Research Article

# Minimization of the Total Traveling Distance and Maximum Distance by Using a Transformed-Based Encoding EDA to Solve the Multiple Traveling Salesmen Problem

## Table 2

The total average distance of the three algorithms.
 Instance One-chromosome TPGA Min Mean Max StDev Min Mean Max StDev Min Mean Max StDev Min Mean Max StDev att48 39195 64157 104400 20065 47960 88032 142234 29831 42765 73320 119821 26312 42446 73416 121381 26676 berlin52 9355 12574 18389 2534 10693 16034 23586 3884 9654 14087 20647 3756 9410 14173 21140 3856 bier127 208466 253086 330415 32864 261954 332874 433197 47074 220310 253968 328622 18768 214928 255589 311903 18317 ch130 13488 17246 23859 3019 17602 24176 32313 3785 12781 15893 19262 1644 12020 15813 18983 1582 eil101 1021.6 1343.3 1832.4 233.2 1328.1 1829.7 2441.7 326.1 1024.4 1270.4 1625.4 183.7 943.9 1256.9 1624.1 197.1 eil51 511.2 738.2 1147.4 190.7 614 963.5 1450.8 260.7 497.2 771.2 1195.1 243.6 491.9 772.6 1186 245.7 eli76 721.8 1036.2 1457.1 226.1 1035.6 1460.9 2151.2 331.4 771.2 1082.3 1640.5 280.4 760 1087 1610.3 285.4 gr96 862 1355.4 2026.5 348.6 1291.9 1972.6 2968.2 519.3 911.3 1396.9 2260.3 405.3 900.2 1396.4 2257.7 421.3 kroa150 70880 89392 121337 14485 91575 124442 164472 18229 62801 78955 104886 8744 60914 77017 93631 7330 kroa200 99818 121945 164443 16620 136530 172730 223643 23919 90234 110421 145046 13832 86536 109347 141175 12517 kroB100 40570 57373 82441 11490 56782 83671 118140 17817 41476 54609 74861 10195 40070 54504 78913 10802 kroB150 69561 90636 122612 15676 98376 128704 171691 20984 62532 79664 93700 8023 63013 79136 97548 8422 kroB200 95106 119595 156774 15559 129137 170888 220721 25313 85875 111429 146582 13879 88753 111071 142722 12021 kroC100 40573 59920 90359 13754 61044 85942 128239 17762 37895 54879 77495 12239 40453 54072 78388 12654 kroD100 36251 57801 85497 12768 55413 85475 129610 19920 40864 56408 82342 12689 40074 56230 81408 12490 kroE100 42230 59632 84089 11448 59108 87720 128825 19932 41706 57851 80784 11665 39912 57714 85800 12747 lin105 30104 45726 71980 12090 41504 70560 107157 19321 30822 48377 79901 14521 30116 48700 77804 15158 lin318 212259 244247 307006 22524 271844 341953 447096 43659 182437 230828 311132 38487 183700 231180 318757 39493 mtsp100 42551 58361 87622 12581 57443 85849 123128 19325 42190 56268 81858 12583 39444 56187 83089 13184 mtsp150 84018 105130 139427 15595 110196 144405 184927 20654 76189 94674 115786 9230 76317 93618 118046 8784 mtsp51 524.7 744.9 1107.2 192.9 600.5 960.9 1436.8 265 514.1 771.5 1188 239.1 506.4 776.3 1198.2 241.1 pr124 150254 235652 346625 51913 244964 349702 507277 74210 133373 202203 298646 49945 134543 200514 296597 50491 pr136 225315 304074 428602 58108 300700 446351 634173 89691 223163 286062 383137 50634 200711 287362 390805 52720 pr144 205204 278907 414337 56813 289835 425899 587282 85838 194333 251995 327206 39986 198892 250551 323671 39774 pr152 279221 375123 530527 76952 380235 559885 790537 115996 207562 304803 409260 58957 217451 302093 403995 58259 pr226 465922 598166 796733 87652 645486 890751 1223229 146404 329781 488266 687780 83403 343841 489202 698623 85134 pr264 285262 373461 479017 37923 385908 527207 698832 78944 172047 230943 311573 33215 173869 230313 314209 36013 pr299 241958 295390 381982 33177 343357 432610 585709 60203 218292 272548 337654 28996 220328 272507 341877 27987 pr76 164907 249381 389365 73419 231932 363181 560341 107747 175830 268514 434977 84973 168656 269631 440088 88178 rat195 6740 8679 12038 1491 9573 12711 16873 2107 7200.4 8721.7 10212.1 884.8 7059.3 8739.1 10285.1 887.8 rat99 2149.2 3295.3 5008.3 913.2 3148 4989 7707 1417 2270 3672 5940 1198 2279 3651 5924 1221 rd400 82572 91903 104639 4786 101925 114910 135460 9463 53411 80713 117869 20490 53204 82324 119892 21221 st70 1023.9 1487.8 2264.9 372 1309.4 2163.9 3315.9 609.2 939.3 1594.3 2594 530.9 972.7 1606.4 2641.4 537 tsp225 13022 16756 22477 2559 18365 24630 32360 4086 13615 16592 20431 1548 13417 16775 20124 1553 Average 95930 126303 173878 21187 131434 182519 252133 33230 82825 112163 154056 19785 82557 112010 154332 20041