Table 8 Comparison results with the same maximum number of iterations.
Instance | GA | DE | PSO | GWO | HHO | ARO | ||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
B(Cmax) | Av | Sd | RPD | B(Cmax) | Av | Sd | RPD | B(Cmax) | Av | Sd | RPD | B(Cmax) | Av | Sd | RPD | B(Cmax) | Av | Sd | RPD | B(Cmax) | Av | Sd | RPD | |
EMK01(s) | 48 | 54.2 | 2.7 | 14.3 | 46 | 46.6 | 0.7 | 9.5 | 42 | 47.9 | 3.8 | 0.0 | 45 | 47.7 | 2.5 | 7.1 | 43 | 50.3 | 3.5 | 2.4 | 43 | 45.6 | 0.9 | 2.4 |
EMK01(d) | 51 | 52.2 | 1.2 | 30.8 | 42 | 43.7 | 1.1 | 7.7 | 42 | 44.1 | 2.3 | 5.1 | 40 | 44.8 | 3.2 | 2.6 | 46 | 48.3 | 1.5 | 17.9 | 39 | 41.5 | 1.2 | 0.0 |
EMK02(s) | 43 | 46.4 | 2.5 | 59.3 | 38 | 40.1 | 1.0 | 40.7 | 34 | 37.4 | 1.7 | 25.9 | 37 | 39.9 | 1.8 | 37.0 | 39 | 44.9 | 2.5 | 44.4 | 36 | 37.8 | 1.7 | 33.3 |
EMK02(d) | 44 | 46.6 | 2.0 | 57.1 | 37 | 39.2 | 1.3 | 32.1 | 35 | 38.1 | 2.2 | 21.4 | 35 | 39.3 | 2.8 | 25.0 | 46 | 48.0 | 2.6 | 64.3 | 34 | 37.1 | 1.6 | 21.4 |
EMK03(s) | 284 | 295.4 | 8.9 | 39.2 | 277 | 286.6 | 5.4 | 35.8 | 219 | 225.2 | 7.7 | 6.9 | 216 | 231.7 | 10.6 | 5.9 | 252 | 279.8 | 12.1 | 23.5 | 228 | 241.1 | 6.0 | 11.8 |
EMK03(d) | 270 | 296.6 | 11.6 | 44.4 | 267 | 274.8 | 6.1 | 42.8 | 213 | 220.1 | 5.3 | 11.8 | 218 | 235.7 | 10.5 | 16.6 | 266 | 287.3 | 10.4 | 42.2 | 223 | 235.7 | 8.3 | 19.3 |
EMK04(s) | 72 | 74.1 | 1.5 | 9.1 | 79 | 81.1 | 1.4 | 19.7 | 75 | 78.4 | 3.5 | 10.6 | 74 | 77.3 | 2.8 | 12.1 | 79 | 85.1 | 5.2 | 19.7 | 73 | 77.9 | 2.9 | 10.6 |
EMK04(d) | 83 | 90.7 | 5.3 | 25.8 | 81 | 82.5 | 1.2 | 22.7 | 73 | 79.3 | 3.8 | 10.6 | 72 | 77.2 | 5.1 | 9.1 | 76 | 82.9 | 3.6 | 15.2 | 72 | 74.5 | 2.1 | 9.1 |
EMK05(s) | 209 | 219.4 | 6.6 | 20.8 | 195 | 200.8 | 3.5 | 12.7 | 181 | 187.7 | 4.0 | 4.6 | 186 | 193.5 | 4.9 | 7.5 | 189 | 200.2 | 7.6 | 9.2 | 186 | 188.8 | 1.9 | 7.5 |
EMK05(d) | 207 | 214.7 | 4.2 | 21.1 | 199 | 203.7 | 2.9 | 16.4 | 185 | 189.3 | 2.4 | 7.0 | 180 | 190.5 | 5.6 | 5.3 | 196 | 204.4 | 5.5 | 14.6 | 185 | 189.3 | 2.4 | 8.2 |
EMK06(s) | 142 | 151.3 | 5.6 | 97.2 | 138 | 140.1 | 1.9 | 91.7 | 107 | 116.0 | 7.6 | 43.1 | 102 | 114.4 | 7.4 | 41.7 | 138 | 145.8 | 7.6 | 91.7 | 107 | 116.5 | 5.7 | 48.6 |
EMK06(d) | 142 | 154.6 | 9.1 | 105.8 | 140 | 143.3 | 2.0 | 102.9 | 108 | 113.0 | 3.8 | 58.8 | 105 | 118.8 | 6.5 | 52.2 | 136 | 146.4 | 7.0 | 97.1 | 109 | 117.1 | 4.3 | 58.0 |
EMK07(s) | 198 | 215.2 | 8.6 | 43.5 | 194 | 199.3 | 3.7 | 40.6 | 165 | 175.2 | 7.7 | 19.6 | 159 | 167.0 | 7.0 | 15.2 | 179 | 194.9 | 8.7 | 29.7 | 164 | 171.1 | 4.6 | 18.8 |
EMK07(d) | 202 | 216.8 | 10.9 | 47.4 | 199 | 210.7 | 4.9 | 45.3 | 168 | 179.4 | 9.2 | 18.2 | 165 | 173.8 | 5.0 | 20.4 | 209 | 215.8 | 10.0 | 52.6 | 171 | 178.2 | 5.6 | 24.8 |
EMK08(s) | 599 | 624.8 | 18.8 | 14.5 | 583 | 596.3 | 7.5 | 11.5 | 535 | 542.5 | 5.8 | 1.9 | 538 | 556.1 | 15.7 | 2.9 | 572 | 596.1 | 11.8 | 9.4 | 548 | 560.7 | 7.2 | 4.8 |
EMK08(d) | 599 | 609.6 | 9.2 | 16.8 | 582 | 595.6 | 8.8 | 13.5 | 523 | 542.1 | 10.7 | 1.9 | 541 | 553.8 | 9.5 | 5.5 | 583 | 595.5 | 12.5 | 13.6 | 549 | 561.8 | 7.4 | 7.0 |
EMK09(s) | 495 | 513.8 | 14.9 | 55.2 | 484 | 495.9 | 6.7 | 51.7 | 380 | 413.0 | 23.5 | 18.2 | 387 | 423.1 | 21.2 | 21.3 | 454 | 484.6 | 18.5 | 42.3 | 411 | 428.0 | 13.4 | 28.8 |
EMK09(d) | 484 | 522.9 | 17.0 | 51.3 | 492 | 503.2 | 5.4 | 53.8 | 403 | 423.4 | 11.4 | 23.0 | 391 | 417.6 | 12.5 | 22.2 | 459 | 483.7 | 14.7 | 43.4 | 418 | 441.5 | 16.4 | 30.6 |
EMK10(s) | 420 | 437.7 | 9.3 | 74.3 | 407 | 413.0 | 3.8 | 68.9 | 341 | 363.4 | 19.2 | 36.4 | 347 | 353.6 | 11.8 | 44.0 | 402 | 422.3 | 17.9 | 66.8 | 348 | 370.6 | 9.8 | 44.4 |
EMK10(d) | 421 | 436.3 | 13.1 | 84.6 | 402 | 416.0 | 8.0 | 76.3 | 327 | 348.8 | 20.6 | 40.8 | 345 | 361.9 | 13.0 | 51.3 | 412 | 431.1 | 14.0 | 80.7 | 338 | 361.6 | 13.0 | 48.2 |
EMK11(s) | 722 | 772.1 | 24.6 | 17.4 | 727 | 735.1 | 5.9 | 18.2 | 646 | 663.1 | 12.5 | 5.0 | 651 | 673.2 | 17.4 | 5.9 | 695 | 717.0 | 19.7 | 13.0 | 665 | 675.9 | 7.4 | 8.1 |
EMK11(d) | 704 | 752.0 | 19.6 | 14.8 | 696 | 718.3 | 8.7 | 13.5 | 657 | 664.1 | 5.0 | 7.2 | 643 | 671.6 | 15.8 | 4.9 | 680 | 702.6 | 12.4 | 10.9 | 644 | 655.8 | 6.2 | 5.1 |
EMK12(s) | 634 | 670.7 | 18.0 | 24.8 | 603 | 610.8 | 5.3 | 18.7 | 531 | 566.7 | 16.1 | 4.5 | 534 | 551.0 | 12.3 | 5.1 | 562 | 595.4 | 29.5 | 10.6 | 538 | 561.5 | 12.4 | 5.9 |
EMK12(d) | 668 | 688.5 | 16.4 | 31.5 | 599 | 609.3 | 5.4 | 17.9 | 541 | 572.2 | 16.6 | 6.5 | 535 | 558.1 | 16.0 | 5.3 | 603 | 635.4 | 29.3 | 18.7 | 540 | 558.1 | 16.0 | 6.3 |
EMK13(s) | 679 | 735.3 | 31.7 | 61.3 | 676 | 692.3 | 9.4 | 60.6 | 528 | 565.8 | 16.3 | 24.0 | 531 | 561.0 | 18.8 | 26.1 | 605 | 649.8 | 29.7 | 43.7 | 563 | 586.6 | 17.7 | 33.7 |
EMK13(d) | 716 | 733.3 | 13.9 | 71.7 | 677 | 686.5 | 6.5 | 62.4 | 556 | 582.5 | 19.6 | 29.5 | 542 | 561.1 | 14.3 | 30.0 | 605 | 683.3 | 40.7 | 45.1 | 582 | 594.5 | 8.6 | 39.6 |
EMK14(s) | 932 | 972.9 | 24.1 | 34.3 | 804 | 822.6 | 8.6 | 15.9 | 721 | 761.4 | 26.8 | 3.9 | 707 | 733.0 | 11.4 | 1.9 | 752 | 816.6 | 29.1 | 8.4 | 694 | 724.1 | 17.6 | 0.0 |
EMK14(d) | 947 | 985.5 | 29.1 | 36.5 | 765 | 792.4 | 12.4 | 10.2 | 707 | 764.8 | 29.0 | 1.9 | 707 | 729.3 | 18.1 | 1.9 | 772 | 837.2 | 48.7 | 11.2 | 712 | 728.5 | 9.2 | 2.6 |
EMK15(s) | 618 | 654.6 | 21.4 | 68.9 | 616 | 632.4 | 9.4 | 68.3 | 527 | 552.6 | 17.9 | 39.6 | 514 | 543.8 | 20.1 | 40.4 | 575 | 614.9 | 23.6 | 57.1 | 533 | 561.2 | 17.3 | 45.6 |
EMK15(d) | 633 | 672.8 | 32.7 | 65.7 | 626 | 644.9 | 10.7 | 63.9 | 515 | 531.3 | 14.1 | 34.3 | 521 | 542.8 | 16.8 | 36.4 | 590 | 629.0 | 21.7 | 54.5 | 528 | 560.3 | 14.5 | 38.2 |
SdMean | 13.1 | 5.3 | 11.0 | 10.7 | 15.4 | 8.1 | ||||||||||||||||||
RPDMean | 44.6 | 38.2 | 18.8 | 18.8 | 35.1 | 20.8 | ||||||||||||||||||
Instance | WO | MVO | OMA | TLBO | PRO | eWaOA | ||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
B(Cmax) | Av | Sd | RPD | B(Cmax) | Av | Sd | RPD | B(Cmax) | Av | Sd | RPD | B(Cmax) | Av | Sd | RPD | B(Cmax) | Av | Sd | RPD | B(Cmax) | Av | Sd | RPD | |
EMK01(s) | 48 | 51.1 | 2.0 | 14.3 | 47 | 49.4 | 2.4 | 11.9 | 49 | 51.1 | 1.1 | 16.7 | 45 | 46.8 | 1.7 | 7.1 | 48 | 52.1 | 1.8 | 14.3 | 42 | 42.0 | 0.0 | 0.0 |
EMK01(d) | 43 | 47.3 | 3.3 | 10.3 | 41 | 46.1 | 3.2 | 5.1 | 46 | 48.1 | 1.7 | 17.9 | 39 | 40.6 | 1.3 | 0.0 | 48 | 53.0 | 2.4 | 23.1 | 39 | 39.1 | 0.3 | 0.0 |
EMK02(s) | 36 | 43.6 | 3.2 | 33.3 | 36 | 40.1 | 2.0 | 33.3 | 46 | 47.4 | 1.2 | 70.4 | 33 | 38.0 | 2.6 | 22.2 | 39 | 43.3 | 2.7 | 44.4 | 27 | 28.1 | 0.7 | 0.0 |
EMK02(d) | 39 | 43.8 | 3.5 | 39.3 | 34 | 40.3 | 3.6 | 21.4 | 43 | 45.1 | 1.0 | 53.6 | 35 | 39.2 | 3.0 | 25.0 | 39 | 42.3 | 2.1 | 39.3 | 28 | 28.6 | 0.8 | 0.0 |
EMK03(s) | 238 | 263.2 | 26.3 | 16.7 | 222 | 248.3 | 19.5 | 8.8 | 268 | 279.4 | 6.0 | 31.4 | 216 | 249.3 | 21.2 | 5.9 | 281 | 291.9 | 5.4 | 37.7 | 204 | 204.0 | 0.0 | 0.0 |
EMK03(d) | 249 | 285.9 | 25.2 | 33.2 | 219 | 240.7 | 14.9 | 17.1 | 266 | 280.3 | 7.4 | 42.2 | 204 | 237.0 | 20.5 | 9.1 | 286 | 298.3 | 9.1 | 52.9 | 187 | 187.0 | 0.0 | 0.0 |
EMK04(s) | 73 | 80.6 | 5.1 | 10.6 | 79 | 82.2 | 3.3 | 19.7 | 81 | 83.6 | 1.9 | 22.7 | 68 | 74.5 | 3.7 | 3.0 | 85 | 89.7 | 2.9 | 28.8 | 66 | 68.1 | 2.5 | 0.0 |
EMK04(d) | 73 | 79.8 | 5.1 | 10.6 | 77 | 80.9 | 2.8 | 16.7 | 80 | 83.7 | 1.7 | 21.2 | 73 | 76.9 | 2.0 | 10.6 | 84 | 88.3 | 3.3 | 27.3 | 66 | 68.3 | 2.5 | 0.0 |
EMK05(s) | 190 | 200.2 | 7.6 | 9.8 | 188 | 198.0 | 7.8 | 8.7 | 203 | 207.2 | 3.1 | 17.3 | 186 | 195.7 | 6.3 | 7.5 | 213 | 223.8 | 4.6 | 23.1 | 173 | 175.3 | 1.7 | 0.0 |
EMK05(d) | 180 | 192.7 | 5.6 | 5.3 | 191 | 197.6 | 6.1 | 11.7 | 202 | 204.0 | 1.5 | 18.1 | 175 | 189.1 | 6.6 | 2.3 | 213 | 221.1 | 5.3 | 24.6 | 171 | 172.7 | 1.0 | 0.0 |
EMK06(s) | 119 | 138.9 | 18.0 | 65.3 | 115 | 127.2 | 7.4 | 59.7 | 142 | 147.3 | 3.4 | 97.2 | 113 | 127.4 | 9.0 | 56.9 | 153 | 160.7 | 5.5 | 112.5 | 72 | 75.8 | 2.7 | 0.0 |
EMK06(d) | 111 | 139.5 | 14.5 | 60.9 | 114 | 127.6 | 9.3 | 65.2 | 141 | 147.9 | 3.7 | 104.3 | 107 | 126.1 | 12.1 | 55.1 | 146 | 156.1 | 6.5 | 111.6 | 69 | 75.7 | 3.5 | 0.0 |
EMK07(s) | 176 | 201.2 | 13.4 | 27.5 | 172 | 185.8 | 7.3 | 24.6 | 191 | 200.4 | 4.8 | 38.4 | 164 | 179.5 | 11.4 | 18.8 | 204 | 214.8 | 7.5 | 47.8 | 138 | 142.5 | 2.5 | 0.0 |
EMK07(d) | 182 | 201.8 | 12.8 | 32.8 | 179 | 189.6 | 11.5 | 30.7 | 206 | 209.3 | 4.6 | 50.4 | 156 | 171.1 | 9.2 | 13.9 | 201 | 214.1 | 8.4 | 46.7 | 137 | 142.2 | 3.7 | 0.0 |
EMK08(s) | 548 | 582.2 | 30.2 | 4.8 | 553 | 573.9 | 17.5 | 5.7 | 582 | 590.3 | 4.5 | 11.3 | 563 | 581.6 | 10.9 | 7.6 | 604 | 613.4 | 8.2 | 15.5 | 523 | 532.0 | 3.0 | 0.0 |
EMK08(d) | 526 | 586.6 | 45.3 | 2.5 | 552 | 576.5 | 21.4 | 7.6 | 573 | 584.8 | 6.7 | 11.7 | 535 | 574.4 | 17.9 | 4.3 | 599 | 634.6 | 15.6 | 16.8 | 513 | 521.0 | 4.0 | 0.0 |
EMK09(s) | 423 | 483.9 | 32.3 | 32.6 | 413 | 439.2 | 14.0 | 29.5 | 493 | 503.2 | 6.1 | 54.5 | 439 | 462.1 | 17.2 | 37.6 | 481 | 523.3 | 20.9 | 50.8 | 319 | 327.8 | 6.3 | 0.0 |
EMK09(d) | 485 | 495.3 | 28.9 | 51.6 | 418 | 441.1 | 15.6 | 30.6 | 500 | 505.9 | 4.0 | 56.3 | 396 | 443.3 | 39.2 | 23.8 | 503 | 538.8 | 17.9 | 57.2 | 318 | 329.9 | 5.7 | 0.0 |
EMK10(s) | 357 | 414.3 | 41.4 | 48.1 | 345 | 375.5 | 20.2 | 43.2 | 417 | 429.3 | 7.7 | 73.0 | 383 | 421.3 | 15.4 | 58.9 | 436 | 453.0 | 11.9 | 80.9 | 241 | 250.6 | 7.7 | 0.0 |
EMK10(d) | 378 | 417.7 | 41.4 | 65.8 | 344 | 372.3 | 15.0 | 50.9 | 434 | 443.0 | 7.1 | 90.4 | 368 | 410.0 | 24.3 | 61.4 | 430 | 454.4 | 15.3 | 88.6 | 228 | 248.0 | 3.9 | 0.0 |
EMK11(s) | 677 | 702.1 | 24.3 | 10.1 | 666 | 686.7 | 14.9 | 8.3 | 691 | 708.2 | 8.4 | 12.4 | 682 | 695.9 | 10.4 | 10.9 | 714 | 738.5 | 16.4 | 16.1 | 615 | 619.2 | 2.9 | 0.0 |
EMK11(d) | 683 | 717.7 | 33.2 | 11.4 | 670 | 682.3 | 10.6 | 9.3 | 714 | 726.5 | 6.9 | 16.5 | 695 | 718.6 | 15.4 | 13.4 | 723 | 757.7 | 14.5 | 17.9 | 613 | 624.5 | 2.5 | 0.0 |
EMK12(s) | 552 | 605.0 | 36.2 | 8.7 | 573 | 591.7 | 15.1 | 12.8 | 572 | 581.2 | 5.6 | 12.6 | 529 | 549.7 | 13.6 | 4.1 | 639 | 655.4 | 9.8 | 25.8 | 508 | 513.8 | 9.2 | 0.0 |
EMK12(d) | 564 | 589.0 | 34.0 | 11.0 | 540 | 584.0 | 28.7 | 6.3 | 572 | 596.4 | 11.1 | 12.6 | 533 | 558.1 | 17.6 | 4.9 | 617 | 654.7 | 18.6 | 21.5 | 508 | 517.5 | 7.1 | 0.0 |
EMK13(s) | 605 | 665.3 | 49.9 | 43.7 | 564 | 612.2 | 33.7 | 34.0 | 687 | 716.9 | 13.3 | 63.2 | 541 | 635.0 | 50.3 | 28.5 | 711 | 745.6 | 23.1 | 68.9 | 421 | 452.1 | 9.1 | 0.0 |
EMK13(d) | 552 | 668.0 | 74.3 | 32.4 | 566 | 612.6 | 30.8 | 35.7 | 718 | 727.1 | 5.6 | 72.2 | 493 | 607.3 | 54.2 | 18.2 | 680 | 725.6 | 30.3 | 63.1 | 417 | 448.6 | 6.8 | 0.0 |
EMK14(s) | 727 | 756.1 | 22.4 | 4.8 | 727 | 782.4 | 41.5 | 4.8 | 734 | 757.1 | 14.1 | 5.8 | 694 | 716.2 | 10.2 | 0.0 | 882 | 915.0 | 25.5 | 27.1 | 694 | 694.0 | 0.0 | 0.0 |
EMK14(d) | 733 | 779.0 | 38.2 | 5.6 | 759 | 808.7 | 22.9 | 9.4 | 748 | 767.6 | 15.8 | 7.8 | 694 | 705.1 | 11.8 | 0.0 | 873 | 926.2 | 35.8 | 25.8 | 694 | 694.0 | 0.0 | 0.0 |
EMK15(s) | 541 | 628.1 | 46.0 | 47.8 | 517 | 565.8 | 29.0 | 41.3 | 621 | 643.2 | 10.7 | 69.7 | 630 | 650.8 | 13.2 | 72.1 | 648 | 673.8 | 16.1 | 77.0 | 366 | 395.9 | 5.1 | 0.0 |
EMK15(d) | 548 | 611.8 | 58.6 | 43.5 | 535 | 573.9 | 32.1 | 40.1 | 640 | 657.1 | 7.8 | 67.5 | 548 | 620.7 | 31.2 | 43.5 | 673 | 688.9 | 11.3 | 76.2 | 382 | 404.6 | 5.0 | 0.0 |
sdMean | 26.1 | 15.5 | 5.9 | 15.4 | 12.0 | 3.3 | ||||||||||||||||||
RPDMean | 26.5 | 23.5 | 41.3 | 20.9 | 45.4 | 0.0 | ||||||||||||||||||
