Seite - 90 - in Algorithms for Scheduling Problems

Algorithms 2018,11, 68 Table16.Optimumparametercombinationforbi-objectiveGA. No. Comb. Cr Mu Pcr Pmu Pob 1 156 PMX Displacement 0.9 0.2 50 Selected 2 129 OX Displacement 0.9 0.2 50 3 120 OX Displacement 0.7 0.2 50 7. ExperimentalAnalysis 7.1. ExperimentalSetup Inmultiobjectiveoptimization, there isusuallynosinglebest solution,butasetof solutions that areequallygood.Ourobjective is toobtainagoodapproximationof thePareto front regardingtwo objective functions [40]. Ourbi-objectivegeneticalgorithmis tunedupusingthefollowingparametersobtainedduring the calibration step: crossover, PMX;mutation,Displacement; crossoverprobability, 0.9;mutation probability,0.2;populationsize,50. Weconsiderfive jobs ineachof the30workloads,obtainingthenumberofbatches foreach job basedonauniformrandomdistribution(Table4). 7.2. Bi-ObjectiveAnalysis Figures 21–23 show the solution sets and thePareto fronts. In each front, 1500 solutions are included,being50(individuals)×30 (workloads). 96.45 96.65 96.85 97.05 97.25 97.45 6,820 6,900 6,980 7,060 7,140 ܧop (kW) Figure21.Pareto front for twomachinesperstage. 43.92 44.12 44.32 44.52 44.72 12,230 12,310 12,390 12,470 12,550 ܧop (kW) Figure22.Pareto front for fourmachinesperstage. 90