## 5 Numerical Tests and Comparisons
### Comparison of Proposed Hybrid PSO(PHPSO) with Fink and Vob, DPSOVND, Pan-Ruiz, and HPSO
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**Instance** & **F\&V** & **DPSO** & **Pan+Ruiz** & **HPSO** & **PHPSO** & **Instance** & **F\&V** & **DPSO** & **Pan+Ruiz** & **HPSO** & **PHPSO** \\ \hline ta0(33 & 78,282 & 78,103 & 63,162 & 63,162 & **57,420** & ta093 & 1,515,535 & 1,493,502 & **1,046,902** & 1,046,902 & 1,046,902 \\ ta034 & 82,737 & 82,467 & 68,226 & 68,226 & 60,470 & ta094 & 1,489,457 & 1,462,300 & 1,030,481 & 1,030,481 & **997,214** \\ ta0(35 & 83,901 & 83,493 & 69,351 & 69,351 & **58,900** & 1,095 & 1,513,281 & 1,483,894 & **1,043,027** & 1,034,027 \\ ta036 & 80,924 & 80,749 & 66,841 & 66,841 & 57,620 & ta096 & 1,508,331 & 1,474,000 & **1,066,195** & 1,006,195 & 1,006,195 \\ ta037 & 78,791 & 78,604 & 66,253 & 66,253 & 58,893 & ta097 & 1,541,419 & 1,521,861 & **1,053,951** & 1,053,051 & 1,053,051 \\ ta038 & 79,007 & 78,796 & 44,332 & 64,332 & 56,646 & ta098 & 1,533,397 & 4,199,380 & 1,044,875 & 1,044,875 & 983,816 \\ ta039 & 75,842 & 75,825 & 62,981 & 62,981 & 54,424 & ta099 & 1,507,422 & 1,481,283 & 1,026,137 & 1,026,137 & **962,641** \\ ta040 & 83,829 & 83,430 & 68,770 & 68,770 & 57,533 & ta100 & 1,520,800 & 1,489,218 & 1,030,299 & 1,030,299 & 955,843 \\ ta041 & 143,398 & 114,051 & **87,114** & 87,114 & ta101 & 2,012,785 & 1,988,772 & 1,227,733 & 1,227,373 & 949,205 \\ ta042 & 112,725 & 112,427 & **82,820** & 82,820 & 82,820 & ta102 & 2,057,409 & 2,025,561 & 1,245,271 & 1,245,271 & 1,245,271 \\ ta043 & 105,433 & 105,345 & 79,931 & 79,931 & 64,446 & ta103 & 2,050,169 & 2,017,216 & 1,269,673 & 1,254,162 & **1,254,162** \\ ta044 & 113,554 & 113,367 & 86,446 & 86,446 & 68,770 & ta104 & 2,040,946 & 2,010,121 & 1,238,439 & 1,238,349 & **1,238,349** \\ ta045 & 115,441 & 115,295 & 86,377 & 86,377 & 62,523 & ta105 & 2,027,138 & 2,002,299 & 1,227,244 & 1,227,214 & 1,227,214 \\ ta046 & 112,645 & 112,459 & 86,587 & 86,587 & 62,005 & ta106 & 2,046,542 & 2,017,240 & 1,227,604 & 1,227,604 & **976,118** \\ ta047 & 116,560 & 116,631 & **85,750** & 88,750 & 88,750 & t107 & 2,045,906 & 2,018,945 & 1,243,707 & 1,243,707 \\ ta048 & 115,056 & 115,065 & 86,727 & 86,727 & 67,669 & ta108 & 2,044,218 & 2,028,861 & 1,246,123 & 1,235,460 & 983,816 \\ ta049 & 110,482 & 110,367 & 85,441 & 85,441 & 67,144 & ta109 & 2,037,040 & 2,007,678 & 1,234,936 & 1,234,936 & 962,641 \\ ta050 & 113,462 & 113,427 & 87,998 & 57,998 & 61,460 & ta110 & 2,046,966 & 2,020,806 & 1,225,966 & 1,250,99,958 \\ ta051 & 172,845 & 172,981 & 125,831 & 125,831 & 62,857 & ta111 & – & – & 6,698,866 & 6,698,566 & 6,263,859 \\ ta052 & 161,092 & 160,836 & 119,247 & 119,247 & 117,137 & ta112 & – & – & 6,770,735 & 6,723,548 & **6,413,646** \\ ta053 & 160,213 & 160,104 & 116,459 & 116,459 & 101,810 & ta113 & – & – & 6,739,645 & 6,739,645 & 6,437,528 \\ ta054 & 161,557 & 161,690 & 120,261 & 120,261 & 100,074 & ta114 & – & – & 6,785,91 & 6,745,989 & 6,437,528 \\ ta055 & 167,640 & 167,336 & 118,184 & 118,184 & 114,468 & ta115 & – & – & 6,729,468 & 6,729,468 & 6,312,830 \\ ta056 & 161,784 & 161,784 & 120,586 & 120,586 & 103,248 & ta116 & – & – & 6,724,085 & 6,724,085 & 6,361,035 \\ ta057 & 167,233 & 167,064 & 122,880 & 122,880 & 122,880 & ta117 & – & – & 6,691,468 & 6,691,468 & 6,539,854 \\ ta058 & 168,100 & 167,822 & 122,489 & 122,489 & 119,449 & ta118 & – & – & 6,783,916 & 6,755,489 & 6,126,127 \\ ta059 & 165,292 & 165,207 & 121,872 & 121,872 & 111,571 & ta119 & – & – & 6,711,305 & 6,711,305 \\ ta060 & 168,386 & 168,386 & 123,954 & 123,954 & 120,849 & ta120 & – & – & **6,755,722** & 6,755,722 & 6,755,722 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: _Cont._Table 10 shows that the proposed algorithm improves 103 out of 120 instances of the Taillard dataset. This shows that the optimal results obtained by the PHPSO are better than values obtained by various metaheuristics to date, exhibiting the effective searching quality of PHPSO.