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

Table 7.

Comparison results of RZOA and DSSA 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
DSSA 33,522 33,522 0.00 0.00 0.00 1
eil-51 426 RZOA 426 427 0.83 0.00 0.23 1
DSSA 426 427 0.68 0.00 0.23 2
berlin-52 7542 RZOA 7542 7566 10.70 0.00 0.32 2
DSSA 7542 7542 0.00 0.00 0.00 1
st-70 675 RZOA 675 677 1.43 0.00 0.30 2
DSSA 675 675 0.00 0.00 0.00 1
pr-76 108,159 RZOA 108,159 108,474 85.20 0.00 0.29 2
DSSA 108,159 108,159 0.00 0.00 0.00 1
eil-76 538 RZOA 538 539 0.70 0.00 0.19 1
DSSA 538 543 2.83 0.00 0.93 2
kro-A100 21,282 RZOA 21,297 21,393 45.20 0.07 0.52 2
DSSA 21,282 21,290 17.14 0.00 0.04 1
kro-B100 22,141 RZOA 22,158 22,269 79.30 0.08 0.58 2
DSSA 22,141 22,173 36.30 0.00 0.14 1
kro-C100 20,749 RZOA 20,770 20,838 42.50 0.10 0.43 2
DSSA 20,749 20,770 42.54 0.00 0.10 1
kro-D100 21,294 RZOA 21,325 21,405 43.10 0.15 0.52 2
DSSA 21,294 21,319 44.15 0.00 0.12 1
kro-E100 22,068 RZOA 22,079 22,151 49.10 0.05 0.38 2
DSSA 22,068 22,092 32.85 0.00 0.11 1
eil-101 629 RZOA 630 632 1.63 0.16 0.48 1
DSSA 634 641 3.62 0.79 1.91 2
lin-105 14,379 RZOA 14,393 14,453 18.87 0.10 0.51 2
DSSA 14,379 14,379 0.00 0.00 0.00 1
pr-107 44,303 RZOA 44,329 44,452 42.62 0.06 0.34 2
DSSA 44,303 44,322 34.75 0.00 0.04 1
pr-124 59,030 RZOA 59,110 59,298 57.32 0.14 0.45 2
DSSA 59,030 59,030 0.00 0.00 0.00 1
ch-130 6110 RZOA 6168 6250 51.89 0.95 2.29 2
DSSA 6110 6154 26.38 0.00 0.72 1
pr-136 96,772 RZOA 96,890 97,900 459.08 0.12 1.17 2
DSSA 96,920 97,302 265.94 0.15 0.55 1
pr-144 58,537 RZOA 58,621 59,057 236.48 0.14 0.89 2
DSSA 59,537 58,537 0.00 1.71 0.00 1
ch-150 6528 RZOA 6547 6595 26.31 0.29 1.03 2
DSSA 6528 6590 34.53 0.00 0.95 1
kro-A200 29,368 RZOA 29,520 29,819 138.65 0.52 1.54 2
DSSA 29,459 29,682 130.55 0.31 1.07 1
kro-B200 29,437 RZOA 29,539 29,920 48.94 0.35 1.64 2
DSSA 29,564 29,851 178.27 0.43 1.41 1
tsp-225 3916 RZOA 3978 4001 15.60 1.58 2.17 2
DSSA 3916 3926 12.53 0.00 0.26 1
pr-226 80,369 RZOA 80,638 81,540 346.96 0.33 1.46 2
DSSA 80,369 80,369 0.00 0.00 0.00 1
pr-264 49,135 RZOA 49,455 49,855 144.92 0.65 1.47 2
DSSA 49,135 49,272 155.73 0.00 0.28 1
lin-318 42,029 RZOA 42,456 43,661 572.97 1.02 3.88 2
DSSA 42,495 42,743 184.42 1.11 1.70 1