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Table 18 Simulation results for TSys-4 (40-unit system)

From: An advanced hybrid meta-heuristic algorithm for solving small- and large-scale engineering design optimization problems

Power output (MW) Compared algorithms Proposed algorithms
MTVPSO THS DEPSO DPD MPSO IABC DHS aDE aPSO haDEPSO
1 110.7998 114 110.802 111.7629 111.3021 110.8067 110.7998 110.8069 110.7998 110.7993
2 110.7998 113.3808 110.801 111.6926 110.8937 110.8163 110.7998 110.7937 110.8001 111.1416
3 97.3999 97.4102 97.400 97.40940 97.4024 97.4000 97.3999 97.3998 97.401 97.4122
4 179.7331 179.7357 179.733 179.7721 179.7417 179.7330 179.7331 179.7332 179.7327 179.7443
5 87.7999 96.9973 87.800 88.30690 96.2717 87.8133 87.7999 87.9566 87.8019 88.1519
6 140.0000 140.0000 140.000 139.9833 140.0000 139.9999 140.0000 140.0000 139.9977 139.9957
7 259.5997 259.6047 259.600 259.7218 259.5998 259.5996 259.5997 259.5996 259.5986 259.6064
8 284.5997 284.6041 284.600 284.7273 284.6047 284.6008 284.5997 284.5996 284.6058 284.6046
9 284.5997 284.6018 284.600 284.6157 284.6048 284.5997 284.5997 284.5996 284.6004 284.6149
10 130.0000 130 130.000 130.0583 130.0020 130.0000 130.0000 130.0000 130.0000 130.0000
11 94.0000 168.8034 94.000 168.7990 168.7993 168.7998 94.0000 168.7998 94.0007 168.8029
12 94.0000 214.7619 94.000 168.7894 94.0019 94.0000 94.0000 94.0000 94.0000 94.0000
13 214.7598 394.2794 214.760 214.7593 214.7600 125.0000 214.7598 214.7597 214.7579 214.7593
14 394.2794 304.5215 394.279 304.5391 394.2799 400.0000 394.2794 394.2795 394.2796 394.2717
15 394.2794 304.5209 394.279 394.2707 394.2789 394.2791 394.2794 304.5197 394.2784 304.5205
16 394.2794 489.2841 394.279 394.2713 304.5202 394.2793 394.2794 394.2793 394.2799 394.2835
17 489.2794 489.2891 489.279 489.2894 489.2798 489.2796 489.2794 489.2796 489.2787 489.2911
18 489.2794 511.2813 489.279 489.3177 489.2823 489.2794 489.2794 489.2792 489.279 489.2878
19 511.2794 511.2790 511.279 511.2724 511.2796 511.2792 511.2794 511.2794 511.2785 511.2976
20 511.2794 523.2838 511.279 511.2800 511.2823 511.2793 511.2794 511.2794 511.2793 511.2792
21 523.2794 523.2819 523.279 523.3291 523.2799 523.2798 523.2794 523.2794 523.2787 523.2957
22 523.2794 523.2779 523.279 523.2992 523.2794 523.2793 523.2794 523.2794 523.2793 523.2848
23 523.2794 523.2801 523.279 523.3545 523.2815 523.2793 523.2794 523.2794 523.2798 523.2857
24 523.2794 523.2824 523.279 523.2793 523.2800 523.2793 523.2794 523.2794 523.2793 523.2979
25 523.2794 523.2799 523.279 523.3890 523.2799 523.2793 523.2794 523.2794 523.2783 523.2799
26 523.2794 523.2799 523.279 523.2776 523.2812 523.2793 523.2794 523.2794 523.2787 523.291
27 10.0000 10 10.000 10.00000 10.0010 10.0000 10.0000 10.0000 10.0002 10.0064
28 10.0000 10 10.000 10.00000 10.0002 10.0000 10.0000 10.0000 10.0010 10.0018
29 10.0000 10 10.000 10.00000 10.0021 10.0000 10.0000 10.0000 10.0011 10.0000
30 87.7999 96.99 87.800 88.72800 88.0447 91.4006 87.7999 97.0000 87.8000 96.2132
31 190.0000 190 190.000 189.9811 189.9997 189.9999 190.0000 190.0000 189.9996 189.9997
32 190.0000 190 190.000 189.9982 189.9996 189.9999 190.0000 190.0000 189.9979 189.9997
33 190.0000 190 190.000 189.9795 189.9999 190.0000 190.0000 190.0000 189.9981 189.9981
34 164.7998 164.8838 164.800 164.8962 164.8005 164.7997 164.7998 164.7997 199.8696 164.9126
35 200.0000 200 194.395 165.0916 199.9950 199.9978 200.0000 200.0000 194.5334 199.9941
36 194.3978 200 200.000 165.2998 199.9953 199.9999 194.3978 200.0000 164.8003 200.0000
37 110.0000 110 110.000 109.9827 109.9987 110.0000 110.0000 110.0000 109.9992 109.9988
38 110.0000 110 110.000 109.9824 109.9997 109.9998 110.0000 110.0000 109.9984 109.9994
39 110.0000 110 110.000 109.9634 109.9990 110.0000 110.0000 110.0000 109.9974 109.9974
40 511.2794 511.2795 511.279 511.5279 511.2957 511.2793 511.2794 511.2793 511.2797 511.2800
Total power (MW) 10,500 10,500 10,500 10,500 10,500 10,500 10,500 10,500 10,500 10,500
Min cost ($/h) 121,403.5355 121,467.44 121,412.56 121,410.5355 121,379.43 121,491.2751 121,403.5355 121,405.7384 121,404.5378 121,403.5454
Mean cost ($/h) 121,410.5967 121,524.26 121,419.31 121,412.5729 121,384.43 121,539.4175 121,410.5967 121,411.5829 121,410.5977 121,410.4658
Max cost ($/h) 121,417.2274 121,598.65 121,468.25 121,441.9027 121,391.07 121,582.3865 121,417.2274 121,415.2314 121,416.3319 121,413.9827
Std. of cost ($/h) 0.001714 36.7026 0.00584 0.437608 2.3685 0.00548 4.80 0.0037608 0.001754 0.001473
CPU mean time (s) 11.32101 13.5846 7.895 21.76485 5.43 1.950 1.32 11.12101 12.78485 11.02356