Seite - 78 - in Algorithms for Scheduling Problems

Algorithms 2018,11, 68 3.RelatedWorks 3.1. Energy-AwareFlowShopScheduling Investment in new equipment and hardware can certainly contribute to energy savings [9]. Theuseof“soft” techniques toachieve thesameobjective isalsoaneffectiveoption[10]. The advance schedule could play an important role in reducing the energy consumption of themanufacturing processes. Meta-heuristics, e.g., genetic algorithms (GA) [11], particle swarm optimization [12], and simulated annealing [13] are greatly popularity for use in the design of productionsystems. However, studiesofflowshopschedulingproblemsforenergysavingappeartobelimited[14,15]. In fact,most production systems that allow changing of the speedof themachines belong to the mechanicalengineering industryandusually take theconfigurationofaworkshopinsteadofaflow shop[16]. Oneof thefirstattempts toreduceenergyconsumptionthroughproductionschedulingcanbe foundin theworkofMouzonetal. [17]. Theauthorscollectedoperational statistics for fourmachines inaflowshopand found thatnonbottleneckmachines consumeaconsiderable amountof energy when left idle. As a result, theypropose a framework for schedulingpower on andoff events to controlmachines forachievingareductionof totalenergyconsumption.Daietal. [18]applied this on/off strategy inaflexibleflowshop,obtainingsatisfactorysolutions tominimize the totalenergy consumptionandmakespan. Zhang andChiong [16] proposed amultiobjective genetic algorithm incorporated into two strategies for local improvements to specificproblems, tominimizepowerconsumption,basedon machinespeedscaling. Mansourietal. [19]analyzedthebalancebetweenminimizingthemakespan,ameasureof the levelof serviceandenergyconsumption, inapermutationflowshopwithasequenceof twomachines. Theauthorsdevelopeda linearmodelofmixed-integermultiobjectiveoptimization tofindthePareto frontiercomposedofenergyconsumptionandtotalmakespan. Heckeretal. [20]usedevolutionaryalgorithmsforscheduling inanon-waithybridflowshopto optimize theallocationof tasks inproduction linesofbread,usingparticleswarmoptimizationand antcolonyoptimization.Heckeretal. [21]usedamodifiedgeneticalgorithm,antcolonyoptimization, and randomsearchprocedure to study themakespanand total timeof idlemachines in ahybrid permutationflowmodel. LiuandHuang[14]studiedaschedulingproblemwithbatchprocessingmachinesinahybridflow shopwithenergy-relatedcriteriaandtotalweightedtardiness. TheauthorsappliedtheNondominated SortingGeneticAlgorithmII (NSGA-II). Additionally, in time completion problems, Yaurima et al. [3] proposed a heuristic and meta-heuristic method to solve hybrid flow shop (HFS) problems with unrelated machines, sequence-dependentsetuptime(SDST),availabilityconstraints, andlimitedbuffers. 3.2.MultiobjectiveOptimization Differentoptimizationcriteriaareusedto improvemodelsofahybridflowshop.Anoverview of thesecriteria canbe found in [4]. Genetic algorithmshavereceivedconsiderableattentionasan approachtomultiobjectiveoptimization[6,22,23]. Deb et al. [24] proposed a computationally efficient multiobjective algorithm called NSGA-II (Nondominated SortingGeneticAlgorithm II),which canfindPareto-optimal solutions. Thecomputationalcomplexityof thealgorithmisO ( MN2 ) ,whereM is thenumberof targetsandN is thesizeof thedataset. In thisarticle,weconsider it tosolveourproblemwith twocriteria.Anexperimentalanalysis of two crossover operators, threemutation operators, three crossover andmutationprobabilities, 78