Addendum to the paper Heuristics for the multi-period orienteering problem with multiple time windows Fabien Tricoire, Martin Romauch, Karl F. Doerner and Richard F. Hartl Department of Business Administration, University of Vienna, Bruenner Strasse 72, 1210 Vienna, Austria
[email protected]
Abstract This is an addendum to the paper by Tricoire et al. on various orienteering problems [1]. We present experimental results on the orienteering problem with time windows (OPTW) and team orienteering problem with time windows (TOPTW) test instances introduced by Montemanni et al. [2].
Introduction The instances by Montemanni et al. [2] are separated into four classes, based on the number of vehicles available (1, 2, 3 or 4). For each instance we run the variable neighborhood search (VNS) presented in our previous paper [1] 10 times. We present for each instance the minimal, average and maximal profit found, as well as the average CPU time needed to reach a termination criterion. For the sake of clarity, we separate the experiment tables following the classes based on the number of vehicles. Our results are compared with those presented in [2] (Ant Colony System, ACS). For each instance, the best average value is boldfaced and the best value overall is in italics. Average CPU time needed to reach a termination criterion is also provided for each method (in seconds).
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Results with 1 vehicle Instance name c101 100 c102 100 c103 100 c104 100 c105 100 c106 100 c107 100 c108 100 c109 100 c201 100 c202 100 c203 100 c204 100 c205 100 c206 100 c207 100 c208 100 r101 100 r102 100 r103 100 r104 100 r105 100 r106 100 r107 100 r108 100 r109 100 r110 100 r111 100 r112 100 r201 100 r202 100 r203 100 r204 100 r205 100 r206 100 r207 100 r208 100 r209 100 r210 100 r211 100
Min 320 360 390 410 340 340 370 370 380 870 920 960 970 900 920 930 940 198 284 293 303 247 289 299 308 277 284 297 297 795 891 991 1068 951 1005 1040 1091 946 969 1019
VNS Avg Max 320 320 360 360 398 400 418 420 340 340 340 340 370 370 370 370 380 380 870 870 928 930 960 960 972 980 908 910 927 930 930 930 949 950 198 198 285.2 286 293 293 303 303 247 247 292.2 293 299 299 308 308 277 277 284 284 297 297 297.9 298 796.7 797 905.6 915 1007.9 1016 1076.3 1081 952.6 953 1014 1022 1061.5 1072 1101.5 1112 947.8 950 975.9 978 1024.2 1042
CPU(s) 72.233 102.231 106.156 124.336 87.066 86.66 88.738 99.327 118.72 507.791 454.779 614.327 484.033 645.442 616.542 599.532 558.891 49.888 77.919 90.162 95.937 85.392 89.56 105.459 119.081 77.416 85.996 95.389 96.959 1021.74 1057.47 1139.85 1253.45 745.102 1168.09 1065.3 1160.81 925.875 1065.6 1120.69
Min 320 360 400 420 340 340 370 370 380 870 930 960 970 900 920 920 940 198 286 292 303 247 293 293 303 277 282 295 295 795 895 983 1035 933 961 1016 1048 910 944 1002
ACS Avg Max 320.0 320 360.0 360 400.0 400 420.0 420 340.0 340 340.0 340 370.0 370 370.0 370 380.0 380 870.0 870 930.0 930 960.0 960 970.0 970 906.0 910 920.0 920 920.0 920 940.2 950 198.0 198 286.0 286 292.6 293 303.0 303 247.0 247 293.0 293 294.6 299 306.0 308 277.0 277 283.2 284 296.6 297 297.4 298 795.8 797 899.6 903 989.8 993 1046.4 1053 939.2 949 983.0 1008 1026.6 1035 1057.2 1071 923.4 938 956.4 970 1006.8 1016
CPU(s) 0.47 0.69 16.88 33.47 0.86 1.02 2.06 0.76 0.84 189.81 319.02 361.01 1617.48 28.19 87.86 48.50 89.01 0.05 11.11 640.63 164.00 3.01 86.31 922.61 696.10 27.98 617.57 484.37 947.06 2339.94 1724.42 2641.66 1549.15 1125.36 1671.45 1090.34 1260.93 1453.24 979.10 1288.08
Table 1: Comparison of VNS and ACS for m=1 (part 1).
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Instance name rc101 100 rc102 100 rc103 100 rc104 100 rc105 100 rc106 100 rc107 100 rc108 100 rc201 100 rc202 100 rc203 100 rc204 100 rc205 100 rc206 100 rc207 100 rc208 100 pr01 48 pr02 96 pr03 144 pr04 192 pr05 240 pr06 288 pr07 72 pr08 144 pr09 216 pr10 288 pr11 48 pr12 96 pr13 144 pr14 192 pr15 240 pr16 288 pr17 72 pr18 144 pr19 216 pr20 288
Min 219 266 266 301 244 252 277 288 795 904 967 1098 837 866 920 1025 308 403 374 480 579 585 293 431 466 561 323 442 438 542 652 622 356 504 537 642
VNS Avg Max 219 219 266 266 266 266 301 301 244 244 252 252 277 277 297 298 795 795 925.6 936 988.2 1003 1120.8 1136 845.9 857 878.4 895 960.8 983 1043.5 1053 308 308 403.9 404 390.5 394 488.1 489 586.1 595 588.2 590 297.5 298 452.2 463 481.5 493 575.5 594 328 330 442 442 453.7 461 550.1 567 663.2 678 637 674 358.3 359 519.4 535 551.6 562 647.8 662
CPU(s) 61.306 53.277 62.902 58.037 78.645 71.853 69.601 66.058 640.791 951.498 938.391 970.286 726.611 838.68 893.52 995.506 81.233 251.533 419.82 733.239 1663.22 1628.37 141.524 450.171 1079.14 1772.44 131.413 309.568 514.087 1163.79 1900.89 1854.1 140.537 760.862 1242.17 2441.9
Min 219 266 266 301 244 252 277 298 795 931 974 1079 844 881 954 1002 308 403 394 473 576 555 298 461 481 578 327 435 439 483 522 509 358 465 467 547
ACS Avg Max 219.0 219 266.0 266 266.0 266 301.0 301 244.0 244 252.0 252 277.0 277 298.0 298 795.0 795 931.6 932 976.6 979 1086.2 1107 848.4 855 884.0 888 960.8 967 1013.2 1040 308.0 308 403.8 404 394.0 394 482.6 485 576.8 577 564.6 567 298.0 298 462.6 463 481.8 482 588.4 591 327.8 328 436.4 437 441.0 442 494.0 501 524.8 528 517.8 525 358.0 358 488.8 504 475.0 480 552.4 556
CPU(s) 0.20 30.91 57.22 29.37 9.74 308.64 502.07 207.51 590.80 2545.89 1705.07 1353.17 1549.22 1776.39 1324.46 1511.37 256.23 1147.78 2024.26 1404.67 2075.65 2199.78 20.11 2475.96 2318.19 2343.51 1743.72 2017.56 2312.73 23.11 18.20 25.73 1330.85 1350.04 30.04 24.57
Table 2: Comparison of VNS and ACS for m=1 (part 2).
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Results with 2 vehicles Instance name c101 100 c102 100 c103 100 c104 100 c105 100 c106 100 c107 100 c108 100 c109 100 c201 100 c202 100 c203 100 c204 100 c205 100 c206 100 c207 100 c208 100 r101 100 r102 100 r103 100 r104 100 r105 100 r106 100 r107 100 r108 100 r109 100 r110 100 r111 100 r112 100 r201 100 r202 100 r203 100 r204 100 r205 100 r206 100 r207 100 r208 100 r209 100 r210 100 r211 100
Min 580 650 710 750 640 620 660 680 710 1440 1450 1470 1480 1450 1460 1460 1470 349 494 487 527 438 509 521 529 505 500 530 520 1219 1329 1396 1449 1351 1408 1449 1458 1377 1399 1457
VNS Avg Max 587 590 653 660 717 720 759 760 640 640 620 620 669 670 680 680 719 720 1447 1450 1457 1460 1471 1480 1480 1480 1457 1460 1464 1470 1469 1480 1473 1480 349 349 498.5 508 515.4 522 542.5 549 451.5 453 518.1 529 529 535 547.3 555 505 505 509.4 525 537.4 544 535.2 544 1232.1 1250 1333.5 1338 1402.7 1407 1455.3 1458 1366.8 1378 1422.4 1427 1453.6 1458 1458 1458 1393 1405 1408.6 1423 1457 1457
CPU(s) 83.843 99.998 93.826 96.722 68.922 95.799 92.477 89.654 70.622 634.542 658.727 568.858 420.318 593.423 509.432 496.59 483.286 35.313 64.1 51.01 66.878 66.835 66.389 73.924 63.685 66.252 62.49 71.447 73.197 1401.57 1421.47 1148.43 785.18 1275.97 1015.91 723.189 448.686 1076 911.973 957.45
Min 580 660 710 750 640 620 670 680 720 1450 1440 1440 1430 1450 1460 1450 1460 349 505 517 538 453 515 526 548 505 523 533 539 1231 1288 1341 1397 1336 1367 1367 1416 1344 1351 1396
ACS Avg Max 588 590 660 660 710 710 754 760 640 640 620 620 670 670 680 680 720 720 1452 1460 1446 1460 1446 1460 1436 1440 1452 1460 1460 1460 1452 1460 1462 1470 349 349 506.6 508 518.8 520 540 544 453 453 523.8 529 527.4 529 553.6 556 505.4 506 523.4 525 535.6 538 541.6 543 1236 1239 1298.6 1310 1349.4 1358 1399 1404 1342 1346 1373.8 1381 1385 1400 1425.4 1433 1350.6 1361 1355.4 1360 1403 1411
CPU(s) 110.83 1427.36 938.86 1355.04 1436.61 104.61 76.02 95.34 1817.29 508.59 1568.22 2334.8 1373.22 925.37 1876.39 1433.98 1164.2 36.48 2006.59 1095.06 2291.8 1037.28 2034.73 2357.58 1906.24 1386.61 1180.21 1726.17 1653.61 2693.58 2482.22 3057.4 2713.46 2593.74 2954.37 2624.08 2828.88 2988.88 2423.89 2726.1
Table 3: Comparison of VNS and ACS for m=2 (part 1).
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Instance name rc101 100 rc102 100 rc103 100 rc104 100 rc105 100 rc106 100 rc107 100 rc108 100 rc201 100 rc202 100 rc203 100 rc204 100 rc205 100 rc206 100 rc207 100 rc208 100 pr01 48 pr02 96 pr03 144 pr04 192 pr05 240 pr06 288 pr07 72 pr08 144 pr09 216 pr10 288 pr11 48 pr12 96 pr13 144 pr14 192 pr15 240 pr16 288 pr17 72 pr18 144 pr19 216 pr20 288
Min 419 504 512 564 478 460 482 519 1335 1464 1556 1704 1425 1507 1542 1662 471 671 693 888 1041 982 537 770 800 1015 526 722 783 948 1120 1163 634 888 946 1142
VNS Avg Max 419 419 504.1 505 519 524 568.2 575 479.8 480 477.9 483 519.3 534 535.8 556 1359.7 1368 1487.6 1500 1593.4 1621 1710.2 1716 1436.3 1455 1523.4 1546 1552.2 1566 1676.1 1691 487.3 502 696.9 713 715.3 742 906.4 924 1064.8 1088 1004.4 1036 550.1 566 799.6 821 855.7 900 1067.6 1114 537.8 544 747 761 801.3 831 990.6 1017 1182.4 1212 1192.5 1209 646.1 652 904 938 970.5 995 1173.1 1223
CPU(s) 54.85 61.085 53.138 53.011 45.287 57.488 63.223 53.2 897.132 909.147 821.005 740.817 766.84 769.636 835.862 698.199 80.123 216.045 355.992 578.511 982.655 932.909 130.037 344.652 608.516 1018.85 91.809 233.76 334.402 724.972 1019.14 1191.96 127.962 416.741 819.465 1227.58
Min 427 494 506 565 478 480 526 531 1354 1457 1523 1608 1405 1473 1501 1587 502 702 727 877 1016 977 566 808 851 1053 544 759 788 936 1090 1089 635 874 932 1102
ACS Avg Max 427 427 497.2 505 510.2 516 568.8 575 478.4 480 480.2 481 530.2 534 541.6 550 1365.4 1376 1464.8 1472 1542.2 1573 1614.8 1622 1417.4 1428 1495.6 1514 1523 1544 1608.4 1646 502 502 705.2 714 731.4 740 883.6 899 1021.8 1034 987.6 995 566 566 813 819 862 880 1064.6 1078 544.8 547 763.4 768 798.8 816 943.6 952 1100 1120 1101 1119 646.2 652 888.4 907 940.8 950 1113 1122
CPU(s) 27.9 1496.91 1965.91 2381.26 1676.74 1865.07 771.48 820.99 1654.27 2619.56 2176.18 2561.77 2115.17 2105.05 2937.45 2572.3 602.21 1017.6 2083.02 2439.32 2278.5 1724.14 972.26 1729.99 3130.95 2918.58 880.3 2706.06 3240.72 2100.7 3188.79 2833.99 1378 1960.26 2366.93 3192.33
Table 4: Comparison of VNS and ACS for m=2 (part 2).
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Results with 3 vehicles Instance name c101 100 c102 100 c103 100 c104 100 c105 100 c106 100 c107 100 c108 100 c109 100 c201 100 c202 100 c203 100 c204 100 c205 100 c206 100 c207 100 c208 100 r101 100 r102 100 r103 100 r104 100 r105 100 r106 100 r107 100 r108 100 r109 100 r110 100 r111 100 r112 100 r201 100 r202 100 r203 100 r204 100 r205 100 r206 100 r207 100 r208 100 r209 100 r210 100 r211 100
Min 810 890 960 1010 850 850 890 910 960 1810 1810 1810 1810 1800 1810 1810 1810 477 677 706 742 615 694 745 745 685 698 742 741 1418 1443 1458 1458 1458 1458 1458 1458 1458 1458 1458
VNS Avg Max 810 810 916 920 972 980 1020 1030 858 870 867 870 905 910 913 920 967 970 1810 1810 1810 1810 1810 1810 1810 1810 1809 1810 1810 1810 1810 1810 1810 1810 482.3 484 681.7 685 726.6 747 759.7 777 619.2 620 717.4 726 755.8 760 781.2 797 703.9 709 721.9 737 763.4 773 760 771 1428.2 1436 1453.7 1458 1458 1458 1458 1458 1458 1458 1458 1458 1458 1458 1458 1458 1458 1458 1458 1458 1458 1458
CPU(s) 67.044 89.259 91.436 78.868 93.845 89.524 91.782 85.318 82.299 256.494 321.468 185.431 201.605 236.613 265.853 233.261 231.793 42.927 66.854 61.215 60.219 52.743 65.706 60.685 70.884 64.022 63.501 64.989 69.191 814.379 519.729 257.263 211.654 296.275 240.273 220.092 216.57 271.951 289.889 200.128
Min 810 910 960 990 870 870 910 910 950 1810 1780 1710 1750 1790 1780 1780 1780 481 674 726 750 619 708 748 777 695 722 718 750 1424 1441 1443 1458 1449 1455 1458 1458 1455 1454 1457
ACS Avg Max 810 810 918 920 972 980 1004 1020 870 870 870 870 910 910 912 920 954 970 1810 1810 1784 1790 1738 1760 1758 1770 1796 1800 1788 1800 1784 1790 1786 1800 481 481 682 691 729.8 736 760.6 773 619.2 620 715 722 751.6 757 781.8 790 701.8 710 732.6 737 755.4 770 758.8 769 1428.4 1432 1445.6 1449 1452.4 1456 1458 1458 1454.8 1458 1456.8 1458 1458 1458 1458 1458 1456.8 1458 1456.2 1458 1457.8 1458
CPU(s) 1515.58 442.8 1415.3 681.7 1010.01 1132.31 892.65 971.24 1327.54 259.2 1603.23 1039.94 1025.8 2007.29 1861.98 1222.95 1542.72 240.56 2435.4 2694.89 2531.35 795.97 755.45 1998.89 2388.53 1098.83 1708.47 1286.72 2091.22 1399.97 1966.22 2564.33 174.66 1830.71 1328.82 598.63 425.64 1163.74 1428.08 7.33
Table 5: Comparison of VNS and ACS for m=3 (part 1).
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Instance name rc101 100 rc102 100 rc103 100 rc104 100 rc105 100 rc106 100 rc107 100 rc108 100 rc201 100 rc202 100 rc203 100 rc204 100 rc205 100 rc206 100 rc207 100 rc208 100 pr01 48 pr02 96 pr03 144 pr04 192 pr05 240 pr06 288 pr07 72 pr08 144 pr09 216 pr10 288 pr11 48 pr12 96 pr13 144 pr14 192 pr15 240 pr16 288 pr17 72 pr18 144 pr19 216 pr20 288
Min 609 708 742 790 670 645 719 749 1679 1705 1724 1724 1690 1724 1724 1724 603 899 961 1243 1405 1392 722 1064 1136 1454 640 975 1040 1286 1573 1594 803 1200 1288 1579
VNS Avg Max 619.8 621 710.3 711 746.5 747 824.5 833 677.2 682 686.2 705 761.6 773 778 795 1689.4 1698 1711.6 1719 1724 1724 1724 1724 1696.7 1709 1724 1724 1724 1724 1724 1724 613.5 619 919.2 937 983.6 1003 1261.9 1280 1441.1 1459 1411.4 1449 730.2 738 1089 1113 1190.8 1275 1493.3 1520 649.6 654 982.2 988 1081.3 1111 1318.7 1343 1597.1 1619 1615.8 1635 824.3 830 1220.4 1242 1339.1 1378 1640.2 1682
CPU(s) 58.725 60.425 67.295 59.794 63.848 49.726 58.209 66.932 786.637 491.159 313.913 222.804 573.162 339.855 295.073 209.461 79.172 205.958 330.616 592.894 779.262 844.674 136.105 297.507 542.348 923.496 58.522 194.754 309.534 549.835 885.034 1035.33 114.461 326.307 630.904 1070.14
Min 618 695 735 793 669 688 742 757 1663 1690 1714 1721 1656 1699 1702 1721 619 935 984 1220 1379 1345 735 1112 1203 1418 649 960 1080 1252 1455 1461 T 1174 1289 1484
ACS Avg Max 620.4 621 698.8 710 741.4 747 813.2 823 677.8 682 692.4 695 748 755 768.2 783 1672 1681 1701.4 1706 1719.6 1724 1722.2 1724 1672.2 1698 1712.6 1722 1714.8 1722 1722.2 1724 619 619 938.4 942 991 999 1226.4 1243 1386.6 1417 1359 1370 738.4 744 1115 1118 1210 1227 1457.2 1492 649 649 970.6 985 1088.8 1101 1258.6 1263 1486.8 1509 1481.8 1516 821 822.6 1209 1229 1299.4 1320 1491.2 1505
CPU(s) 195.67 1145.53 2753.95 2276.97 1092.01 1748.26 1158.45 1443.67 1084.91 2230.74 1213.17 1261.26 1439.79 2185.22 2553.89 893.85 116.95 2333.11 876.82 2909.04 2746.66 2719.67 1330.57 2544.33 3187.73 2873.12 237.25 2883.74 2515.51 2084.66 2671.82 2284.53 832 2854.33 3094.8 2822.96
Table 6: Comparison of VNS and ACS for m=3 (part 2).
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Results with 4 vehicles Instance name c101 100 c102 100 c103 100 c104 100 c105 100 c106 100 c107 100 c108 100 c109 100 c201 100 c202 100 c203 100 c204 100 c205 100 c206 100 c207 100 c208 100 r101 100 r102 100 r103 100 r104 100 r105 100 r106 100 r107 100 r108 100 r109 100 r110 100 r111 100 r112 100 r201 100 r202 100 r203 100 r204 100 r205 100 r206 100 r207 100 r208 100 r209 100 r210 100 r211 100
Min 1010 1130 1160 1240 1050 1050 1090 1120 1160 1810 1810 1810 1810 1810 1810 1810 1810 606 817 890 924 761 847 924 944 857 883 913 953 1458 1458 1458 1458 1458 1458 1458 1458 1458 1458 1458
VNS Avg Max 1013 1020 1139 1150 1180 1190 1248 1260 1055 1060 1062 1080 1108 1120 1123 1130 1174 1190 1810 1810 1810 1810 1810 1810 1810 1810 1810 1810 1810 1810 1810 1810 1810 1810 610.2 611 828.4 840 909.9 921 954.8 972 768 778 890.9 905 930.4 938 973.2 988 870.5 884 898.1 914 936.6 949 964.4 971 1458 1458 1458 1458 1458 1458 1458 1458 1458 1458 1458 1458 1458 1458 1458 1458 1458 1458 1458 1458 1458 1458
CPU(s) 78.506 90.127 93.787 79.712 84.965 82.208 83.302 70.364 73.822 92.455 114.766 84.729 106.996 106.642 109.28 114.951 108.425 40.409 59.381 68.843 62.876 62.501 63.664 62.605 60.414 55.278 70.703 63.83 63.559 294.588 171.477 137.318 135.906 153.578 131.918 111.936 126.952 138.961 140.924 114.599
Min 1010 1140 1180 1220 1050 1050 1110 1110 1160 1810 1810 1810 1810 1810 1810 1760 1810 608 817 893 931 761 885 930 964 873 886 916 940 1458 1458 1458 1458 1458 1458 1458 1458 1458 1458 1458
ACS Avg Max 1018 1020 1142 1150 1186 1190 1226 1240 1052 1060 1058 1070 1114 1120 1112 1120 1172 1190 1810 1810 1810 1810 1810 1810 1810 1810 1810 1810 1810 1810 1800 1810 1810 1810 608 608 825.6 836 902.2 909 944.2 957 766 771 889.8 893 932.4 937 976.2 994 876.6 879 900 908 932.4 944 947.6 954 1458 1458 1458 1458 1458 1458 1458 1458 1458 1458 1458 1458 1458 1458 1458 1458 1458 1458 1458 1458 1458 1458
CPU(s) 1049.07 1211.26 2329.56 1493.94 716.48 556.8 411.26 820.09 915.97 1.15 8.87 43.9 1.31 0.25 0.13 5.8 0.15 55.13 1924.54 2622.17 2343.92 838.47 929.5 2660.9 2596.16 1374.46 926.27 1896.35 1662.61 376.41 936.24 73.92 0.01 1.31 0.01 0 0.01 0 3.13 0
Table 7: Comparison of VNS and ACS for m=4 (part 1).
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Instance name rc101 100 rc102 100 rc103 100 rc104 100 rc105 100 rc106 100 rc107 100 rc108 100 rc201 100 rc202 100 rc203 100 rc204 100 rc205 100 rc206 100 rc207 100 rc208 100 pr01 48 pr02 96 pr03 144 pr04 192 pr05 240 pr06 288 pr07 72 pr08 144 pr09 216 pr10 288 pr11 48 pr12 96 pr13 144 pr14 192 pr15 240 pr16 288 pr17 72 pr18 144 pr19 216 pr20 288
Min 753 889 937 1017 851 850 929 977 1724 1724 1724 1724 1724 1724 1724 1724 654 1047 1161 1478 1762 1767 838 1314 1438 1813 657 1107 1268 1599 1907 1914 919 1455 1614 1975
VNS Avg Max 777.2 811 893.4 902 945.4 950 1033.5 1059 859 875 894.4 909 958 980 1011.5 1025 1724 1724 1724 1724 1724 1724 1724 1724 1724 1724 1724 1724 1724 1724 1724 1724 656.4 657 1057.8 1070 1195.2 1215 1502.1 1530 1775.9 1799 1798.1 1829 849 860 1336.3 1371 1492.4 1558 1855 1887 657 657 1117.6 1132 1302.6 1320 1612.9 1625 1934 1958 1968.9 2016 924.7 930 1485.5 1510 1659.8 1695 1988.3 2008
CPU(s) 55.283 66.996 64.053 64.779 53.646 49.604 53.812 59.561 231.943 208.783 157.521 120.277 192.924 145.535 135.133 124.326 50.094 196.257 271.034 436.047 653.667 782.665 97.779 268.511 475.345 800.31 28.014 143.723 250.641 423.473 690.019 824.461 78.869 255.136 523.325 862.423
Min 801 896 937 982 860 888 952 995 1724 1724 1724 1724 1724 1722 1722 1724 654 1063 1190 1503 1710 1709 860 1337 1544 1813 657 1110 1303 1521 1800 1833 923 1455 1567 1811
ACS Avg Max 805.4 808 899.4 903 941.8 948 1013.2 1052 867.2 875 901.4 908 959.2 964 1000.2 1007 1724 1724 1724 1724 1724 1724 1724 1724 1724 1724 1723.6 1724 1722.4 1724 1724 1724 655.2 657 1067.8 1072 1204.6 1222 1506 1515 1722.2 1740 1723.5 1740 865.4 872 1351.6 1376 1554.2 1561 1819.8 1827 657 657 1114 1118 1316.4 1329 1534.4 1568 1822.8 1854 1867.2 1887 923.8 925 1464.8 1470 1579.4 1596 1821.4 1841
CPU(s) 1324.33 2218.81 2005.21 2139.3 1052.3 2106.67 1763.11 2222.29 2327.4 1095.77 308.58 53.33 1313.73 2.79 72.12 0 15.43 2164.96 2073.95 2986.02 2818.47 2935.83 1940.19 2804.25 3371.92 3365.93 0.09 2486.72 2926.28 2730.2 2631.27 2614.66 2749.67 3209.13 3293.94 3193.02
Table 8: Comparison of VNS and ACS for m=4 (part 2).
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References [1] F. Tricoire, M. Romauch, K.F. Doerner and R.F. Hartl. Heuristics for the multi-period orienteering problem with multiple time windows. Computers & Operations Research, 37 : 351-367, 2010. [2] R. Montemanni and L.M. Gambardella. Ant Colony System for Team Orienteering Problems with Time Windows. Foundations of Computing and Decision Sciences, 34 : 287306, 2009.
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