A Fuzzy Multidimensional Multiple-Choice Knapsack - Dr. Madjid ...

472 Ann Oper Res (2013) 206:449–483Table 11The solution structureEECEpsilonTime periods1 2 3 4 5 6 7 8 9 100 12 1, 2, 6, 11 2, 4, 10 4, 12 3, 7 1, 8, 9, 11 3 6, 8 5, 7, 9 5, 100.1 12 1, 2, 6, 11 2, 10 4, 12 3, 7 1, 8, 9, 11 3 6, 8 5, 7, 9 5, 100.2 12 1, 2, 11 2, 4 4, 12 3, 7 1, 8, 9, 11 3 6, 8 5, 7, 9 5, 100.3 12 1, 2, 11 2, 5 3, 4, 12 1, 7, 10 6, 8, 9, 11 3 8 5, 7, 9 6, 100.4 1, 2 1, 11, 12 2 12 3, 7, 10 8, 9, 11 3 8 5, 7, 9 5, 100.5 1, 7 1, 2, 11 2 12 5 8, 11, 12 3 5 5, 7, 9 90.6 1, 7 8, 9, 11 2 12 10 11, 12 7 8 5 90.7 11 11 2 12 9 8 7 12 8 90.8 3,10 2,4,11 2,5,12 4,7 3,7 1,8,9,11 1,6 6,8 9,12 5,100.9 3, 10, 12 2, 11, 12 2 4, 5 1, 7, 10 1, 8, 9, 11 3, 4, 6 8 7, 9 5, 6Modified NSGA-IISolutionTime periods1 2 3 4 5 6 7 8 9 101 4 2, 9, 11 1, 12 5, 12 3, 7 2, 9, 11 1, 4 6, 8 3, 8 5, 62 1, 3, 4 2, 9 3 5, 10 5, 11 8 1, 2 8, 9 7, 12 6, 7, 103 4 2, 9, 11 1, 12 5, 12 3, 7 2, 9, 11 4, 10 6, 8 3, 8 5, 64 1,6 11 5,7 4,6 4,8 1,3,12 2,7,11 8,9 9,12 35 1, 3 1, 8, 11 11, 12 5, 12 4, 7 3, 8 2, 10 7, 9 5 96 3, 6 1, 2 11, 12 3, 4, 5 1, 9 8 5 8, 9 7, 12 6, 77 2, 6 1, 9 11, 12 5, 10 1, 4 8 10, 11 8, 9 7, 12 3, 78 1, 7 11 6, 10 4, 6 4, 8 3, 5, 11 1, 10 8, 9 9, 12 39 4 3, 7, 11 1, 12 6, 9 10, 12 6, 8 1, 2 8, 9 5 5, 710 4 1, 9 11, 12 2, 5 1, 10 8 3 8, 9 7, 12 6, 7Table 12EECThe fitted parameters for the EEC and modified NSGA-II methodsModified NSGA-IIArchive size 30 Chromosome no. 20Upper bound of cost 277068 Archive size 30Upper bound of time 47.8 Maximum iteration no. 1000Lower bound of cost 0 Cross rate Change linearly in [0.8, 0.7]Lower bound of time 0 Mutation rate Change linearly in [0.02, 0.04]Step size of cost 0.1 Alpha 1Step size of time 0.1 Beta 5