Table 11.
Comparison results of RZOA, DDCS, DKA and DSSA on TSP instances.
| Problem | Algorithm | Optimal | Best | Average | Worst | SD | PDA % | Rank |
|---|---|---|---|---|---|---|---|---|
| eil-51 | RZOA | 426 | 426 | 427 | 430 | 0.83 | 0.23 | 1 |
| DDCS | 426 | 429 | 435 | 2.67 | 0.70 | 3 | ||
| DKA | 427 | 430 | 438 | 3.14 | 0.94 | 4 | ||
| DSSA | 426 | 427 | 428 | 0.68 | 0.23 | 2 | ||
| berlin-52 | RZOA | 7542 | 7542 | 7566 | 7568 | 10.70 | 0.32 | 3 |
| DDCS | 7542 | 7542 | 7542 | 0.00 | 0.00 | 1 | ||
| DKA | 7542 | 7646 | 7869 | 97.12 | 1.38 | 4 | ||
| DSSA | 7542 | 7542 | 7542 | 0.00 | 0.00 | 2 | ||
| st-70 | RZOA | 675 | 675 | 677 | 680 | 1.43 | 0.30 | 2 |
| DDCS | 675 | 679 | 686 | 3.89 | 0.59 | 3 | ||
| DKA | 675 | 684 | 691 | 4.81 | 1.33 | 4 | ||
| DSSA | 675 | 675 | 678 | 0.67 | 0.00 | 1 | ||
| pr-76 | RZOA | 108,159 | 108,159 | 108,474 | 109,495 | 85.20 | 0.29 | 2 |
| DDCS | 108,159 | 110,341 | 113,404 | 1155.50 | 2.02 | 4 | ||
| DKA | 108,304 | 110,135 | 114,610 | 1311.37 | 1.83 | 3 | ||
| DSSA | 108,159 | 108,159 | 108,159 | 0.00 | 0.00 | 1 | ||
| eil-76 | RZOA | 538 | 538 | 539 | 542 | 0.70 | 0.19 | 1 |
| DDCS | 538 | 541 | 550 | 2.86 | 0.56 | 2 | ||
| DKA | 539 | 548 | 558 | 5.69 | 1.86 | 4 | ||
| DSSA | 538 | 543 | 548 | 2.83 | 0.93 | 3 | ||
| kro-A100 | RZOA | 21,282 | 21,297 | 21,393 | 21,420 | 45.20 | 0.52 | 2 |
| DDCS | 21,282 | 21,444 | 21,810 | 156.23 | 0.76 | 4 | ||
| DKA | 21,282 | 21,437 | 21,825 | 143.48 | 0.73 | 3 | ||
| DSSA | 21,282 | 21,290 | 21,353 | 17.14 | 0.04 | 1 | ||
| kro-B100 | RZOA | 22,141 | 22,158 | 22,269 | 22,354 | 79.30 | 0.58 | 2 |
| DDCS | 22,199 | 22,357 | 22,533 | 90.98 | 0.98 | 3 | ||
| DKA | 22,258 | 22,454 | 23,035 | 166.77 | 1.41 | 4 | ||
| DSSA | 22,141 | 22,173 | 22,258 | 36.30 | 0.14 | 1 | ||
| kro-C100 | RZOA | 20,749 | 20,770 | 20,838 | 20,879 | 42.50 | 0.43 | 2 |
| DDCS | 20,749 | 21,011 | 21,357 | 166.59 | 1.26 | 3 | ||
| DKA | 20,769 | 21,081 | 21,516 | 232.09 | 1.60 | 4 | ||
| DSSA | 20,749 | 20,770 | 20,880 | 42.54 | 0.10 | 1 | ||
| kro-D100 | RZOA | 21,294 | 21,325 | 21,405 | 21,409 | 43.10 | 0.52 | 2 |
| DDCS | 21,374 | 21,860 | 22,477 | 316.32 | 2.66 | 4 | ||
| DKA | 21,398 | 21,750 | 22,481 | 223.87 | 2.14 | 3 | ||
| DSSA | 21,294 | 21,319 | 21,410 | 44.15 | 0.12 | 1 | ||
| kro-E100 | RZOA | 22,068 | 22,079 | 22,151 | 22,256 | 49.10 | 0.38 | 2 |
| DDCS | 22,121 | 22,227 | 22,466 | 109.96 | 0.72 | 3 | ||
| DKA | 22,146 | 22,455 | 22,950 | 203.42 | 1.75 | 4 | ||
| DSSA | 22,068 | 22,092 | 22,174 | 32.85 | 0.11 | 1 | ||
| lin-105 | RZOA | 14,379 | 14,393 | 14,453 | 14,536 | 18.87 | 0.51 | 2 |
| DDCS | 14,379 | 14,543 | 15,042 | 168.62 | 1.14 | 3 | ||
| DKA | 14,426 | 14,687 | 15,391 | 229.62 | 2.14 | 4 | ||
| DSSA | 14,379 | 14,379 | 14,379 | 0.00 | 0.00 | 1 | ||
| pr-107 | RZOA | 44,303 | 44,329 | 44,452 | 44,584 | 42.62 | 0.34 | 3 |
| DDCS | 44,303 | 44,437 | 44,617 | 88.78 | 0.30 | 2 | ||
| DKA | 44,303 | 44,748 | 45,221 | 219.43 | 1.00 | 4 | ||
| DSSA | 44,303 | 44,322 | 44,387 | 34.75 | 0.04 | 1 | ||
| pr-124 | RZOA | 59,030 | 59,110 | 59,297 | 59,375 | 57.32 | 0.45 | 2 |
| DDCS | 59,030 | 59,300 | 59,767 | 227.64 | 0.46 | 3 | ||
| DKA | 59,164 | 59,985 | 61,412 | 590.62 | 1.62 | 4 | ||
| DSSA | 59,030 | 59,030 | 59,030 | 0.00 | 0.00 | 1 | ||
| ch-130 | RZOA | 6110 | 6168 | 6250 | 6356 | 51.89 | 2.29 | 2 |
| DDCS | 6140 | 6269 | 6378 | 64.04 | 2.60 | 3 | ||
| DKA | 6201 | 6308 | 6423 | 58.11 | 3.24 | 4 | ||
| DSSA | 6110 | 6154 | 6205 | 26.38 | 0.72 | 1 | ||
| pr-136 | RZOA | 96,772 | 96,890 | 97,899 | 98,257 | 459.08 | 1.16 | 2 |
| DDCS | 97,144 | 101,512 | 103,155 | 1312.63 | 4.90 | 3 | ||
| DKA | 99,692 | 102,297 | 104,440 | 1347.85 | 5.71 | 4 | ||
| DSSA | 96,920 | 97,302 | 97,956 | 265.94 | 0.55 | 1 | ||
| pr-144 | RZOA | 58,537 | 58,621 | 59,057 | 59,353 | 236.48 | 0.89 | 3 |
| DDCS | 58,537 | 58,697 | 58,763 | 90.85 | 0.27 | 2 | ||
| DKA | 58,603 | 59,372 | 60,961 | 732.71 | 1.43 | 4 | ||
| DSSA | 58,537 | 58,537 | 58,537 | 0.00 | 0.00 | 1 | ||
| ch-150 | RZOA | 6528 | 6547 | 6595 | 6625 | 26.31 | 1.03 | 3 |
| DDCS | 6544 | 6560 | 6599 | 13.93 | 0.49 | 1 | ||
| DKA | 6553 | 6654 | 6898 | 91.49 | 1.93 | 4 | ||
| DSSA | 6528 | 6590 | 6658 | 34.53 | 0.95 | 2 | ||
| kro-A200 | RZOA | 29,368 | 29,520 | 29,819 | 30,155 | 138.65 | 1.54 | 2 |
| DDCS | 25,962 | 29,837 | 30,264 | 140.30 | 1.60 | 3 | ||
| DKA | 29,688 | 30,202 | 30,812 | 326.46 | 2.84 | 4 | ||
| DSSA | 29,459 | 29,682 | 29,882 | 130.55 | 1.07 | 1 | ||
| kro-B200 | RZOA | 29,437 | 29,539 | 29,920 | 29,989 | 48.94 | 1.64 | 2 |
| DDCS | 29,927 | 30,406 | 30,882 | 277.08 | 3.29 | 3 | ||
| DKA | 30,170 | 30,912 | 32,037 | 457.45 | 5.01 | 4 | ||
| DSSA | 29,564 | 29,851 | 30,126 | 178.27 | 1.41 | 1 | ||
| tsp-225 | RZOA | 3916 | 3978 | 4001 | 4013 | 15.60 | 2.17 | 2 |
| DDCS | 3957 | 4016 | 4086 | 34.21 | 2.55 | 3 | ||
| DKA | 3989 | 4096 | 4246 | 65.08 | 4.60 | 4 | ||
| DSSA | 3916 | 3926 | 3952 | 12.53 | 0.26 | 1 | ||
| pr-226 | RZOA | 80,369 | 80,638 | 81,540 | 82,352 | 346.96 | 1.46 | 2 |
| DDCS | 80,860 | 81,549 | 82,706 | 557.77 | 1.47 | 3 | ||
| DKA | 81,168 | 83,232 | 86,350 | 1120.22 | 3.56 | 4 | ||
| DSSA | 80,369 | 80,369 | 80,373 | 0.89 | 0.00 | 1 |