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

Table 2.

Results of the proposed RZOA for TSP samples.

Problem Optimal Best Average SD PDB (%) PDA (%)
oliver-30 420 420 421 1.33 0.00 0.24
att-48 33,522 33,522 33,627 47.77 0.00 0.31
rand-50 5553 5553 5566 6.81 0.00 0.23
eil-51 426 426 427 0.83 0.00 0.23
berlin-52 7542 7542 7566 10.70 0.00 0.32
st-70 675 675 677 1.43 0.00 0.30
pr-76 108,159 108,159 108,474 85.20 0.00 0.29
eil-76 538 538 539 0.70 0.00 0.19
rat-99 1211 1212 1214 1.33 0.08 0.25
kro-A100 21,282 21,297 21,393 45.20 0.07 0.52
kro-B100 22,141 22,158 22,269 79.30 0.08 0.58
kro-C100 20,749 20,770 20,838 42.50 0.10 0.43
kro-D100 21,294 21,325 21,405 43.10 0.15 0.52
kro-E100 22,068 22,079 22,151 49.10 0.05 0.38
rd-100 7910 7921 7948 42.90 0.14 0.48
eil-101 629 630 632 1.63 0.16 0.48
lin-105 14,379 14,393 14,453 18.87 0.10 0.51
pr-107 44,303 44,329 44,452 42.62 0.06 0.34
pr-124 59,030 59,110 59,297 57.32 0.14 0.45
bier-127 118,282 118,420 119,893 525.61 0.12 1.36
ch-130 6110 6168 6250 51.89 0.95 2.29
pr-136 96,772 96,890 97,899 459.08 0.12 1.16
pr-144 58,537 58,621 59,057 236.48 0.14 0.89
ch-150 6528 6547 6595 26.31 0.29 1.03
d-198 15,780 15,820 15,930 58.20 0.25 0.95
kro-A200 29,368 29,520 29,819 138.65 0.52 1.54
kro-B200 29,437 29,539 29,920 48.94 0.35 1.64
tsp-225 3916 3978 4001 15.60 1.58 2.17
pr-226 80,369 80,638 81,540 346.96 0.33 1.46
pr-264 49,135 49,455 49,855 144.92 0.65 1.47
a-280 2579 2600 2631 43.72 0.81 2.02
pr-299 48,191 48,358 48,923 195.12 0.35 1.52
lin-318 42,029 42,456 43,661 572.97 1.02 3.88
rd-400 15,281 15,320 15,602 89.35 0.26 2.10
fl-417 11,861 12,020 12,154 103.54 1.34 2.47
pr-439 107,217 107,985 109,937 1010.35 0.72 2.54
pcb-442 50,778 51,238 51,998 415.55 0.91 2.40
rat-575 6773 6820 6934 58.43 0.69 2.38
rat-783 8806 8908 9143 169.09 1.16 3.83
pr-1002 259,047 262,358 273,645 16985.31 1.28 5.64
fl-1400 20,127 20,335 21,221 312.40 1.03 5.44
pr-2392 378,032 381,251 394,033 3982.01 0.85 4.23