Table 8.
Comparison of the algorithms for PFSVRP problem.
| Problem | SA | GA | PSO | ISSA | PIS | PIG | PIP |
|---|---|---|---|---|---|---|---|
| C001 | 180411 | 180411 | 180411 | 180411 | 0.00 | 0.00 | 0.00 |
| C002 | 186048 | 186048 | 186048 | 186048 | 0.00 | 0.00 | 0.00 |
| C003 | 156571 | 156571 | 156571 | 156571 | 0.00 | 0.00 | 0.00 |
| C004 | 177144 | 177144 | 177144 | 177144 | 0.00 | 0.00 | 0.00 |
| C005 | 176111 | 176111 | 176111 | 176111 | 0.00 | 0.00 | 0.00 |
| C006 | 172111 | 172111 | 172111 | 172111 | 0.00 | 0.00 | 0.00 |
| C007 | 176511 | 176511 | 176511 | 176011 | 0.00 | 0.00 | 0.00 |
| C008 | 173211 | 173211 | 173211 | 173211 | 0.00 | 0.00 | 0.00 |
| C009 | 173835 | 171246 | 171246 | 171246 | 0.01 | 0.00 | 0.00 |
| C010 | 174271 | 170503 | 170503 | 170503 | 0.02 | 0.00 | 0.00 |
| C011 | 217903 | 217903 | 217903 | 217903 | 0.00 | 0.00 | 0.00 |
| C012 | 223827 | 223827 | 223827 | 223827 | 0.00 | 0.00 | 0.00 |
| C013 | 205763 | 205763 | 205763 | 205763 | 0.00 | 0.00 | 0.00 |
| C014 | 197403 | 197403 | 197403 | 217356 | − 0.10 | − 0.10 | − 0.10 |
| C015 | 205371 | 201603 | 201603 | 216024 | − 0.05 | − 0.07 | − 0.07 |
| C016 | 206555 | 199118 | 199118 | 199394 | 0.03 | 0.00 | 0.00 |
| C017 | 208052 | 208052 | 208052 | 209747 | − 0.01 | − 0.01 | − 0.01 |
| C018 | 308873 | 307898 | 307675 | 308150 | 0.00 | 0.00 | 0.00 |
| C019 | 291123 | 289773 | 289773 | 289773 | 0.00 | 0.00 | 0.00 |
| C020 | 272131 | 270574 | 271274 | 273301 | 0.00 | − 0.01 | − 0.01 |
| C021 | 335000 | 329264 | 329264 | 329264 | 0.02 | 0.00 | 0.00 |
| C022 | 340364 | 339644 | 339744 | 339644 | 0.00 | 0.00 | 0.00 |
| C023 | 351295 | 347995 | 377995 | 347995 | 0.01 | 0.00 | 0.08 |
| C024 | 329286 | 328173 | 327354 | 329286 | 0.00 | 0.00 | − 0.01 |
| C025 | 323570 | 323570 | 323870 | 323570 | 0.00 | 0.00 | 0.00 |
| C026 | 334662 | 336321 | 334862 | 335661 | 0.00 | 0.00 | 0.00 |
| C027 | 336773 | 336689 | 335834 | 336689 | 0.00 | 0.00 | 0.00 |
| C028 | 325690 | 328189 | 325990 | 325990 | 0.00 | 0.01 | 0.00 |
| C029 | 316910 | 316910 | 316910 | 316910 | 0.00 | 0.00 | 0.00 |
| C030 | 334656 | 334236 | 334236 | 334236 | 0.00 | 0.00 | 0.00 |
| C031 | 401046 | 381375 | 399222 | 381375 | 0.05 | 0.00 | 0.04 |
| C032 | 401272 | 392051 | 392251 | 392051 | 0.02 | 0.00 | 0.00 |
| C033 | 389300 | 370751 | 381734 | 370751 | 0.05 | 0.00 | 0.03 |
| C034 | 392109 | 382764 | 389907 | 382764 | 0.02 | 0.00 | 0.02 |
| C035 | 414769 | 395275 | 395275 | 395275 | 0.05 | 0.00 | 0.00 |
| C036 | 412995 | 391875 | 391875 | 391875 | 0.05 | 0.00 | 0.00 |
| C037 | 401296 | 381475 | 401455 | 381475 | 0.05 | 0.00 | 0.05 |
| C038 | 377275 | 377275 | 377275 | 377275 | 0.00 | 0.00 | 0.00 |
| C039 | 364175 | 364175 | 374654 | 364175 | 0.00 | 0.00 | 0.03 |
| C040 | 403239 | 386640 | 386740 | 386740 | 0.04 | 0.00 | 0.00 |
| C041 | 427539 | 410640 | 413640 | 410840 | 0.04 | 0.00 | 0.01 |
| C042 | 428186 | 398623 | 399923 | 395723 | 0.08 | 0.01 | 0.01 |
| C043 | 400298 | 392616 | 394416 | 390716 | 0.02 | 0.00 | 0.01 |
| C044 | 440322 | 415423 | 415523 | 414723 | 0.06 | 0.00 | 0.00 |
| C045 | 439437 | 408223 | 410823 | 406823 | 0.07 | 0.00 | 0.01 |
| C046 | 418494 | 410763 | 417135 | 408963 | 0.02 | 0.00 | 0.02 |
| C047 | 433985 | 417836 | 418936 | 416336 | 0.04 | 0.00 | 0.01 |
| C048 | 620844 | 621894 | 645439 | 617910 | 0.00 | 0.01 | 0.04 |
| C049 | 564532 | 566767 | 570916 | 564280 | 0.00 | 0.00 | 0.01 |
| C050 | 552590 | 542227 | 547331 | 543168 | 0.02 | 0.00 | 0.01 |
| C051 | 582175 | 578515 | 586493 | 579793 | 0.00 | 0.00 | 0.01 |
| C052 | 655989 | 650606 | 656525 | 647980 | 0.01 | 0.00 | 0.01 |
| C053 | 621925 | 612988 | 622188 | 609231 | 0.02 | 0.01 | 0.02 |
| C054 | 601657 | 589950 | 600644 | 592945 | 0.01 | − 0.01 | 0.01 |
| C055 | 558272 | 555176 | 558880 | 553020 | 0.01 | 0.00 | 0.01 |
| C056 | 615321 | 610506 | 619610 | 608010 | 0.01 | 0.00 | 0.02 |
| C057 | 597370 | 582614 | 599131 | 582014 | 0.03 | 0.00 | 0.03 |
| C058 | 589785 | 586009 | 600383 | 587794 | 0.00 | 0.00 | 0.02 |
| C059 | 577456 | 574289 | 577263 | 568493 | 0.02 | 0.01 | 0.02 |
| C060 | 634465 | 620631 | 623621 | 626673 | 0.01 | − 0.01 | 0.00 |
| C061 | 797982 | 797982 | 797982 | 797982 | 0.00 | 0.00 | 0.00 |
| C062 | 797031 | 775482 | 782097 | 775482 | 0.03 | 0.00 | 0.01 |
| C063 | 800337 | 773649 | 783474 | 765918 | 0.04 | 0.01 | 0.02 |
| C064 | 772285 | 748834 | 788575 | 748834 | 0.03 | 0.00 | 0.05 |
| C065 | 838146 | 773682 | 773682 | 773682 | 0.08 | 0.00 | 0.00 |
| C066 | 772010 | 762182 | 762182 | 762182 | 0.01 | 0.00 | 0.00 |
| C067 | 790745 | 773282 | 773282 | 773282 | 0.02 | 0.00 | 0.00 |
| C068 | 811518 | 758082 | 788304 | 758082 | 0.07 | 0.00 | 0.04 |
| C069 | 802110 | 793482 | 846003 | 793482 | 0.01 | 0.00 | 0.06 |
| C070 | 784719 | 709668 | 709668 | 709668 | 0.10 | 0.00 | 0.00 |
| C071 | 808756 | 754468 | 756468 | 754468 | 0.07 | 0.00 | 0.00 |
| C072 | 800639 | 717261 | 719965 | 712251 | 0.11 | 0.01 | 0.01 |
| C073 | 775042 | 753516 | 753816 | 745080 | 0.04 | 0.01 | 0.01 |
| C074 | 812600 | 755864 | 761564 | 755864 | 0.07 | 0.00 | 0.01 |
| C075 | 763621 | 723247 | 727947 | 723247 | 0.05 | 0.00 | 0.01 |
| C076 | 751888 | 707587 | 707287 | 706787 | 0.06 | 0.00 | 0.00 |
| C077 | 783718 | 736996 | 736696 | 736396 | 0.06 | 0.00 | 0.00 |
| C078 | 1084317 | 1060186 | 1066314 | 1057930 | 0.02 | 0.00 | 0.01 |
| C079 | 1054859 | 1031667 | 1037985 | 1029586 | 0.02 | 0.00 | 0.01 |
| C080 | 972169 | 952939 | 958034 | 951049 | 0.02 | 0.00 | 0.01 |
| C081 | 955382 | 931539 | 956670 | 927365 | 0.03 | 0.00 | 0.03 |
| C082 | 1069636 | 1051301 | 1067531 | 1040681 | 0.03 | 0.01 | 0.03 |
| C083 | 1020984 | 1024938 | 1033895 | 1009305 | 0.01 | 0.02 | 0.02 |
| C084 | 983055 | 968871 | 988055 | 955947 | 0.03 | 0.01 | 0.03 |
| C085 | 946634 | 947817 | 957566 | 925623 | 0.02 | 0.02 | 0.03 |
| C086 | 1021645 | 1016376 | 1030106 | 997046 | 0.02 | 0.02 | 0.03 |
| C087 | 990036 | 983210 | 989945 | 960881 | 0.03 | 0.02 | 0.03 |
| C088 | 982117 | 978800 | 996691 | 966560 | 0.02 | 0.01 | 0.03 |
| C089 | 959120 | 946552 | 957210 | 931629 | 0.03 | 0.02 | 0.03 |
| C090 | 1008158 | 1007402 | 1011869 | 1009886 | 0.00 | 0.00 | 0.00 |
| C091 | 2069001 | 1899871 | 1929057 | 1899871 | 0.08 | 0.00 | 0.02 |
| C092 | 2035139 | 1859695 | 1898537 | 1862495 | 0.08 | 0.00 | 0.02 |
| C093 | 2110338 | 1899084 | 2081733 | 1920721 | 0.09 | − 0.01 | 0.08 |
| C094 | 2072675 | 1893635 | 2184492 | 1919791 | 0.07 | − 0.01 | 0.12 |
| C095 | 2041914 | 1863015 | 1983424 | 1864315 | 0.09 | 0.00 | 0.06 |
| C096 | 2092703 | 1844912 | 2064127 | 1844012 | 0.12 | 0.00 | 0.11 |
| C097 | 2090504 | 1905975 | 2166661 | 1901011 | 0.09 | 0.00 | 0.12 |
| C098 | 2050390 | 1881181 | 2187853 | 1882384 | 0.08 | 0.00 | 0.14 |
| C099 | 2009435 | 1869290 | 2191852 | 1858513 | 0.08 | 0.01 | 0.15 |
| C100 | 2117202 | 1890478 | 2284856 | 1896296 | 0.10 | 0.00 | 0.17 |
| C101 | 1737448 | 1729103 | 1758246 | 1732872 | 0.00 | 0.00 | 0.01 |
| C102 | 1864338 | 1722322 | 1744093 | 1697795 | 0.09 | 0.01 | 0.03 |
| C103 | 1897530 | 1695291 | 1743369 | 1707530 | 0.10 | − 0.01 | 0.02 |
| C104 | 1751463 | 1683859 | 1732606 | 1690785 | 0.03 | 0.00 | 0.02 |
| C105 | 1840417 | 1708208 | 1744444 | 1738023 | 0.06 | − 0.02 | 0.00 |
| C106 | 1786274 | 1726374 | 1735160 | 1696234 | 0.05 | 0.02 | 0.02 |
| C107 | 1852195 | 1709295 | 1786040 | 1749669 | 0.06 | − 0.02 | 0.02 |
| C108 | 1781766 | 1731276 | 1732535 | 1737445 | 0.02 | 0.00 | 0.00 |
| C109 | 1808818 | 1690635 | 1732210 | 1693284 | 0.06 | 0.00 | 0.02 |
| C110 | 1792084 | 1683999 | 1741498 | 1694290 | 0.05 | − 0.01 | 0.03 |
| C111 | 7981671 | 6882329 | 8717713 | 6820131 | 0.15 | 0.01 | 0.22 |
| C112 | 7558146 | 6740658 | 8471094 | 6708112 | 0.11 | 0.00 | 0.21 |
| C113 | 7403232 | 6795878 | 8390107 | 6498469 | 0.12 | 0.04 | 0.23 |
| C114 | 6849689 | 6625029 | 8641742 | 6483350 | 0.05 | 0.02 | 0.25 |
| C115 | 7876287 | 6798660 | 8936198 | 6780136 | 0.14 | 0.00 | 0.24 |
| C116 | 7634913 | 6830576 | 9316573 | 6766349 | 0.11 | 0.01 | 0.27 |
| C117 | 7775337 | 6812021 | 9475893 | 6770335 | 0.13 | 0.01 | 0.29 |
| C118 | 7760294 | 6835550 | 9756810 | 6787157 | 0.13 | 0.01 | 0.30 |
| C119 | 7476513 | 6655581 | 8814226 | 6560400 | 0.12 | 0.01 | 0.26 |
| C120 | 7130745 | 6815017 | 9129559 | 6754467 | 0.05 | 0.01 | 0.26 |