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Table 1: The levels of parameters for 2‘ factorial design The optimal values of parameters are determined by Design of Experiment (DOE) using 2* factorial design. The parameters are comprised of the population size, the crossover rate, the number of generations, the number of tours and the number of leader birds. There are 4 replications for each experiment plan. The response variable of this DOE is the IGD since the convergence and diversity metric are the major performances of this problem. The total runs of experiment plan for NSGA-II equals to 32 (2x2x2x4) while total runs of experiment for MBNSGA-II is 128 (2%2x2x2x2%4). Then, the levels of these parameters are shown Table 1. The optimal parameters for both algorithms obtained from the response optimizer are presented in Table 2.

Table 1 The levels of parameters for 2‘ factorial design The optimal values of parameters are determined by Design of Experiment (DOE) using 2* factorial design. The parameters are comprised of the population size, the crossover rate, the number of generations, the number of tours and the number of leader birds. There are 4 replications for each experiment plan. The response variable of this DOE is the IGD since the convergence and diversity metric are the major performances of this problem. The total runs of experiment plan for NSGA-II equals to 32 (2x2x2x4) while total runs of experiment for MBNSGA-II is 128 (2%2x2x2x2%4). Then, the levels of these parameters are shown Table 1. The optimal parameters for both algorithms obtained from the response optimizer are presented in Table 2.

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Figure 4: Pseudo Code of MBO for mutation step in MBNSGA-IL
Figure 4: Pseudo Code of MBO for mutation step in MBNSGA-IL
Table 2: The optimum level of parameters W. Laoraksakiat and K. Asawarungsaengkul, “‘Bi-objective Hybrid Flow Shop Scheduling with Family Setup Times Using Hybrid Genetic and Migrating Birds Optimization Algorithms.”
Table 2: The optimum level of parameters W. Laoraksakiat and K. Asawarungsaengkul, “‘Bi-objective Hybrid Flow Shop Scheduling with Family Setup Times Using Hybrid Genetic and Migrating Birds Optimization Algorithms.”
Table 3: IGD metric values and spacing metric values found by each algorithm
Table 3: IGD metric values and spacing metric values found by each algorithm
Figure 7: Boxplot of IGD for large size problems. Figure 6: Boxplot of IGD for medium size problems.
Figure 7: Boxplot of IGD for large size problems. Figure 6: Boxplot of IGD for medium size problems.
Figure 5: Boxplot of IGD for small size problems.
Figure 5: Boxplot of IGD for small size problems.
Figure 9: Boxplot of spacing value of all instances. Figure 8: The average of IGD of all instances in each problem size.
Figure 9: Boxplot of spacing value of all instances. Figure 8: The average of IGD of all instances in each problem size.
Figure 10: The average of spacing value of all instances in each problem size.
Figure 10: The average of spacing value of all instances in each problem size.
Figure 11: Average number of non-dominated solutions from 5 runs in each algorithm.
Figure 11: Average number of non-dominated solutions from 5 runs in each algorithm.
Figure 12: Pareto front of each algorithm for small size problems. (a) Pareto front of 12x5 (b) Pareto front of 1210 (c) Pareto front of 185 (d) Pareto front of 1810 (e) Pareto front of 245 (e) Pareto front of 32x5S.
Figure 12: Pareto front of each algorithm for small size problems. (a) Pareto front of 12x5 (b) Pareto front of 1210 (c) Pareto front of 185 (d) Pareto front of 1810 (e) Pareto front of 245 (e) Pareto front of 32x5S.
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Computer ScienceFlow Shop Scheduling
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