Skip to main content
. 2026 May 26;16:27069. doi: 10.1038/s41598-026-53013-5

Table 8.

Comparison results of RZOA and D-GWO on TSP instances.

Problem Optimal Algorithm Best Average SD PDB (%) PDA (%) Rank
att-48 33,522 RZOA 33,522 33,627 47.77 0.00 0.31 2
D-GWO 33,523 33,600 - 0.00 0.23 1
pr-76 108,159 RZOA 108,159 108,474 85.20 0.00 0.29 1
D-GWO 108,159 108,900 - 0.00 0.69 2
kro-B100 22,141 RZOA 22,158 22,269 79.30 0.08 0.58 1
D-GWO 22,159 22,445 - 0.08 1.37 2
kro-C100 20,749 RZOA 20,770 20,838 42.50 0.10 0.43 1
D-GWO 20,749 21,078 - 0.00 1.59 2
kro-E100 22,068 RZOA 22,079 22,151 49.10 0.05 0.38 1
D-GWO 22,131 22,410 - 0.29 1.55 2
lin-105 14,379 RZOA 14,393 14,453 18.87 0.10 0.51 1
D-GWO 14,382 14,520 - 0.02 0.98 2
pr-107 44,303 RZOA 44,329 44,452 42.62 0.06 0.34 1
D-GWO 44,303 44,685 - 0.00 0.86 2
pr-124 59,030 RZOA 59,110 59,298 57.32 0.14 0.45 1
D-GWO 59,030 59,391 - 0.00 0.61 2
pr-136 96,772 RZOA 96,890 97,900 459.08 0.12 1.17 1
D-GWO 97,826 99,310 - 1.09 2.62 2
pr-144 58,537 RZOA 58,621 59,057 236.48 0.14 0.89 2
D-GWO 58,537 58,600 - 0.00 0.11 1
pr-226 80,369 RZOA 80,638 81,540 346.96 0.33 1.46 2
D-GWO 80,648 81,136 - 0.34 0.95 1
pr-439 107,217 RZOA 107,985 109,937 1010.35 0.72 2.54 1
D-GWO 110,415 112,850 - 2.98 5.25 2
pr-1002 259,047 RZOA 262,358 273,645 16985.31 1.28 5.64 2
D-GWO 264,922 267,713 - 2.27 3.35 1