1 24 1 4 3 4 6 5 8 4 1 3 7 2

4 2 7 5 1 8 3 1 2 4 36 1 3 4 2 8 4 5 3 7 2 8 4

8 4 3 7 2 1 6 1 2 3 45 1 2 3 4 5 2 8 4 1 3 7 6

Parent

Offspring

Chromosome

Crossover

Mutation

Figure 4 Example of crossover and mutation operations


presents the simulation results of PSO GA and BATViewed generally we can find that the GA performs betterthan others the BFV of GA compared with PSO and BATshows more optimization with less time of CPU

However with the increase of the number of containersthe computation time has been increased sharply the timewas still long that we used the metaheuristic algorithm tosolve this problem which may not meet the needs ofscheduling in current container terminals so we tried to takeadvantage of the improved heuristic algorithms to solve thisoptimization problems faster and more stably So the hybridGA-PSO algorithm (HGA-PSO) and hybrid BAT-GA(HBAT-GA) were used to solve the large-sized problemsand the results are given in Table 3

From our experiments uniting Tables 2 and 3 weconclude that (1) our proposed hybrid GA-PSO algorithmperforms more stably to obtain near-optimal solutions tolarge-sized problems (examples 15 25 30 and 31 in Ta-ble 3) from example 31 the number of containers is 1000

and the CPU time is less than 8 minutes (45208 s) whichcomply with the requirements of scheduling operation interminals (2) the BFV increases with the number ofcontainers as well as it takes longer time to obtain thesolution with the increased number of QCs AGVs andblocks (3) the appropriate integrated scheduling scheme isvery important with the sharp increase of containers italways choose to add the equipment number of QCsAGVs and blocks but it may not truly reduce the com-pletion time and improve overall operational efficiency(examples 16 17 and 18 in Table 2 examples 17 18 and 19in Table 3)

Figures 6ndash8 show the performance comparisons fordifferent algorithms Figure 6 shows the simulation of 650containers 18 AGVs 6 QCs and 6 blocks GA and PSOreach the convergence at the 350 and 420 generations butHGA-PSO achieves the convergence before 130 generationsand has a better optimal fitness value e HGA-PSOcombines the stability of GA and the velocity of PSO which

Table 1 Result of computational experiments in small sizes

No Containers AGVsQCsblockBampB GA

BFV gap rate ()CPU (s) BFV (s) CPU (s) BFV (s)

1 4 2-2-2 1237 157 346 157 02 8 2-2-2 2156 338 274 338 03 10 3-2-2 1890 280 188 281 0354 15 4-2-3 2467 384 459 386 0525 20 4-2-3 24489 433 436 438 1156 30 5-3-4 57378 394 885 405 2797 40 6-3-3 1153482 405 1076 422 4208 50 7-3-4 mdash mdash 1595 517 mdash9 60 8-3-5 mdash mdash 2117 594 mdash10 70 8-3-3 mdash mdash 1083 643 mdash11 80 9-4-4 mdash mdash 1464 897 mdash12 90 9-4-5 mdash mdash 1898 942 mdash13 100 10-4-5 mdash mdash 1266 816 mdash

Table 2 Result of large-sized problems by heuristic algorithms

No Container AGVQCblockPSO GA BAT

CPU (s) BFV CPU (s) BFV (s) CPU(s) BFV (s)14 150 843 2539 1556 2351 1359 2264 140215 200 944 3520 1709 2908 1408 3129 146916 250 1045 5652 1673 4286 1426 4457 164417 300 1146 7967 1526 6356 1759 6815 150918 350 1253 10677 1782 8922 1643 8843 168819 400 1354 14329 1653 12047 1726 13498 209320 450 1455 18488 1864 15780 1831 16849 184921 500 1556 23396 1926 19731 2150 21938 243322 550 1667 27649 2364 24680 2110 26760 204223 600 1765 31976 2399 30547 2331 31197 248324 650 1866 34801 2697 35971 2509 36749 260825 700 1967 44915 2907 42706 2776 42261 239426 750 2077 58067 3028 50072 2507 50826 307727 800 2177 69077 3597 58469 3144 64578 338428 850 2278 83016 3960 65724 3820 79248 402229 900 2378 119712 4838 74950 3643 95864 428230 950 2488 143816 4697 85714 3926 119765 430831 1000 2488 172252 5213 100926 4418 152806 4836


performs surpassingly in terms of both solution time andquality Figure 7 shows our simulation of 700 containers 19AGVs 6 QCs and 7 blocks the HPSO-GA reaches theconvergence at 320 generations which has been comparedwith the GA and BAT and shows better optimization insolving time and quality But due to the instability of BAT ithas limited inlaquouence on the time of obtaining solutionsFigure 8 illustrates the performance of ve algorithmsComparison of heuristic algorithms such as GA PSO andBAT shows that the GA is more stable and reliable theconvergence speed of the PSO is the slowest and unstableand the BAT has certain laquouctuations and slow speed in theprocess of getting solutions e improved metaheuristic

algorithms of HGA-PSO and HBAT-GA compared with thebasic metaheuristic algorithm (GA BAT and PSO) have afaster convergence speed e HBAT-GA reaches the con-vergence at 320 generations but HGA-PSO realizes theconvergence almost at 210 generations and has a betteroptimal tness value e HGA-PSO outperforms thesimilar HBAT-GA in terms of both solution time andquality

In order to test the stability of each algorithm in dealingwith the tness value in terms of iterations the CPU time isreported and compared in Figure 9 It shows that the HGA-PSO outperforms the other algorithms in terms of executiontime which ensures to yield quality solution in reasonableruntimee performance trend of 31 examples with the vealgorithms in Tables 1ndash3 is depicted in Figure 10 ere aresome gaps between the tness values of GA and HGA-PSO

Table 3 Result of large-sized problems by improved heuristicalgorithm

No Container AGVQCblock

HGA-PSO HBAT-GACPU(s)

BFV(s)

CPU(s)

BFV(s)

14 150 843 1438 1355 2167 128615 200 944 1726 1285 2358 131216 250 1045 2164 1310 2611 146117 300 1146 2655 1309 3209 160618 350 1253 3249 1391 3877 147719 400 1354 3886 1328 4962 152120 450 1455 4491 1696 7381 139721 500 1556 5113 1548 10122 165322 550 1667 5876 1613 15434 179723 600 1765 7041 1683 21307 176824 650 1866 8237 1856 24608 193225 700 1967 10655 1838 31764 228826 750 2077 13884 2027 38269 271127 800 2177 18243 2068 43055 248628 850 2278 23611 2262 49970 286429 900 2378 34005 2737 56278 268830 950 2488 39671 3094 65907 380831 1000 2488 45208 3275 76604 3989

0 50 100 150 200 250 300 350 400 450 5001600

2000

2400

2800

3200

3600

PSOGAHGA-PSO

Fitn

ess v

alue

Iterations

Figure 6 Typical convergence of PSO GA and HGA-PSO al-gorithms for example with 650 containers 18 AGVs 6 QCs and 6blocks

Fitn

ess v

alue

0 50 100 150 200 250 300 350 400 450 500

2000

2400

2800

3200

3600

4000

GABATHBAT-GA

Iterations

Figure 7 Typical convergence of GA BAT and HBAT-GA forexample with 700 containers 19 AGVs 6 QCs and 7 blocks

0 50 100 150 200 250 300 350 400 450 500

2000

2500

3000

3500

4000

4500

5000

5500

PSOBATGA

HBAT-GAHGA-PSO

Fitn

ess v

alue

Iterations

Figure 8 Performance of the ve algorithms for 800 containers 21AGVs 7 QCs and 7 blocks


the gap is less in the small-sized problems However theincrease of gap as the number of containers increases in thelarge-sized problems has become a signicant problem Inother words the HGA-PSO is markedly superior to GAPSO BAT and HBAT-GA in solving these large-scalecalculation problems ese promising results are duemainly to the hybrid that balances disadvantages of thealgorithm and enhances the ability and diversication inHGA-PSO

To clarify the eciency and robustness of the improvedalgorithms taking example 31 as a case of statistical analysisdata in Table 4 according to mean optimal tness and CPUtime we compared the results of dierent algorithms with theactual operation (in Xiamen Port) and performed the Paretooptimization for the percent of deviation and improvementthat weighs the optimization in terms of solution time andquality e result shows that the HGA-PSO has the leastvalue in the percent of deviation and improvement compared

with the actual operation Although the advantages of HGA-PSO are reduced through the comprehensive balance insolving time and quality the value of Pareto optimization ofHGA-PSO is 1898 which is smaller than the others andcloser to the actual operation We fully demonstrate that theproposed HGA-PSO has better robustness and eectivenesscompared with other algorithms in solving this problem

Taken together our simulation experiments indicate thatthe proposed HGA-PSO is reliable in solving this problem ofvarying scales and can be readily applied to the integratedscheduling of QCs AGVs and ARMGs in current auto-mated terminals

6 Conclusion

An integrated scheduling of QCs AGVs and ARMGs wasproposed in this paper for improving the working eciencyand service level of automated terminals We established an

50 100 150 200 250 300 350 400 450 5000

50

100

150

200

250

HGA-PSOHBAT-GAGA

BATPSO

CPU

tim

e (S)

Iterations

Figure 9 Evaluation of CPU time in terms of the number of iterations in ve algorithms

5 10 15 20 25 30

1000

2000

3000

4000

5000

PSOGABAT

HGA-PSOHBAT-GA

Fitn

ess v

alue

Number

Figure 10 Performance trends of ve algorithms with 31 examples


MIP model with the goal of minimizing the loading andunloading time of ships and then using the accurate algorithm(BampB) the basic metaheuristic algorithm (PSO GA andBAT) and the improved metaheuristic algorithm (HGA-PSOand HBAT-GA) to check the validity of the model

We improved the HGA-PSO with adaptive autotuningapproaches by fuzzy control and compared with the otheralgorithms (PSO GA BAT and HBAT-GA) to validate thefavorable convergence speed of HGA-PSO rough a series ofnumerical experiments we show that the proposed HGA-PSOhas better robustness and effectiveness compared with otheralgorithms in terms of solution time and quality of this problemWhen the number of containers was 1000 the best fitness valuewas 3275 s the computation time was 45208 s and the value ofpareto optimization was the smallest with 1898 It illustratedthis method can effectively reduce the working time and ad-vance the operating efficiency in automated terminals

As future work the computation time of HGA-PSO isstill relatively lengthy in solving large-sized experimentsrendering it inapplicable to dynamic real-time schedulingproblems We can try using GPU parallel computing toreduce the computation time We also believe that applyingother new improved metaheuristic algorithms such as ar-tificial intelligence or machine learning may yield evenbetter results than this HGA-PSO Besides the followingresearch of automated terminals on the balance ofthroughput and energy the AGVs path planing and effiencyoptimizationwill be more meaningful

Data Availability

e automated container terminals data used to support thefindings of this study are included within the article

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is work was supported by the Shanghai Science and Tech-nology Commission (nos 19595810700 and 18295801100) andYunnan Science and Technology Commission (no 2018IB022)

References

[1] G Parise L Parise L Martirano P Ben Chavdarian andA Ferrante ldquoWise port and business energy managementport facilities electrical power distributionrdquo IEEE

Transactions on Industry Applications vol 52 no 1 pp 18ndash24 2016

[2] Y Yang M Zhong H Yao F Yu X Yu and O PostolacheldquoInternet of things for smart ports technologies and chal-lengesrdquo IEEE Instrumentation amp Measurement Magazinevol 21 no 1 pp 34ndash43 2018

[3] Y Yang M Zhong and Y Dessouky ldquoAn integratedscheduling method for AGV routing in automated containerterminalsrdquo Computers amp Industrial Engineering vol 126pp 482ndash493 2018

[4] G Alsoufi X Yang and A Salhi ldquoCombined quay craneassignment and quay crane scheduling with crane inter-vesselmovement and non-interference constraintsrdquo Journal of theOperational Research Society no 4 pp 1ndash12 2017

[5] P Angeloudis andM G H Bell ldquoAn uncertainty-aware AGVassignment algorithm for automated container terminalsrdquoTransportation Research Part E Logistics and TransportationReview vol 46 no 3 pp 354ndash366 2010

[6] H Rashidi and E P K Tsang ldquoA complete and an incompletealgorithm for automated guided vehicle scheduling in con-tainer terminalsrdquo Computers amp Mathematics with Applica-tions vol 61 no 3 pp 630ndash641 2011

[7] H Zhang and K H Kim ldquoMaximizing the number of dual-cycle operations of quay cranes in container terminalsrdquoComputers amp Industrial Engineering vol 56 no 3 pp 979ndash992 2009

[8] L Chen A Langevin and Z Lu ldquoIntegrated scheduling ofcrane handling and truck transportation in a maritimecontainer terminalrdquo European Journal of Operational Re-search vol 225 no 1 pp 142ndash152 2013

[9] S Hartmann ldquoScheduling reefer mechanics at containerterminalsrdquo Transportation Research Part E Logistics andTransportation Review vol 51 no 51 pp 17ndash27 2013

[10] Z-H Hu J-B Sheu and J X Luo ldquoSequencing twin au-tomated stacking cranes in a block at automated containerterminalrdquo Transportation Research Part C Emerging Tech-nologies vol 69 pp 208ndash227 2016

[11] N Kaveshgar and N Huynh ldquoIntegrated quay crane and yardtruck scheduling for unloading inbound containersrdquo In-ternational Journal of Production Economics vol 159 no 3pp 168ndash177 2015

[12] L Tang J Zhao and J Liu ldquoModeling and solution of thejoint quay crane and truck scheduling problemrdquo EuropeanJournal of Operational Research vol 236 no 3 pp 978ndash9902014

[13] H Dkhil A Yassine and H Chabchoub ldquoMulti-objectiveoptimization of the integrated problem of location assignmentand straddle carrier scheduling in maritime container ter-minal at importrdquo Journal of the Operational Research Societyvol 2017 pp 1ndash23 2017

[14] S M Homayouni S H Tang and O Motlagh ldquoA geneticalgorithm for optimization of integrated scheduling of cranes

Table 4 Test results of example 31 of the optimization algorithm

Algorithm Mean optimal fitness Percent of deviationD ()

Mean CPUtime

Percent of improvementI ()

Pareto optimizationzD + ϕI()

Actual operation 3607 0 59381 0 0BampB 3382 624 Exceed capacity mdash mdashPSO 5213 4452 172252 19007 14155GA 4418 2248 100926 6996 5413BAT 4836 3407 152806 15733 11624HGA-PSO 3275 920 45208 2387 1898HBAT-GA 3989 1059 76604 2900 2286


vehicles and storage platforms at automated container ter-minalsrdquo Journal of Computational and Applied Mathematicsvol 270 pp 545ndash556 2014

[15] J Luo and Y Wu ldquoModelling of dual-cycle strategy forcontainer storage and vehicle scheduling problems at auto-mated container terminalsrdquo Transportation Research Part ELogistics and Transportation Review vol 79 pp 49ndash64 2015

[16] X Zhang Q Zeng and Z Yang ldquoModeling the mixed storagestrategy for quay crane double cycling in container terminalsrdquoTransportation Research Part E Logistics and TransportationReview vol 94 pp 171ndash187 2016

[17] D Pjevcevic I Vladisavljevic K Vukadinovic et al ldquoAp-plication of DEA to the analysis of AGV fleet operations in aport container terminalrdquo Procedia-Social and BehavioralSciences vol 20 no 6 pp 816ndash825 2011

[18] X J Jiang and J G Jin ldquoA branch-and-price method forintegrated yard crane deployment and container allocation intransshipment yardsrdquo Transportation Research Part BMethodological vol 98 pp 62ndash75 2017

[19] N Al-Dhaheri and A Diabat ldquoA Lagrangian relaxation-basedheuristic for the multi-ship quay crane scheduling problemwith ship stability constraintsrdquoAnnals of Operations Researchvol 248 no 1-2 pp 1ndash24 2016

[20] S Emde and N Boysen ldquoBerth allocation in container ter-minals that service feeder ships and deep-sea vesselsrdquo Journalof the Operational Research Society vol 67 no 4 pp 551ndash5632016

[21] A Santini H A Friberg and S Ropke ldquoA note on amodel forquay crane scheduling with non-crossing constraintsrdquo En-gineering Optimization vol 47 no 6 pp 860ndash865 2015

[22] R T Moghaddam A Makui A Salahi et al ldquoAn efficientalgorithm for solving a new mathematical model for a quaycrane scheduling problem in container portsrdquo Computers ampIndustrial Engineering vol 56 pp 241ndash248 2009

[23] Y Lu and M Le ldquoe integrated optimization of containerterminal scheduling with uncertain factorsrdquo Computers ampIndustrial Engineering vol 75 no 1 pp 209ndash216 2014

[24] A Salhi G Alsoufi and X Yang ldquoAn evolutionary approachto a combined mixed integer programming model of seasideoperations as arise in container portsrdquo Annals of OperationsResearch vol 4 pp 1ndash30 2017

[25] J He Y Huang W Yan and S Wang ldquoIntegrated internaltruck yard crane and quay crane scheduling in a containerterminal considering energy consumptionrdquo Expert Systemswith Applications vol 42 no 5 pp 2464ndash2487 2015

[26] A Wang M Ranjbar and N Jamili ldquoScheduling of loadingand unloading operations in a multi stations transshipmentterminal with release date and inventory constraintsrdquo Com-puters amp Industrial Engineering vol 106 pp 20ndash31 2017

[27] P Guo W Cheng Z Zhang M Zhang and J Liang ldquoGantrycrane scheduling with interference constraints in railwaycontainer terminalsrdquo International Journal of ComputationalIntelligence Systems vol 6 no 2 pp 244ndash260 2013

[28] O Mustapha A E H Alaoui and J Boukachour ldquoAn effi-cient genetic algorithm to solve the intermodal terminal lo-cation problemrdquo Endocrinology vol 75 no 5 pp 586ndash5912015

[29] P Guo W Cheng and Y Wang ldquoParallel machine sched-uling with step-deteriorating jobs and setup times by a hybriddiscrete cuckoo search algorithmrdquo Engineering Optimizationvol 47 no 11 pp 1564ndash1585 2015

[30] M Wang B Li G Zhang et al ldquoPopulation evolvabilitydynamic fitness landscape analysis for population-based

metaheuristic algorithmsrdquo IEEE Transactions on EvolutionaryComputation vol 99 p 1 2017

[31] S Wang K Zheng J Zheng et al ldquoAn improved discreteparticle swarm optimization for tugboat scheduling problemin container terminalrdquo Medical Education vol 34 no 7pp 573ndash579 2010

[32] N Kaveshgar H Nathan R Saeed et al ldquoAn efficient geneticalgorithm for solving the quay crane scheduling problemrdquoExpert Systems with Applications no 39 pp 13108ndash131172012

[33] P Legato R Trunfio and F Meisel ldquoModeling and solvingrich quay crane scheduling problemsrdquo Computers amp Oper-ations Research vol 39 no 9 pp 2063ndash2078 2012

[34] T Gu T Gu B Lu et al ldquoGenetic mechanism-based couplingalgorithm for solving coordinated scheduling problems ofyard systems in container terminalsrdquo Computers amp IndustrialEngineering vol 89 pp 34ndash42 2015

[35] F Shu W Mi X Li N Zhao C Mi and X Yang ldquoA double-population genetic algorithm for ASC loading sequence op-timization in automated container terminalsrdquo Journal ofCoastal Research vol 73 pp 64ndash70 2015

[36] M-W Li W-C Hong J Geng and J Wang ldquoBerth and quaycrane coordinated scheduling using multi-objective chaoscloud particle swarm optimization algorithmrdquo NeuralComputing and Applications vol 28 no 11 pp 3163ndash31822017

[37] A Wang S K Kumar A Gunasekaran and M K TiwarildquoSustainable maritime inventory routing problem with timewindow constraintsrdquo Engineering Applications of ArtificialIntelligence vol 61 pp 77ndash95 2017

[38] W Tiwari Y Wang P Gupta et al ldquoA novel hybrid heuristicalgorithm for a new uncertain mean-variance-skewnessportfolio selection model with real constraintsrdquo Applied In-telligence vol 48 pp 2996ndash3018 2018

[39] T G Crainic M Hewit M Toulouse et al ldquoService networkdesign with resource constraintsrdquo Transportation Sciencevol 50 no 4 2016

[40] E Li and H Wang ldquoAn alternative adaptive differentialevolutionary algorithm assisted by expected improvementcriterion and cut-HDMR expansion and its application intime-based sheet forming designrdquo Advances in EngineeringSoftware vol 97 pp 96ndash107 2016

[41] P Liu G Cui Y Xiao et al ldquoA new heuristic algorithm withthe step size adjustment strategy for heat exchanger networksynthesisrdquo Energy vol 143 pp 24ndash37 2018

[42] M Gen and R Cheng Genetic Algorithms and EngineeringOptimization pp 512ndash520 Wiley Hoboken NJ USA 2000

[43] M Gen R Cheng and L Lin Network Models and Opti-mization Multiobjective Genetic Algorithm Approachpp 710ndash715 Springer Nature Switzerland 2008

[44] C Sangsawang K Sethanan T Fujimoto and M GenldquoMetaheuristics optimization approaches for two-stage re-entrant flexible flow shop with blocking constraintrdquo ExpertSystems with Applications vol 42 no 5 pp 2395ndash2410 2015

[45] A Gen D Srinivasan S Biswas and T Reindl ldquoA geneticalgorithm-differential evolution based hybrid framework casestudy on unit commitment scheduling problemrdquo InformationSciences vol 354 pp 275ndash300 2016

[46] Y Reindl and M Gen ldquoPerformance analysis of adaptivegenetic algorithms with fuzzy logic and heuristicsrdquo FuzzyOptimization and Decision Making vol 2 no 2 pp 161ndash1752003

[47] T Jamrus C-F Chien M Gen and K Sethanan ldquoMultistageproduction distribution under uncertain demands with


integrated discrete particle swarm optimization and extendedpriority-based hybrid genetic algorithmrdquo Fuzzy Optimizationand Decision Making vol 14 no 3 pp 265ndash287 2015

[48] T Sethanan C F Chien M Gen et al ldquoHybrid particleswarm optimization combined with genetic operators forflexible job-shop scheduling under uncertain processing timefor semiconductor manufacturingrdquo IEEE Transactions onSemiconductor Manufacturing vol 31 no 1 pp 32ndash41 2017

[49] M Mussetta ldquoGenetical swarm optimization self-adaptivehybrid evolutionary algorithm for electromagneticsrdquo IEEETransactions on Antennas amp Propagation vol 55 no 3pp 781ndash785 2007

[50] X Zhou X Zhao and Y Liu ldquoA multiobjective discrete batalgorithm for community detection in dynamic networksrdquoApplied Intelligence vol 1 pp 1ndash13 2018

[51] K E Heraguemi N Kamel and H Drias ldquoMulti-swarm batalgorithm for association rule mining using multiple co-operative strategiesrdquo Applied Intelligence vol 45 no 4pp 1ndash13 2016

[52] N S Jaddi S Abdullah and A R Hamdan ldquoMulti-pop-ulation cooperative bat algorithm-based optimization of ar-tificial neural network modelrdquo Information Sciences vol 294pp 628ndash644 2015

[53] T Vidal T G Crainic M Gendreau N Lahrichi andW ReildquoA hybrid genetic algorithm for multidepot and periodicvehicle routing problemsrdquo Operations Research vol 60 no 3pp 611ndash624 2012


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equipment is paper considers the actual situation ofloading and unloading operation modes putting forward amethod to realize the integrated scheduling of QCs AGVsand ARMGs with the objective to minimize overall oper-ation timeis well-thought-out model is more reliable andrealistic and has better schedule optimization

e second is that most of the research studies of op-timization algorithms in solving this kind of problem usebasic metaheuristic algorithms We perform extensive nu-merical experiments to clearly compare the accurate algo-rithm (branch and bound) the basic metaheuristicalgorithms (genetic algorithm particle swarm optimizationand bat algorithm) and the improved metaheuristic algo-rithm (hybrid GA-PSO algorithm and hybrid BAT-GA) tobetter illustrate this problem obtaining optimum solutionsin short time And this result shows that the hybrid GA-PSOalgorithm with a fuzzy logic controller for adaptive auto-tuning is effective and shows significant improvementcompared with other methods

is paper is organized as follows Section 2 reviews therelevant literature In Section 3 the integrated schedulingproblem is formulated as a mixed integer programming(MIP) model Several algorithms are proposed in Section 4Numerical experiments based on simulation optimizationare conducted to examine effectiveness of the proposedmethod and the performance of different algorithms inSection 5 Finally some conclusions of this research aredrawn in Section 6

2 Literature Review

Automated terminal system is very complex involving mul-tiple subsystemsere are numerous studies on the schedulingand optimization of automated terminals such as the sched-uling of a single equipment separately [4ndash7] the collaborativescheduling between two handling equipment [8ndash12] and theintegrated scheduling between three handling equipment[13ndash16] Because automated terminals are a complex integratedsystem the research of single- or two-equipment scheduling isnot significant for the improvement of operation efficiency ofautomated terminals which also does not accord with theactual situation of automated terminals

21 Accurate Algorithms of Automated Terminals For ac-curate algorithms of container terminals most of the researchstudies focused on branch and bound algorithm (BampB) anddata envelopment analysis (DEA) For example Pjevcevicet al [17] studied the collaborative scheduling of QCs andAGVs in automated terminals used the DEA method toanalyze the operation efficiency of unloading containers andfinally obtained the reasonable scheduling scheme Jiang andJin [18] researched the integrated scheduling problem of QCsAGVs and YCs with the goal of minimizing cost of QCs bythe BampB method to solve the built mixed integer pro-gramming model through numerical experiments showingthat this method can improve the efficiency of terminalsere are also some comparisons of accurate algorithms andother algorithms Alsoufi et al [4] based on the scheduling

problem of QCs used the CPLEX to evaluate and compare theBampBmethod with the genetic algorithm from small- to large-scale examples but the results showed that the genetic al-gorithm had better performance

As mentioned above the accurate algorithm can get theexact solution but when the scale is relatively large it showslack of feasibility due to the influence of computation timeand complex logic relation in program [19ndash21] So moreworks chose to use metaheuristic algorithms

22 Basic Metaheuristic Algorithm of Automated TerminalsFor basic metaheuristic algorithms of container terminalsmost of the literature mainly used genetic algorithm (GA)particle swarm optimization (PSO) and simulated annealing(SA) which are usually based on the perception or expe-rience to construct algorithms For example Moghaddamet al [22] proposed a mixed integer programming model ofQC scheduling and it was hard to obtain the optimal so-lution through optimization software in reasonable time butthe GA solved this problem and showed the certain supe-riority Lu and Le [23] solved the collaborative schedulingmodel of AGVs and YCs by using PSO algorithm and theresults showed that this method could obtain the optimizedsolution Combining berth allocation with the QC sched-uling problem Salhi et al [24] compared the results of GAwith those of the exact CPLEX and showed the rationality ofusing the GA to find the optimal solution However inrecent years there has been much research on the com-parison of different algorithms of automated terminalsHomayouni et al [14] researched the integrated schedulingof container terminals adopting the GA and comparing itwith the SA and the result indicated that with the increase inthe number of containers the solving efficiency of the GA isobviously better than the SA Tominimize the delay time andenergy consumption of ships He et al [25] used the GA andPSO algorithm to effectively solve this problem and dis-cussed the solving ability of different algorithms

Although the basic metaheuristic algorithms may notobtain the exact solution it can obtain the suboptimal so-lution and the complexity of computing time is relativelylow and comparatively its applicability and stability arebetter than those of the accurate algorithm [26ndash28] How-ever taking more factors into consideration in automatedterminals the model is more complex and the basic met-aheuristic algorithm has shown up the disadvantages such aslonger computing time and slow convergence speed [29 30]

23 Improved Metaheuristic Algorithm of AutomatedTerminals For the application of improved metaheuristicalgorithms to container terminals many attempts have beenmade to improve different algorithms For example to solvethe ship scheduling problem Wang et al [31] used the im-proved discrete chaotic PSO algorithm and the simulationoptimization results showed that this method was suitable forthis problem Kaveshgar et al [32] proposed that the extendedGA designed to solve the scheduling problem of QCs can findthe optimal solution of a large-scale example in a shorter timeAccording to the working efficiency of QC scheduling




3 Model Formulation












Yard crane

Quay crane

Ship

AGV guide path

AGV-mate

Storage yard









0-1 variables






Fk maxkisinOF


Sk minkisinOS



1Discharging

Loading2

Maintrolley

Portaltrolley




1113944lisinOF

1113944jisinL


1113944kisinOS

1113944iisinU


1113944cisinV


1113944iisinNk


1113944bisinB


1113944iisinNk




pik + 1113944cisinV





zik + 1113944cisinV



(13)


gjl + 1113944bisinB


zjl + 1113944cisinV




pjl + 1113944cisinV



(17)






(20)










(22)

xk(t + 1) xk(t) + vk(t + 1) (23)




(t) 1Ps

1113944

Ps

k1fk(t) minus

1Os

1113944

Os

k1fk(t)

(24)











Xt+1i Xt

i + Vt+1i

Xnewi Xold




(25)





51 Initial Setting








begin







end

end

end











+ 1t t








begin








end for


end

i i + 1

i i + 1

t o


Parent 1 1 5 2 7 6 8 3 1 2 3 44 1 2 3 4 5 2 8 4 1 3 7 6

Parent 2


8 3 7 5 1 2 4 1 3 2 46 1 4 2 3 6 1 5 3 7 2 8 4

Offspring 1 4 2 7 5 1 8 3 1 2 4 36 1 3 4 2 8 4 5 3 7 2 8 4

Offspring 2 8 3 2 7 6 5 1 3 2 1 24 1 4 3 4 6 5 8 4 1 3 7 2

4 2 7 5 1 8 3 1 2 4 36 1 3 4 2 8 4 5 3 7 2 8 4

8 4 3 7 2 1 6 1 2 3 45 1 2 3 4 5 2 8 4 1 3 7 6

Parent

Offspring

Chromosome

Crossover

Mutation






















BFV(s)

CPU(s)

BFV(s)

14 150 843 1438 1355 2167 128615 200 944 1726 1285 2358 131216 250 1045 2164 1310 2611 146117 300 1146 2655 1309 3209 160618 350 1253 3249 1391 3877 147719 400 1354 3886 1328 4962 152120 450 1455 4491 1696 7381 139721 500 1556 5113 1548 10122 165322 550 1667 5876 1613 15434 179723 600 1765 7041 1683 21307 176824 650 1866 8237 1856 24608 193225 700 1967 10655 1838 31764 228826 750 2077 13884 2027 38269 271127 800 2177 18243 2068 43055 248628 850 2278 23611 2262 49970 286429 900 2378 34005 2737 56278 268830 950 2488 39671 3094 65907 380831 1000 2488 45208 3275 76604 3989

0 50 100 150 200 250 300 350 400 450 5001600

2000

2400

2800

3200

3600

PSOGAHGA-PSO

Fitn

ess v

alue

Iterations


Fitn

ess v

alue

0 50 100 150 200 250 300 350 400 450 500

2000

2400

2800

3200

3600

4000

GABATHBAT-GA

Iterations


0 50 100 150 200 250 300 350 400 450 500

2000

2500

3000

3500

4000

4500

5000

5500

PSOBATGA

HBAT-GAHGA-PSO

Fitn

ess v

alue

Iterations







6 Conclusion


50 100 150 200 250 300 350 400 450 5000

50

100

150

200

250

HGA-PSOHBAT-GAGA

BATPSO

CPU

tim

e (S)

Iterations


5 10 15 20 25 30

1000

2000

3000

4000

5000

PSOGABAT

HGA-PSOHBAT-GA

Fitn

ess v

alue

Number






Data Availability




Acknowledgments


References


















Mean CPUtime
























































Journal of












Journal of







Volume 2018






Volume 2018










3 Model Formulation












Yard crane

Quay crane

Ship

AGV guide path

AGV-mate

Storage yard









0-1 variables






Fk maxkisinOF


Sk minkisinOS



1Discharging

Loading2

Maintrolley

Portaltrolley




1113944lisinOF

1113944jisinL


1113944kisinOS

1113944iisinU


1113944cisinV


1113944iisinNk


1113944bisinB


1113944iisinNk




pik + 1113944cisinV





zik + 1113944cisinV



(13)


gjl + 1113944bisinB


zjl + 1113944cisinV




pjl + 1113944cisinV



(17)






(20)










(22)

xk(t + 1) xk(t) + vk(t + 1) (23)




(t) 1Ps

1113944

Ps

k1fk(t) minus

1Os

1113944

Os

k1fk(t)

(24)











Xt+1i Xt

i + Vt+1i

Xnewi Xold




(25)





51 Initial Setting








begin







end

end

end











+ 1t t








begin








end for


end

i i + 1

i i + 1

t o


Parent 1 1 5 2 7 6 8 3 1 2 3 44 1 2 3 4 5 2 8 4 1 3 7 6

Parent 2


8 3 7 5 1 2 4 1 3 2 46 1 4 2 3 6 1 5 3 7 2 8 4

Offspring 1 4 2 7 5 1 8 3 1 2 4 36 1 3 4 2 8 4 5 3 7 2 8 4

Offspring 2 8 3 2 7 6 5 1 3 2 1 24 1 4 3 4 6 5 8 4 1 3 7 2

4 2 7 5 1 8 3 1 2 4 36 1 3 4 2 8 4 5 3 7 2 8 4

8 4 3 7 2 1 6 1 2 3 45 1 2 3 4 5 2 8 4 1 3 7 6

Parent

Offspring

Chromosome

Crossover

Mutation






















BFV(s)

CPU(s)

BFV(s)

14 150 843 1438 1355 2167 128615 200 944 1726 1285 2358 131216 250 1045 2164 1310 2611 146117 300 1146 2655 1309 3209 160618 350 1253 3249 1391 3877 147719 400 1354 3886 1328 4962 152120 450 1455 4491 1696 7381 139721 500 1556 5113 1548 10122 165322 550 1667 5876 1613 15434 179723 600 1765 7041 1683 21307 176824 650 1866 8237 1856 24608 193225 700 1967 10655 1838 31764 228826 750 2077 13884 2027 38269 271127 800 2177 18243 2068 43055 248628 850 2278 23611 2262 49970 286429 900 2378 34005 2737 56278 268830 950 2488 39671 3094 65907 380831 1000 2488 45208 3275 76604 3989

0 50 100 150 200 250 300 350 400 450 5001600

2000

2400

2800

3200

3600

PSOGAHGA-PSO

Fitn

ess v

alue

Iterations


Fitn

ess v

alue

0 50 100 150 200 250 300 350 400 450 500

2000

2400

2800

3200

3600

4000

GABATHBAT-GA

Iterations


0 50 100 150 200 250 300 350 400 450 500

2000

2500

3000

3500

4000

4500

5000

5500

PSOBATGA

HBAT-GAHGA-PSO

Fitn

ess v

alue

Iterations







6 Conclusion


50 100 150 200 250 300 350 400 450 5000

50

100

150

200

250

HGA-PSOHBAT-GAGA

BATPSO

CPU

tim

e (S)

Iterations


5 10 15 20 25 30

1000

2000

3000

4000

5000

PSOGABAT

HGA-PSOHBAT-GA

Fitn

ess v

alue

Number






Data Availability




Acknowledgments


References


















Mean CPUtime
























































Journal of












Journal of







Volume 2018






Volume 2018














0-1 variables






Fk maxkisinOF


Sk minkisinOS



1Discharging

Loading2

Maintrolley

Portaltrolley




1113944lisinOF

1113944jisinL


1113944kisinOS

1113944iisinU


1113944cisinV


1113944iisinNk


1113944bisinB


1113944iisinNk




pik + 1113944cisinV





zik + 1113944cisinV



(13)


gjl + 1113944bisinB


zjl + 1113944cisinV




pjl + 1113944cisinV



(17)






(20)










(22)

xk(t + 1) xk(t) + vk(t + 1) (23)




(t) 1Ps

1113944

Ps

k1fk(t) minus

1Os

1113944

Os

k1fk(t)

(24)











Xt+1i Xt

i + Vt+1i

Xnewi Xold




(25)





51 Initial Setting








begin







end

end

end











+ 1t t








begin








end for


end

i i + 1

i i + 1

t o


Parent 1 1 5 2 7 6 8 3 1 2 3 44 1 2 3 4 5 2 8 4 1 3 7 6

Parent 2


8 3 7 5 1 2 4 1 3 2 46 1 4 2 3 6 1 5 3 7 2 8 4

Offspring 1 4 2 7 5 1 8 3 1 2 4 36 1 3 4 2 8 4 5 3 7 2 8 4

Offspring 2 8 3 2 7 6 5 1 3 2 1 24 1 4 3 4 6 5 8 4 1 3 7 2

4 2 7 5 1 8 3 1 2 4 36 1 3 4 2 8 4 5 3 7 2 8 4

8 4 3 7 2 1 6 1 2 3 45 1 2 3 4 5 2 8 4 1 3 7 6

Parent

Offspring

Chromosome

Crossover

Mutation






















BFV(s)

CPU(s)

BFV(s)

14 150 843 1438 1355 2167 128615 200 944 1726 1285 2358 131216 250 1045 2164 1310 2611 146117 300 1146 2655 1309 3209 160618 350 1253 3249 1391 3877 147719 400 1354 3886 1328 4962 152120 450 1455 4491 1696 7381 139721 500 1556 5113 1548 10122 165322 550 1667 5876 1613 15434 179723 600 1765 7041 1683 21307 176824 650 1866 8237 1856 24608 193225 700 1967 10655 1838 31764 228826 750 2077 13884 2027 38269 271127 800 2177 18243 2068 43055 248628 850 2278 23611 2262 49970 286429 900 2378 34005 2737 56278 268830 950 2488 39671 3094 65907 380831 1000 2488 45208 3275 76604 3989

0 50 100 150 200 250 300 350 400 450 5001600

2000

2400

2800

3200

3600

PSOGAHGA-PSO

Fitn

ess v

alue

Iterations


Fitn

ess v

alue

0 50 100 150 200 250 300 350 400 450 500

2000

2400

2800

3200

3600

4000

GABATHBAT-GA

Iterations


0 50 100 150 200 250 300 350 400 450 500

2000

2500

3000

3500

4000

4500

5000

5500

PSOBATGA

HBAT-GAHGA-PSO

Fitn

ess v

alue

Iterations







6 Conclusion


50 100 150 200 250 300 350 400 450 5000

50

100

150

200

250

HGA-PSOHBAT-GAGA

BATPSO

CPU

tim

e (S)

Iterations


5 10 15 20 25 30

1000

2000

3000

4000

5000

PSOGABAT

HGA-PSOHBAT-GA

Fitn

ess v

alue

Number






Data Availability




Acknowledgments


References


















Mean CPUtime
























































Journal of












Journal of







Volume 2018






Volume 2018









1113944lisinOF

1113944jisinL


1113944kisinOS

1113944iisinU


1113944cisinV


1113944iisinNk


1113944bisinB


1113944iisinNk




pik + 1113944cisinV





zik + 1113944cisinV



(13)


gjl + 1113944bisinB


zjl + 1113944cisinV




pjl + 1113944cisinV



(17)






(20)










(22)

xk(t + 1) xk(t) + vk(t + 1) (23)




(t) 1Ps

1113944

Ps

k1fk(t) minus

1Os

1113944

Os

k1fk(t)

(24)











Xt+1i Xt

i + Vt+1i

Xnewi Xold




(25)





51 Initial Setting








begin







end

end

end











+ 1t t








begin








end for


end

i i + 1

i i + 1

t o


Parent 1 1 5 2 7 6 8 3 1 2 3 44 1 2 3 4 5 2 8 4 1 3 7 6

Parent 2


8 3 7 5 1 2 4 1 3 2 46 1 4 2 3 6 1 5 3 7 2 8 4

Offspring 1 4 2 7 5 1 8 3 1 2 4 36 1 3 4 2 8 4 5 3 7 2 8 4

Offspring 2 8 3 2 7 6 5 1 3 2 1 24 1 4 3 4 6 5 8 4 1 3 7 2

4 2 7 5 1 8 3 1 2 4 36 1 3 4 2 8 4 5 3 7 2 8 4

8 4 3 7 2 1 6 1 2 3 45 1 2 3 4 5 2 8 4 1 3 7 6

Parent

Offspring

Chromosome

Crossover

Mutation






















BFV(s)

CPU(s)

BFV(s)

14 150 843 1438 1355 2167 128615 200 944 1726 1285 2358 131216 250 1045 2164 1310 2611 146117 300 1146 2655 1309 3209 160618 350 1253 3249 1391 3877 147719 400 1354 3886 1328 4962 152120 450 1455 4491 1696 7381 139721 500 1556 5113 1548 10122 165322 550 1667 5876 1613 15434 179723 600 1765 7041 1683 21307 176824 650 1866 8237 1856 24608 193225 700 1967 10655 1838 31764 228826 750 2077 13884 2027 38269 271127 800 2177 18243 2068 43055 248628 850 2278 23611 2262 49970 286429 900 2378 34005 2737 56278 268830 950 2488 39671 3094 65907 380831 1000 2488 45208 3275 76604 3989

0 50 100 150 200 250 300 350 400 450 5001600

2000

2400

2800

3200

3600

PSOGAHGA-PSO

Fitn

ess v

alue

Iterations


Fitn

ess v

alue

0 50 100 150 200 250 300 350 400 450 500

2000

2400

2800

3200

3600

4000

GABATHBAT-GA

Iterations


0 50 100 150 200 250 300 350 400 450 500

2000

2500

3000

3500

4000

4500

5000

5500

PSOBATGA

HBAT-GAHGA-PSO

Fitn

ess v

alue

Iterations







6 Conclusion


50 100 150 200 250 300 350 400 450 5000

50

100

150

200

250

HGA-PSOHBAT-GAGA

BATPSO

CPU

tim

e (S)

Iterations


5 10 15 20 25 30

1000

2000

3000

4000

5000

PSOGABAT

HGA-PSOHBAT-GA

Fitn

ess v

alue

Number






Data Availability




Acknowledgments


References


















Mean CPUtime
























































Journal of












Journal of







Volume 2018






Volume 2018












(22)

xk(t + 1) xk(t) + vk(t + 1) (23)




(t) 1Ps

1113944

Ps

k1fk(t) minus

1Os

1113944

Os

k1fk(t)

(24)











Xt+1i Xt

i + Vt+1i

Xnewi Xold




(25)





51 Initial Setting








begin







end

end

end











+ 1t t








begin








end for


end

i i + 1

i i + 1

t o


Parent 1 1 5 2 7 6 8 3 1 2 3 44 1 2 3 4 5 2 8 4 1 3 7 6

Parent 2


8 3 7 5 1 2 4 1 3 2 46 1 4 2 3 6 1 5 3 7 2 8 4

Offspring 1 4 2 7 5 1 8 3 1 2 4 36 1 3 4 2 8 4 5 3 7 2 8 4

Offspring 2 8 3 2 7 6 5 1 3 2 1 24 1 4 3 4 6 5 8 4 1 3 7 2

4 2 7 5 1 8 3 1 2 4 36 1 3 4 2 8 4 5 3 7 2 8 4

8 4 3 7 2 1 6 1 2 3 45 1 2 3 4 5 2 8 4 1 3 7 6

Parent

Offspring

Chromosome

Crossover

Mutation






















BFV(s)

CPU(s)

BFV(s)

14 150 843 1438 1355 2167 128615 200 944 1726 1285 2358 131216 250 1045 2164 1310 2611 146117 300 1146 2655 1309 3209 160618 350 1253 3249 1391 3877 147719 400 1354 3886 1328 4962 152120 450 1455 4491 1696 7381 139721 500 1556 5113 1548 10122 165322 550 1667 5876 1613 15434 179723 600 1765 7041 1683 21307 176824 650 1866 8237 1856 24608 193225 700 1967 10655 1838 31764 228826 750 2077 13884 2027 38269 271127 800 2177 18243 2068 43055 248628 850 2278 23611 2262 49970 286429 900 2378 34005 2737 56278 268830 950 2488 39671 3094 65907 380831 1000 2488 45208 3275 76604 3989

0 50 100 150 200 250 300 350 400 450 5001600

2000

2400

2800

3200

3600

PSOGAHGA-PSO

Fitn

ess v

alue

Iterations


Fitn

ess v

alue

0 50 100 150 200 250 300 350 400 450 500

2000

2400

2800

3200

3600

4000

GABATHBAT-GA

Iterations


0 50 100 150 200 250 300 350 400 450 500

2000

2500

3000

3500

4000

4500

5000

5500

PSOBATGA

HBAT-GAHGA-PSO

Fitn

ess v

alue

Iterations







6 Conclusion


50 100 150 200 250 300 350 400 450 5000

50

100

150

200

250

HGA-PSOHBAT-GAGA

BATPSO

CPU

tim

e (S)

Iterations


5 10 15 20 25 30

1000

2000

3000

4000

5000

PSOGABAT

HGA-PSOHBAT-GA

Fitn

ess v

alue

Number






Data Availability




Acknowledgments


References


















Mean CPUtime
























































Journal of












Journal of







Volume 2018






Volume 2018










Xt+1i Xt

i + Vt+1i

Xnewi Xold




(25)





51 Initial Setting








begin







end

end

end











+ 1t t








begin








end for


end

i i + 1

i i + 1

t o


Parent 1 1 5 2 7 6 8 3 1 2 3 44 1 2 3 4 5 2 8 4 1 3 7 6

Parent 2


8 3 7 5 1 2 4 1 3 2 46 1 4 2 3 6 1 5 3 7 2 8 4

Offspring 1 4 2 7 5 1 8 3 1 2 4 36 1 3 4 2 8 4 5 3 7 2 8 4

Offspring 2 8 3 2 7 6 5 1 3 2 1 24 1 4 3 4 6 5 8 4 1 3 7 2

4 2 7 5 1 8 3 1 2 4 36 1 3 4 2 8 4 5 3 7 2 8 4

8 4 3 7 2 1 6 1 2 3 45 1 2 3 4 5 2 8 4 1 3 7 6

Parent

Offspring

Chromosome

Crossover

Mutation






















BFV(s)

CPU(s)

BFV(s)

14 150 843 1438 1355 2167 128615 200 944 1726 1285 2358 131216 250 1045 2164 1310 2611 146117 300 1146 2655 1309 3209 160618 350 1253 3249 1391 3877 147719 400 1354 3886 1328 4962 152120 450 1455 4491 1696 7381 139721 500 1556 5113 1548 10122 165322 550 1667 5876 1613 15434 179723 600 1765 7041 1683 21307 176824 650 1866 8237 1856 24608 193225 700 1967 10655 1838 31764 228826 750 2077 13884 2027 38269 271127 800 2177 18243 2068 43055 248628 850 2278 23611 2262 49970 286429 900 2378 34005 2737 56278 268830 950 2488 39671 3094 65907 380831 1000 2488 45208 3275 76604 3989

0 50 100 150 200 250 300 350 400 450 5001600

2000

2400

2800

3200

3600

PSOGAHGA-PSO

Fitn

ess v

alue

Iterations


Fitn

ess v

alue

0 50 100 150 200 250 300 350 400 450 500

2000

2400

2800

3200

3600

4000

GABATHBAT-GA

Iterations


0 50 100 150 200 250 300 350 400 450 500

2000

2500

3000

3500

4000

4500

5000

5500

PSOBATGA

HBAT-GAHGA-PSO

Fitn

ess v

alue

Iterations







6 Conclusion


50 100 150 200 250 300 350 400 450 5000

50

100

150

200

250

HGA-PSOHBAT-GAGA

BATPSO

CPU

tim

e (S)

Iterations


5 10 15 20 25 30

1000

2000

3000

4000

5000

PSOGABAT

HGA-PSOHBAT-GA

Fitn

ess v

alue

Number






Data Availability




Acknowledgments


References


















Mean CPUtime
























































Journal of












Journal of







Volume 2018






Volume 2018













begin








end for


end

i i + 1

i i + 1

t o


Parent 1 1 5 2 7 6 8 3 1 2 3 44 1 2 3 4 5 2 8 4 1 3 7 6

Parent 2


8 3 7 5 1 2 4 1 3 2 46 1 4 2 3 6 1 5 3 7 2 8 4

Offspring 1 4 2 7 5 1 8 3 1 2 4 36 1 3 4 2 8 4 5 3 7 2 8 4

Offspring 2 8 3 2 7 6 5 1 3 2 1 24 1 4 3 4 6 5 8 4 1 3 7 2

4 2 7 5 1 8 3 1 2 4 36 1 3 4 2 8 4 5 3 7 2 8 4

8 4 3 7 2 1 6 1 2 3 45 1 2 3 4 5 2 8 4 1 3 7 6

Parent

Offspring

Chromosome

Crossover

Mutation






















BFV(s)

CPU(s)

BFV(s)

14 150 843 1438 1355 2167 128615 200 944 1726 1285 2358 131216 250 1045 2164 1310 2611 146117 300 1146 2655 1309 3209 160618 350 1253 3249 1391 3877 147719 400 1354 3886 1328 4962 152120 450 1455 4491 1696 7381 139721 500 1556 5113 1548 10122 165322 550 1667 5876 1613 15434 179723 600 1765 7041 1683 21307 176824 650 1866 8237 1856 24608 193225 700 1967 10655 1838 31764 228826 750 2077 13884 2027 38269 271127 800 2177 18243 2068 43055 248628 850 2278 23611 2262 49970 286429 900 2378 34005 2737 56278 268830 950 2488 39671 3094 65907 380831 1000 2488 45208 3275 76604 3989

0 50 100 150 200 250 300 350 400 450 5001600

2000

2400

2800

3200

3600

PSOGAHGA-PSO

Fitn

ess v

alue

Iterations


Fitn

ess v

alue

0 50 100 150 200 250 300 350 400 450 500

2000

2400

2800

3200

3600

4000

GABATHBAT-GA

Iterations


0 50 100 150 200 250 300 350 400 450 500

2000

2500

3000

3500

4000

4500

5000

5500

PSOBATGA

HBAT-GAHGA-PSO

Fitn

ess v

alue

Iterations







6 Conclusion


50 100 150 200 250 300 350 400 450 5000

50

100

150

200

250

HGA-PSOHBAT-GAGA

BATPSO

CPU

tim

e (S)

Iterations


5 10 15 20 25 30

1000

2000

3000

4000

5000

PSOGABAT

HGA-PSOHBAT-GA

Fitn

ess v

alue

Number






Data Availability




Acknowledgments


References


















Mean CPUtime
























































Journal of












Journal of







Volume 2018






Volume 2018



























BFV(s)

CPU(s)

BFV(s)

14 150 843 1438 1355 2167 128615 200 944 1726 1285 2358 131216 250 1045 2164 1310 2611 146117 300 1146 2655 1309 3209 160618 350 1253 3249 1391 3877 147719 400 1354 3886 1328 4962 152120 450 1455 4491 1696 7381 139721 500 1556 5113 1548 10122 165322 550 1667 5876 1613 15434 179723 600 1765 7041 1683 21307 176824 650 1866 8237 1856 24608 193225 700 1967 10655 1838 31764 228826 750 2077 13884 2027 38269 271127 800 2177 18243 2068 43055 248628 850 2278 23611 2262 49970 286429 900 2378 34005 2737 56278 268830 950 2488 39671 3094 65907 380831 1000 2488 45208 3275 76604 3989

0 50 100 150 200 250 300 350 400 450 5001600

2000

2400

2800

3200

3600

PSOGAHGA-PSO

Fitn

ess v

alue

Iterations


Fitn

ess v

alue

0 50 100 150 200 250 300 350 400 450 500

2000

2400

2800

3200

3600

4000

GABATHBAT-GA

Iterations


0 50 100 150 200 250 300 350 400 450 500

2000

2500

3000

3500

4000

4500

5000

5500

PSOBATGA

HBAT-GAHGA-PSO

Fitn

ess v

alue

Iterations







6 Conclusion


50 100 150 200 250 300 350 400 450 5000

50

100

150

200

250

HGA-PSOHBAT-GAGA

BATPSO

CPU

tim

e (S)

Iterations


5 10 15 20 25 30

1000

2000

3000

4000

5000

PSOGABAT

HGA-PSOHBAT-GA

Fitn

ess v

alue

Number






Data Availability




Acknowledgments


References


















Mean CPUtime
























































Journal of












Journal of







Volume 2018






Volume 2018














BFV(s)

CPU(s)

BFV(s)

14 150 843 1438 1355 2167 128615 200 944 1726 1285 2358 131216 250 1045 2164 1310 2611 146117 300 1146 2655 1309 3209 160618 350 1253 3249 1391 3877 147719 400 1354 3886 1328 4962 152120 450 1455 4491 1696 7381 139721 500 1556 5113 1548 10122 165322 550 1667 5876 1613 15434 179723 600 1765 7041 1683 21307 176824 650 1866 8237 1856 24608 193225 700 1967 10655 1838 31764 228826 750 2077 13884 2027 38269 271127 800 2177 18243 2068 43055 248628 850 2278 23611 2262 49970 286429 900 2378 34005 2737 56278 268830 950 2488 39671 3094 65907 380831 1000 2488 45208 3275 76604 3989

0 50 100 150 200 250 300 350 400 450 5001600

2000

2400

2800

3200

3600

PSOGAHGA-PSO

Fitn

ess v

alue

Iterations


Fitn

ess v

alue

0 50 100 150 200 250 300 350 400 450 500

2000

2400

2800

3200

3600

4000

GABATHBAT-GA

Iterations


0 50 100 150 200 250 300 350 400 450 500

2000

2500

3000

3500

4000

4500

5000

5500

PSOBATGA

HBAT-GAHGA-PSO

Fitn

ess v

alue

Iterations







6 Conclusion


50 100 150 200 250 300 350 400 450 5000

50

100

150

200

250

HGA-PSOHBAT-GAGA

BATPSO

CPU

tim

e (S)

Iterations


5 10 15 20 25 30

1000

2000

3000

4000

5000

PSOGABAT

HGA-PSOHBAT-GA

Fitn

ess v

alue

Number






Data Availability




Acknowledgments


References


















Mean CPUtime
























































Journal of












Journal of







Volume 2018






Volume 2018












6 Conclusion


50 100 150 200 250 300 350 400 450 5000

50

100

150

200

250

HGA-PSOHBAT-GAGA

BATPSO

CPU

tim

e (S)

Iterations


5 10 15 20 25 30

1000

2000

3000

4000

5000

PSOGABAT

HGA-PSOHBAT-GA

Fitn

ess v

alue

Number






Data Availability




Acknowledgments


References


















Mean CPUtime
























































Journal of












Journal of







Volume 2018






Volume 2018











Data Availability




Acknowledgments


References


















Mean CPUtime
























































Journal of












Journal of







Volume 2018






Volume 2018



























































Journal of












Journal of







Volume 2018






Volume 2018























Journal of












Journal of







Volume 2018






Volume 2018















Journal of












Journal of







Volume 2018






Volume 2018








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