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Table 19 Simulation results for TSys-5 (140-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   Compared algorithms Proposed algorithms
  MTVPSO MPSO DHS aDE aPSO haDEPSO   MTVPSO MPSO DHS aDE aPSO haDEPSO
1 116.2518 116.2514 119.0000 116.2528 116.2418 116.2528 71 143.3803 143.3803 500.0000 143.4785 143.8778 143.3804
2 188.8395 188.8395 119.0000 188.8345 188.8295 188.8375 72 388.3236 388.3236 500.0000 388.3785 388.1248 388.7854
3 189.9734 189.9734 164.0000 189.9724 189.9834 189.9734 73 202.9482 202.9482 241.0000 202.7785 202.7854 202.1245
4 189.8984 189.8984 164.0000 189.8974 189.8984 189.8974 74 176.0783 176.0783 241.0000 176.0785 176.0745 176.7854
5 168.6455 168.6455 190.0000 168.6445 168.6655 168.6455 75 175.8523 175.8523 241.0000 175.8785 175.8545 175.4561
6 187.3990 187.3990 190.0000 187.394 187.389 187.391 76 177.8040 177.8040 241.0000 177.8874 177.8045 177.8125
7 489.9976 489.9976 190.0000 489.9946 489.9976 489.9977 77 179.5410 179.5410 774.0000 179.5254 179.5411 179.4856
8 489.8645 489.8645 190.0000 489.8645 489.8745 489.8645 78 330.6797 330.6797 774.0000 330.6258 330.6745 330.6785
9 495.9917 495.9917 168.5398 495.9997 495.9817 495.9918 79 530.9939 530.9939 769.0000 530.9358 530.9488 530.9987
10 495.9000 495.9000 168.5398 495.904 495.91 495.7854 80 530.9852 530.9852 769.0000 530.9154 530.9878 530.9258
11 495.9999 495.9999 190.0000 495.9949 495.9299 495.7896 81 260.0529 260.0529 3.0000 260.0535 260.0787 260.7854
12 495.9418 495.9418 190.0000 495.9408 495.9318 495.9408 82 56.04720 56.0472 82 3.0000 56.04715 56.04748 56.07854
13 505.9503 505.9503 490.0000 505.9513 505.9803 505.9513 83 115.2868 115.2868 83 3.0000 115.2154 115.2487 115.2987
14 508.9842 508.9842 490.0000 508.9832 508.9242 508.9822 84 115.0050 115.0050 84 3.0000 115.0785 115.1452 115.1545
15 505.9854 505.9854 490.0000 505.9844 505.9454 505.9814 85 115.3836 115.3836 250.0000 115.3834 115.3987 115.3886
16 504.9535 504.9535 490.0000 504.9525 504.9435 504.9635 86 207.0000 207.0000 250.0000 207.0788 207.0078 207.0000
17 505.9841 505.9841 496.0000 505.9881 505.9941 505.9741 87 207.0965 207.0965 250.0000 207.0985 207.0965 207.0785
18 505.9365 505.9365 496.0000 505.9365 505.9265 505.9465 88 175.1027 175.1027 250.0000 175.1078 175.1125 175.1485
19 504.9788 504.9788 496.0000 504.9748 504.9688 504.9888 89 175.1656 175.1656 250.0000 175.1678 175.1145 175.1678
20 504.9618 504.9618 496.0000 504.9628 504.9718 504.9418 90 182.1361 182.1361 250.0000 182.1354 182.1361 182.1378
21 504.9769 504.9769 496.0000 504.9779 504.9869 504.9369 91 175.1669 175.1669 250.0000 175.1678 175.1785 175.1754
22 504.9081 504.9081 496.0000 504.9091 504.9281 504.9181 92 579.9855 579.9855 250.0000 579.9854 579.9452 579.9785
23 504.9514 504.9514 496.0000 504.9524 504.9614 504.9814 93 645.0000 645.0000 250.0000 645.0999 645.0089 645.0754
24 504.9742 504.9742 496.0000 504.9742 504.9442 504.9642 94 983.9400 983.9400 250.0000 983.9485 983.9200 983.9487
25 536.9944 536.9944 506.0000 536.9934 536.9844 536.9844 95 977.9925 977.9925 250.000 977.9978 977.9785 977.9925
26 536.9804 536.9804 506.0000 536.9814 536.9704 536.9704 96 681.9838 681.9838 250.0000 681.9825 681.9025 681.9895
27 548.9866 548.9866 509.0000 548.9867 548.9666 548.9466 97 719.9953 719.9953 250.0000 719.9985 719.9954 719.9975
28 548.9698 548.9698 509.0000 548.9699 548.9498 548.9398 98 718.0000 718.0000 250.0000 718.0897 718.0854 718.0045
29 500.9609 500.9609 506.0000 500.9604 500.9309 500.9509 99 719.9553 719.9553 250.0000 719.9558 719.9785 719.9553
30 500.8584 500.8584 506.0000 500.8585 500.8984 500.8484 100 963.8138 963.8138 250.0000 963.8145 963.825 963.8125
31 505.9982 505.9982 505.0000 505.9987 505.9482 505.8982 101 957.9252 957.9252 165.0000 957.9285 957.9152 957.9245
32 505.9890 505.9890 505.0000 505.9899 505.999 505.889 102 1006.9391 1006.9391 165.0000 1006.9381 1006.9321 1006.9311
33 505.9872 505.9872 506.0000 505.9472 505.9472 505.8872 103 1005.9547 1005.9547 165.0000 1010.5031 1005.9547 1005.9547
34 505.8398 505.8398 506.0000 505.8394 505.8398 505.9398 104 1012.9951 1012.9951 165.0000 1012.9981 1012.9971 1012.9781
35 499.9759 499.9759 506.0000 499.9554 499.9759 499.8759 105 1019.9532 1019.9532 165.0000 1019.9512 1019.9512 1019.9572
36 499.8309 499.8309 506.0000 499.7854 499.8801 499.8325 106 953.9784 953.9784 165.0000 953.9785 953.9784 953.9778
37 240.9712 240.9712 505.0000 240.8454 240.9718 240.9745 107 951.9893 951.9893 165.0000 951.9847 951.9893 951.9898
38 240.9668 240.9668 505.0000 280.9596 240.9668 240.9154 108 1005.9502 1005.9502 165.0000 1005.957 1005.9502 1005.9522
39 773.9998 773.9998 505.0000 773.9154 773.9198 773.9896 109 1012.9827 1012.9827 180.0000 1012.9847 1012.9827 1012.9828
40 768.9143 768.9143 505.0000 768.9154 767.9123 768.9145 110 1020.9864 1020.9864 180.0000 1020.9874 1020.9864 1020.9887
41 3.484200 3.4842 505.0000 3.484295 3.984201 3.48422 111 1014.9943 1014.9943 180.0000 1014.9973 1014.9943 1014.9987
42 3.027400 3.0274 505.0000 3.027444 3.087478 3.027401 112 94.03550 94.0355 180.0000 94.78569 94.0355 94.035485
43 186.7539 186.7539 505.0000 186. 9636 186.5847 186.7525 113 94.03730 94.0373 103.0000 132.0374 94.0373 94.037378
44 216.9286 216.9286 505.0000 216.9255 216.4896 216.9287 114 94.01730 94.0173 103.0000 94.25732 94.0173 94.017325
45 249.3928 249.3928 505.0000 298.3924 249.2541 249.3928 115 244.3547 244.3547 198.0000 244.3547 244.3547 244.35474
46 249.9292 249.9292 505.0000 249.9299 249.4856 249.9293 116 244.0590 244.0590 198.0000 244.159 244.059 244.05902
47 246.5461 246.5461 505.0000 246.5445 246.1596 246.5458 117 244.1444 244.1444 312.0000 289.1844 244.1444 241.7985
48 248.6987 248.6987 505.0000 248.7854 248.6562 248.6785 118 95.32550 95.3255 312.0000 95.3215 95.3255 95.32458
49 248.7121 248.7121 537.0000 248.7854 248.7486 248.7485 119 95.01860 95.0186 308.5679 95.0166 95.0186 95.01848
50 248.8088 248.8088 537.0000 248.2541 248.7854 248.8052 120 116.1636 116.1636 308.5881 116.1536 116.1636 116.1645
51 166.6126 166.6126 537.0000 166.1548 166.8526 166.6115 121 175.0352 175.0352 163.0000 175.0152 175.0352 175.0351
52 165.0625 165.0625 537.0000 165.8651 165.7425 165.0156 122 2.00640 2.0064 163.0000 2.00646 2.0064 2.00645
53 169.5018 169.5018 549.0000 169.8745 169.8918 169.5785 123 4.04020 4.0402 95.0000 4.84021 4.0402 4.04022
54 166.3101 166.3101 549.0000 166.9658 166.3101 166.3125 124 15.0993 15.0993 95.0000 15.8992 15.0993 15.0993
55 180.0956 180.0956 549.0000 180.0956 180.7856 180.0154 125 9.00550 9.0055 511.0000 9.9755 9.0055 9.00555
56 180.2748 180.2748 549.0000 180.2254 180.7848 180.2715 126 12.0655 12.0655 511.0000 12.0555 12.0655 12.0654
57 103.1771 103.1771 501.0000 103.1741 103.1521 103.1715 127 10.0080 10.0080 511.0000 10.018 10.008 10.0084
58 198.1757 198.1757 501.0000 198.1351 198.7847 198.1745 128 112.0382 112.0382 511.0000 111.4382 112.0382 112.038
59 309.9475 309.9475 499.0000 309.9874 309.9985 309.9479 129 4.08120 4.0812 490.0000 4.7852 4.0812 4.08123
60 293.8267 293.8267 499.0000 293.8895 293.8157 293.8214 130 5.02750 5.0275 490.0000 5.9255 5.0275 5.0275
61 163.5888 163.5888 506.0000 163.5147 163.5898 163.5145 131 5.05170 5.0517 256.7772 5.0557 5.0517 5.05145
62 95.30030 95.3003 506.0000 95.30454 95.3014 95.30152 132 50.1071 50.1071 256.7802 50.9171 50.1071 50.1458
63 168.1584 168.1584 506.0000 168.1785 168.1244 168.1598 133 5.04680 5.0468 490.0000 5.0468 5.0468 5.78542
64 166.0715 166.0715 506.0000 166.0701 166.0725 166.0025 134 42.0244 42.0244 490.0000 42.9244 42.0244 42.0785
65 486.8818 486.8818 506.0000 486.8458 486.8808 486.8085 135 42.0341 42.0341 490.0000 42.9331 42.0341 42.2548
66 205.5539 205.5539 506.0000 205.7889 205.5529 205.5025 136 41.0343 41.0343 490.0000 41.9343 41.0343 41.7854
67 483.1274 483.1274 506.0000 483.1984 483.1324 483.1215 137 17.0443 17.0443 130.0000 17.9453 16.1243 17.7869
68 486.0292 486.0292 506.0000 486.1442 486.1522 486.0785 138 7.14970 7.1497 130.0000 7.1498 7.1497 7.14948
69 130.2962 130.2962 500.0000 130.2542 130.2252 130.2902 139 7.02920 7.0292 339.4395 7.0291 7.0292 7.02921
70 339.3610 339.3610 500.0000 339.3055 339.314 339.3678 140 26.4594 26.4594 339.4395 26.4894 26.4594 26.4684
        Total power (MW) 49,342.000 49,342 49,342 49,342.000 49,342.000 49,342.000
        Min cost ($/h) 1,560,436.71 1,560,436.0 1,657,944.8622 1,560,436.76 1,560,435.88 1,560,434.54
        Mean cost ($/h) 1,560,446.22 1,560,445.0 1,657,944.8627 1,560,445.43 1,560,444.56 1,560,440.32
        Max cost ($/h) 1,560,460.55 1,560,462.0 1,657,944.8652 1,560,461.66 1,560,461.52 1,560,460.89
        Std. of cost ($/h) 0.00003 0.000458 0.0005 0.0000054 0.0000076 0.0000003
        CPU mean time (s) 17.03 18.43 4.6 5.66 5.98 3.98