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Table 1 Results on the OPTW test instances

From: Iterated local search algorithm for solving the orienteering problem with soft time windows

Instance-n BKS I3CH ABC VNS ILS
Profit Gap (%) CPU (s) Profit Gap (%) CPU (s) Profit Gap (%) CPU (s) Profit Gap (%) CPU (s)
C101-100 320 320 0.0 21.8 320 0.0 0.4 320 0.0 72.2 320 0.0 0.2
C102-100 360 360 0.0 28.1 360 0.0 0.6 360 0.0 102.2 360 0.0 0.3
C103-100 400 400 0.0 27.1 398 0.5 3.6 398 0.5 106.2 400 0.0 0.2
C104-100 420 420 0.0 27.1 420 0.0 15.2 418 0.5 124.3 420 0.0 0.4
C105-100 340 340 0.0 23.4 340 0.0 0.5 340 0.0 87.1 340 0.0 0.4
C106-100 340 340 0.0 23.6 340 0.0 0.5 340 0.0 86.7 340 0.0 0.5
C107-100 370 370 0.0 24.7 370 0.0 1.3 370 0.0 88.7 370 0.0 0.1
C108-100 370 370 0.0 24.8 370 0.0 0.9 370 0.0 99.3 370 0.0 0.5
C109-100 380 380 0.0 26.3 380 0.0 0.5 380 0.0 118.7 380 0.0 6.8
Avg 0.0 25.2   0.1 2.6   0.1 98.4   0.0 1.0
R101-100 198 198 0.0 20.4 190.0 4.2 0.3 198.0 0.0 49.9 198 0.0 0.1
R102-100 286 286 0.0 29.3 281.6 1.6 2.2 285.2 0.3 77.9 286 0.0 0.2
R103-100 293 293 0.0 28.8 292.0 0.3 1.1 293.0 0.0 90.2 293 0.0 1.4
R104-100 303 298 1.7 27.3 299.6 1.1 1.7 303.0 0.0 95.9 303 0.0 1.5
R105-100 247 247 0.0 26.0 242.6 1.8 9.1 247.0 0.0 85.4 247 0.0 0.7
R106-100 293 293 0.0 29.4 289.0 1.4 1.6 292.2 0.3 89.6 293 0.0 0.2
R107-100 299 297 0.7 27.8 299.0 0.0 7.1 299.0 0.0 105.5 299 0.0 0.5
R108-100 308 306 0.7 29.7 308.0 0.0 4.6 308 0.0 119.1 308 0.0 0.9
R109-100 277 277 0.0 31.1 277.0 0.0 1.6 277.0 0.0 77.4 277 0.0 0.2
R110-100 284 284 0.0 33.9 282.2 0.6 8.1 284.0 0.0 86.0 284 0.0 1.3
R111-100 297 295 0.7 27.7 294.0 1.0 1.7 297.0 0.0 95.4 297 0.0 10.9
R112-100 298 289 3.1 32.0 297.0 0.3 2.4 297.9 0.0 97.0 298 0.0 3.3
Avg 0.6 28.6   1.0 3.5   0.1 89.1   0.0 1.8
RC101-100 219 219 0.0 21.8 219 0.0 0.5 219 0.0 61.2 219 0.0 0.2
RC102-100 266 266 0.0 25.5 266 0.0 0.6 266 0.0 54.7 266 0.0 0.4
RC103-100 266 266 0.0 27.1 266 0.0 10.7 266 0.0 69.2 266 0.0 2.0
RC104-100 301 301 0.0 27.2 301 0.0 20.3 301 0.0 62.5 301 0.0 0.3
RC105-100 244 244 0.0 26.4 244 0.0 1.3 244 0.0 65.2 244 0.0 4.3
RC106-100 252 250 0.8 25.0 251.4 0.2 8.1 252 0.0 67.4 252 0.0 0.3
RC107-100 277 274 1.1 26.3 276.2 0.3 10.4 277 0.0 72.4 277 0.0 0.3
RC108-100 298 264 12.9 25.1 298 0.0 11.3 298 0.0 71.5 298 0.0 0.1
Avg 1.9 25.6   0.1 7.9   0.0 65.5   0.0 1.0
PR01-48 308 305 1.0 20.8 307 0.3 5.8 308 0.0 77.9
PR02-96 404 394 2.5 47.9 391.2 3.2 4.9 403.9 0.0 244.6
PR03-144 394 394 0.0 72.9 394 0.0 12.6 390.5 0.9 387.2
PR04-192 489 489 0.0 109.3 486 0.6 67.4 488.1 0.2 541.6
PR05-240 595 594 0.2 185.4 586.8 1.4 91.4 586.1 1.5 1455.2
PR06-288 591 590 0.2 189.9 573.6 2.9 247.4 588.2 0.5 1633.8
PR07-72 298 298 0.0 26.5 298 0.0 4.3 297.5 0.2 131.0
PR08-144 463 454 1.9 77.4 462 0.2 15.0 452.2 2.3 514.1
PR09-216 493 490 0.6 137.8 481.8 2.3 126.3 481.5 2.3 920.8
PR10-288 594 568 4.4 222.2 570.4 4.0 210.3 575.5 3.1 1534.1
Avg 1.1 109.0   1.5 78.5   1.1 744.0    
C201-100 870 870 0.0 70.1 870 0.0 11.2 870 0.0 507.8 870 0.0 36.7
C202-100 930 930 0.0 87.6 930 0.0 15.3 928 0.2 454.8 930 0.0 59.0
C203-100 960 960 0.0 92.3 958 0.2 14.8 960 0.0 614.3 960 0.0 137.2
C204-100 980 970 1.0 117.4 966 1.4 25.7 972 0.8 484 974 0.6 217.6
C205-100 910 900 1.1 70.7 900 1.1 1.7 908 0.2 645.4 908 0.2 56.2
C206-100 930 920 1.1 75.7 928 0.2 6.2 927 0.3 616.5 927 0.3 111.5
C207-100 930 930 0.0 77.4 918 1.3 2.3 930 0.0 599.5 930 0.0 68.1
C208-100 950 950 0.0 84.0 950 0.0 11.8 949 0.1 558.9 950 0.0 33.3
Avg 0.4 84.4   0.5 11.1   0.2 560.2   0.1 90.0
R201-100 797 789 1.0 101.8 787 1.3 20.3 796.7 0.0 1021.7 788.7 1.0 133.7
R202-100 930 930 0.0 175.6 895.8 3.7 40.6 905.6 2.6 1057.5 910.3 2.1 165.6
R203-100 1028 1020 0.8 221.4 1009 1.8 25.6 1007.9 2.0 1139.9 1011.3 1.6 213.5
R204-100 1093 1073 1.8 236.9 1070.4 2.1 34.0 1076.3 1.5 1253.5 1082.8 0.9 171.0
R205-100 953 946 0.7 129.3 953 0.0 32.9 952.6 0.0 745.1 948.4 0.5 169.9
R206-100 1032 1021 1.1 169.3 1018 1.4 21.3 1014 1.7 1168.1 1012.4 1.9 126.5
R207-100 1077 1050 2.5 192.8 1060.8 1.5 20.9 1061.5 1.4 1065.3 1059.5 1.6 174.0
R208-100 1117 1092 2.2 230.0 1084.6 2.9 26.7 1101.5 1.4 1160.8 1107.6 0.8 165.6
R209-100 959 948 1.1 136.5 934.6 2.5 26.3 947.8 1.2 925.9 949.7 1.0 145.8
R210-100 991 982 0.9 176.9 965.4 2.6 29.3 975.9 1.5 1065.6 970.8 2.0 171.8
R211-100 1051 1013 3.6 167.4 1019 3.0 15.0 1024.2 2.5 1120.7 1040.4 1.0 145.7
Avg 1.4 176.2   2.1 26.6   1.4 1065.8   1.3 162.1
RC201-100 795 795 0.0 80.9 784 1.4 24.9 795 0.0 640.8 795 0.0 63.5
RC202-100 938 924 1.5 129.3 926.8 1.2 27.3 925.6 1.3 951.5 929 1.0 156.2
RC203-100 1003 966 3.7 134.3 962.4 4.0 24.8 988.2 1.5 938.4 989.8 1.3 111.5
RC204-100 1140 1093 4.1 167.5 1109.2 2.7 23.4 1120.8 1.7 970.3 1131.3 0.8 165.0
RC205-100 859 847 1.4 99.2 852.3 0.8 27.2 845.9 1.5 726.6 854.7 0.5 100.5
RC206-100 899 863 4.0 98.4 890.2 1.0 24.9 878.4 2.3 838.7 894.1 0.5 152.0
RC207-100 983 957 2.6 122.0 977.0 0.6 15.8 960.8 2.3 893.5 952.1 3.1 129.9
RC208-100 1057 1003 5.1 123.0 1032.8 2.3 26.3 1043.5 1.3 995.5 1040.7 1.5 85.6
Avg 2.8 119.3   1.8 24.3   1.5 869.4   1.1 120.5
PR11-48 353 353 0.0 30.8 350.6 0.7 1.7 328 7.1 131.4
PR12-96 442 433 2.0 59.8 432 2.3 23.5 442 0.0 309.6
PR13-144 467 466 0.2 89.5 458.1 1.9 8.9 453.7 2.8 514.1
PR14-192 567 521 8.1 144.4 560.1 1.2 76.6 550.1 3.0 1163.8
PR15-240 708 707 0.1 248.2 666.4 5.9 274.6 663.2 6.3 1900.9
PR16-288 674 619 8.2 228.6 613.4 9.0 205.1 637 5.5 1854.1
PR17-72 362 360 0.6 34.7 359 0.8 6.6 358.3 1.0 140.5
PR18-144 539 497 7.8 99.0 535 0.7 22.1 519.4 3.6 760.9
PR19-216 562 538 4.3 164.6 541 3.7 70.7 551.6 1.9 1242.2
PR20-288 667 588 11.8 202.7 604.8 9.3 346.9 647.8 2.9 2441.9
Avg 4.3 130.2   3.6 103.7   3.4 1045.9    
Instance-n BKS ACS GVNS GRASP-ELS SSA
Profit Gap (%) CPU (s) Profit Gap (%) CPU (s) Profit Gap (%) CPU (s) Profit Gap (%) CPU (s)
C101-100 320 320 0.0 0.5 320 0.0 0.2 320 0.0 1.2 320 0.0 20.4
C102-100 360 360 0.0 0.7 360 0.0 67.4 360 0.0 16.5 360 0.0 20.7
C103-100 400 400 0.0 16.9 396 1.0 382.4 400 0.0 38.5 400 0.0 24.2
C104-100 420 420 0.0 33.5 410 2.4 1005.9 420 0.0 105.2 420 0.0 21.9
C105-100 340 340 0.0 0.9 340 0.0 3.3 340 0.0 2.3 340 0.0 20.6
C106-100 340 340 0.0 1.0 340 0.0 6.5 340 0.0 3.8 340 0.0 20.3
C107-100 370 370 0.0 2.1 358 3.4 0.7 370 0.0 3.7 370 0.0 20.5
C108-100 370 370 0.0 0.8 354 4.5 1.1 370 0.0 6.6 370 0.0 20.5
C109-100 380 380 0.0 0.8 380 0.0 30.6 380 0.0 25.5 380 0.0 20.5
Avg 0.0 6.4   1.3 166.5   0.0 22.6   0.0 21.1
R101-100 198 198 0.0 0.1 197 0.5 0.2 198 0.0 0.9 198 0.0 19.7
R102-100 286 286 0.0 11.1 274.8 4.1 13.4 286 0.0 2.3 286 0.0 21
R103-100 293 292.6 0.1 640.6 286 2.4 33.8 290.4 0.9 4.8 293 0.0 20.3
R104-100 303 303 0.0 164.0 298.6 1.5 72.7 302.8 0.1 5.1 303 0.0 23.2
R105-100 247 247 0.0 3.0 230.6 7.1 0.3 247 0.0 1.2 247 0.0 20.3
R106-100 293 293 0.0 86.3 280.4 4.5 19.1 293 0.0 3.3 293 0.0 22.1
R107-100 299 294.6 1.5 922.6 287.2 4.1 50.3 296.4 0.9 4.8 297 0.7 21.5
R108-100 308 306 0.7 696.1 301.4 2.2 50.1 306.8 0.4 5.0 306 0.7 40.6
R109-100 277 277 0.0 28.0 276.4 0.2 10.4 277 0.0 2.7 277 0.0 20.4
R110-100 284 283.2 0.3 617.6 279.2 1.7 16.8 283.6 0.1 2.8 284 0.0 20.8
R111-100 297 296.6 0.1 484.4 290.6 2.2 54.2 297 0.0 4.6 297 0.0 27.9
R112-100 298 297.4 0.2 947.1 289.6 2.9 31.9 297.2 0.3 4.6 298 0.0 22.3
Avg 0.2 383.4   2.8 29.4   0.2 3.5   0.1 23.3
RC101-100 219 219 0.0 0.2 219 0.0 2.1 219 0.0 0.6 219 0.0 19.8
RC102-100 266 266 0.0 30.9 246 8.1 5.8 259 2.7 2.1 266 0.0 20.2
RC103-100 266 266 0.0 57.2 253.2 5.1 23.3 265.2 0.3 2.7 266 0.0 20.7
RC104-100 301 301 0.0 29.4 301 0.0 16.2 300.2 0.3 3.1 301 0.0 27.5
RC105-100 244 244 0.0 9.7 227 7.5 2.7 244 0.0 1.4 244 0.0 20.3
RC106-100 252 252 0.0 308.6 252 0.0 2.2 252 0.0 1.2 252 0.0 21
RC107-100 277 277 0.0 502.1 261.2 6.0 15.7 277 0.0 1.9 277 0.0 22
RC108-100 298 298 0.0 207.5 288.8 3.2 10.4 298 0.0 2.9 298 0.0 26
Avg 0.0 143.2   3.7 9.8   0.4 2.0   0.0 22.2
PR01-48 308 308 0.0 256.2 307.2 0.3 1.2 308 0.0 1.2 305 1.0 8.3
PR02-96 404 403.8 0.0 1147.8 403.6 0.1 3.7 402.6 0.3 3.0 404 0.0 29.1
PR03-144 394 394 0.0 2024.7 388 1.5 4.1 394 0.0 3.1 394 0.0 59.9
PR04-192 489 482.6 1.3 1404.7 475.4 2.8 14.7 474.6 2.9 5.3 489 0.0 106.7
PR05-240 595 576.8 3.1 2075.7 578 2.9 20.5 581 2.4 9.1 589 1.0 281.7
PR06-288 591 564.6 4.5 2199.8 584.2 1.2 29.0 583.4 1.3 8.6 575 2.7 253.4
PR07-72 298 298 0.0 20.1 297 0.3 1.7 294.4 1.2 1.6 298 0.0 15.0
PR08-144 463 462.6 0.1 2476.0 463 0.0 3.8 462.8 0.0 3.3 462 0.2 76.0
PR09-216 493 481.8 2.3 2318.2 482 2.2 12.3 477.8 3.1 7.0 482 2.2 102.3
PR10-288 594 588.4 0.9 2343.5 564.4 5.0 32.7 574.2 3.3 8.1 578 2.7 189.7
Avg 1.2 1626.7   1.6 12.4   1.5 5.0   1.0 112.2
C201-100 870 870 0.0 189.8 850 2.3 0.1 870 0.0 2.5 870 0.0 28.3
C202-100 930 930 0.0 319.0 916 1.5 78.7 910 2.2 20.4 930 0.0 33.5
C203-100 960 960 0.0 361.0 956 0.4 329 960 0.0 45.2 960 0.0 59.6
C204-100 980 970 1.0 1617.5 966 1.4 974 970 1.0 130.3 970 1.0 42.3
C205-100 910 906 0.4 28.2 898 1.3 12.5 906 0.4 10.6 910 0.0 46.9
C206-100 930 920 1.1 87.9 922 0.9 34.4 926 0.4 13.4 930 0.0 29
C207-100 930 920 1.1 48.5 928 0.2 36.3 930 0.0 17.3 930 0.0 29.1
C208-100 950 940.2 1.0 89.0 942 0.8 74.2 942 0.8 17.7 950 0.0 31.2
Avg 0.6 342.6   1.1 192.4   0.6 32.2   0.1 37.5
R201-100 797 795.8 0.2 2339.9 775.6 2.7 6.7 788.2 1.1 5.3 794 0.4 51.1
R202-100 930 899.6 3.3 1724.4 881.4 5.2 13.4 909.8 2.2 9.6 914 1.7 46.4
R203-100 1028 989.9 3.7 2641.7 992.2 3.5 34.7 1001.4 2.6 12.6 997 3.0 44.2
R204-100 1093 1046.4 4.3 1549.1 1073.8 1.8 77.6 1071.8 1.9 15.2 1058 3.2 39.7
R205-100 953 939.2 1.4 1125.4 905.8 5.0 15.3 927.2 2.7 7.8 946 0.7 37.8
R206-100 1032 983.0 4.7 1671.4 966.6 6.3 34.9 1023.6 0.8 10.7 1020 1.2 40.9
R207-100 1077 1026.6 4.7 1090.3 1022 5.1 46.6 1049.2 2.6 13.5 1069 0.7 52.5
R208-100 1117 1057.2 5.4 1260.9 1083.6 3.0 52.9 1100.2 1.5 15.9 1079 3.4 35.8
R209-100 959 923.4 3.7 1453.2 926 3.4 37.3 937.4 2.3 10.3 945 1.5 61.6
R210-100 991 956.4 3.5 979.1 961.4 3.0 30.1 969 2.2 10.8 973 1.8 53.6
R211-100 1051 1006.8 4.2 1288.1 1025.6 2.4 22.5 1028.2 2.2 11.3 1041 1.0 40.5
Avg 3.5 1556.7   3.8 33.8   2.0 11.2   1.7 45.8
RC201-100 795 795 0.0 640.8 784 1.4 3.7 786.4 1.1 4.2 795 0.0 44.4
RC202-100 938 931.6 0.7 951.5 890.6 5.1 12.1 922.8 1.6 8.9 930 0.9 46.3
RC203-100 1003 976.6 2.6 938.4 954.4 4.8 22.5 978.2 2.5 9.6 967 3.6 32.4
RC204-100 1140 1086.2 4.7 970.3 1101.8 3.4 31.9 1096.0 3.9 11.9 1140 0.0 46.5
RC205-100 859 848.4 1.2 726.6 843.8 1.8 7 844.6 1.7 6.8 854 0.6 52.6
RC206-100 899 884.0 1.7 838.7 866.6 3.6 11.6 886.8 1.4 6.1 885 1.6 60.2
RC207-100 983 960.8 2.3 893.5 911.4 7.3 14.7 965.4 1.8 7.5 977 0.6 68.4
RC208-100 1057 1013.2 4.1 995.5 1000.2 5.4 24.6 1007.0 4.7 10.7 1041 1.5 51.2
Avg 2.2 869.4   4.1 16.0   2.3 8.2   1.1 50.3
PR11-48 353 327.8 7.1 1743.7 329 6.8 1.9 329.2 6.7 2.0 351.0 0.6 10.3
PR12-96 442 436.4 1.3 2017.6 435 1.6 6.5 442.0 0.0 4.0 430.0 2.7 26.3
PR13-144 467 441.0 5.6 2312.7 452.4 3.1 16.2 456.6 2.2 4.9 452.0 3.2 49.0
PR14-192 567 494.0 12.9 23.1 540.6 4.7 32.4 541.2 4.6 8.8 540.0 4.8 134.3
PR15-240 708 524.8 25.9 18.2 656.6 7.3 29.4 665.0 6.1 13.1 666.0 5.9 118.5
PR16-288 674 517.8 23.2 25.7 643.4 4.5 60.9 652.6 3.2 16.2 616.0 8.6 558.0
PR17-72 362 358.0 1.1 1330.9 354.6 2.0 5.4 356.2 1.6 2.4 362.0 0.0 37.6
PR18-144 539 488.8 9.3 1350.0 530.8 1.5 10.4 517.6 4.0 5.0 539.0 0.0 61.8
PR19-216 562 475.0 15.5 30.0 507.8 9.6 22.1 537.8 4.3 8.7 531.0 5.5 152.9
PR20-288 667 552.4 17.2 24.6 655.0 1.8 57.0 656.6 1.6 13.9 626.0 6.1 475.3
Avg 11.9 887.7   4.3 24.2   3.4 7.9   3.7 162.4
Instance-n BKS IterLS FSA DABC HILS
Profit Gap (%) CPU (s) Profit Gap (%) CPU (s) Profit Gap (%) CPU (s) Profit Gap (%) CPU (s)
C101-100 320 320 0.0 0.4 320 0.0 0.4 312 2.5 0.4 320 0.0 0.4
C102-100 360 360 0.0 0.3 360 0.0 0.3 360 0.0 98.6 360 0.0 0.4
C103-100 400 390 2.6 0.5 390 2.5 0.5 390 2.5 1.0 390 2.5 0.4
C104-100 420 400 5.0 0.3 410 2.4 0.3 420 0.0 10.4 420 0.0 0.7
C105-100 340 340 0.0 0.3 330 2.9 0.3 322 5.3 1.2 340 0.0 0.4
C106-100 340 340 0.0 0.3 340 0.0 0.3 340 0.0 2.0 340 0.0 0.4
C107-100 370 360 2.8 0.3 370 0.0 0.3 350 5.4 1.2 370 0.0 0.4
C108-100 370 370 0.0 0.3 370 0.0 0.3 370 0.0 18.8 370 0.0 0.4
C109-100 380 380 0.0 0.3 380 0.0 0.3 380 0.0 22.0 380 0.0 0.4
Avg 1.2 0.3   0.9 0.3   1.7 17.3   0.3 0.4
R101-100 198 182 8.8 0.1 198 0.0 0.1 182.2 8.0 0.6 198 0.0 0.2
R102-100 286 286 0.0 0.2 282 1.4 0.2 286 0.0 5.4 286 0.0 0.6
R103-100 293 286 2.4 0.2 293 0.0 0.2 293 0.0 49.4 287 2.0 0.7
R104-100 303 297 2.0 0.2 294 3.0 0.2 303 0.0 15 299 1.3 0.7
R105-100 247 247 0.0 0.1 247 0.0 0.1 243.4 1.5 62.2 247 0.0 0.3
R106-100 293 293 0.0 0.2 270 7.8 0.2 293 0.0 0.8 293 0.0 0.6
R107-100 299 288 3.8 0.2 277 7.4 0.2 297 0.7 1.4 299 0.0 0.7
R108-100 308 297 3.7 0.2 294 4.5 0.2 306 0.6 31 308 0.0 0.7
R109-100 277 276 0.4 0.2 264 4.7 0.2 233.4 15.7 0.6 276 0.4 0.4
R110-100 284 281 1.1 0.3 282 0.7 0.3 281.2 1.0 1.0 281 1.1 0.4
R111-100 297 295 0.7 0.2 286 3.7 0.2 295 0.7 85.4 294 1.0 0.7
R112-100 298 295 1.0 0.2 284 4.7 0.2 290.8 2.4 50.8 295 1.0 0.7
Avg 2.0 0.2   3.2 0.2   2.6 25.3   0.6 0.6
RC101-100 219 219 0.0 0.2 216 1.4 0.2 206 5.9 2.2 219 0.0 0.2
RC102-100 266 259 2.7 0.2 249 6.4 0.2 259 2.6 1.0 259 2.6 0.3
RC103-100 266 265 0.4 0.3 265 0.4 0.3 255.8 3.8 6.4 248 6.8 0.3
RC104-100 301 297 1.3 0.3 263 12.6 0.3 288.4 4.2 86.8 275 8.6 0.3
RC105-100 244 221 10.4 0.2 219 10.2 0.2 228 6.6 4.4 244 0.0 0.3
RC106-100 252 239 5.4 0.2 240 4.8 0.2 225 10.7 0.6 244 3.2 0.3
RC107-100 277 274 1.1 0.2 244 11.9 0.2 262.4 5.3 45 276 0.4 0.3
RC108-100 298 288 3.5 0.2 263 11.7 0.2 284 4.7 82.6 278 6.7 0.3
Avg 3.1 0.2   7.4 0.2   5.5 28.6   3.5 0.3
PR01-48 308 304 1.3 0.5 304 1.3 0.5 308 0.0 1.1
PR02-96 404 385 4.7 0.6 392 3.0 0.6 397 1.7 1.2
PR03-144 394 384 2.5 1.0 381 3.3 1.0 378 4.1 1.4
PR04-192 489 447 8.6 1.9 470 3.9 1.9 452 7.6 2.1
PR05-240 595 576 3.2 4.6 527 11.4 4.6 523 12.4 5.5
PR06-288 591 538 9.0 2.5 557 5.8 2.5 496 16.1 5.8
PR07-72 298 291 2.3 0.4 289 3.0 0.4 285 10.7 0.4
PR08-144 463 463 0.0 1.0 438 5.4 1.0 455 1.7 2.1
PR09-216 493 461 6.5 1.4 461 6.5 1.4 447 9.3 2.2
PR10-288 594 539 9.3 3.6 539 9.3 3.6 526 11.4 4.9
Avg 4.7 1.8   5.3 1.8      6.8 2.7
C201-100 870 840 3.4 1.1 870 0.0 1.1 840 3.4 23.8 870 0.0 3.9
C202-100 930 910 2.2 2.8 930 0.0 2.8 930 0.0 127.4 910 2.2 5.7
C203-100 960 940 2.1 1.7 940 2.1 1.7 960 0.0 153.4 960 0.0 6.2
C204-100 980 950 3.1 1.6 950 3.1 1.6 970 1.0 117.6 970 1.0 9.2
C205-100 910 900 1.1 1.2 900 1.1 1.2 906 0.4 23.6 900 1.1 5.3
C206-100 930 910 2.2 1.6 920 1.1 1.6 928 0.2 142 920 1.1 5.9
C207-100 930 910 2.2 2.1 930 0.0 2.1 930 0.0 142.4 920 1.1 6.1
C208-100 950 930 2.1 1.6 940 1.1 1.6 950 0.0 132.2 950 0.0 6.1
Avg 2.3 1.7   1.1 1.7   0.6 107.8   0.8 6.0
R201-100 797 788 1.1 1.2 772 3.1 1.2 784 1.6 49.4 781 2.0 6.1
R202-100 930 880 5.4 1.4 878 5.6 1.4 912.8 1.8 105.4 890 4.3 14.3
R203-100 1028 980 4.7 1.6 988 3.9 1.6 1019.6 0.8 218.6 970 5.6 22.4
R204-100 1093 1073 1.8 1.7 1059 3.1 1.7 1089.4 0.3 77.4 1037 5.1 29.6
R205-100 953 931 2.3 1.4 936 1.8 1.4 951.4 0.2 129.0 894 6.2 11.2
R206-100 1032 996 3.5 1.5 950 7.9 1.5 1024.8 0.7 187.8 994 3.7 18.4
R207-100 1077 1038 3.6 2.0 1033 4.1 2.0 1070.6 0.6 142.2 1015 5.8 23.5
R208-100 1117 1069 4.3 1.6 1066 4.6 1.6 1114 0.3 130.2 1061 5.0 33.7
R209-100 959 926 3.4 2.4 914 4.7 2.4 948.4 1.1 164.4 892 7.0 14.3
R210-100 991 958 3.3 1.9 975 1.6 1.9 972 1.9 170.4 929 6.3 16.3
R211-100 1051 1023 2.7 1.6 1023 2.7 1.6 1037.2 1.3 116.8 996 5.2 21.5
Avg 3.3 1.7   3.9 1.7   1.0 135.6   5.1 19.2
RC201-100 795 780 1.9 1.0 781 1.8 1.0 792 0.4 65.6 771 3.0 1.8
RC202-100 938 882 6.0 1.3 866 7.7 1.3 924.4 1.4 135.2 905 3.5 6.2
RC203-100 1003 960 4.3 2.7 956 4.7 2.7 983.4 2.0 138.0 947 5.6 10.3
RC204-100 1140 1117 2.0 2.3 1061 6.9 2.3 1130.8 0.8 168.8 1068 6.3 19.4
RC205-100 859 840 2.2 1.0 800 6.9 1.0 841.2 2.1 119.2 820 4.5 6.0
RC206-100 899 860 4.3 1.1 866 3.7 1.1 884.8 1.6 81.4 851 5.3 6.1
RC207-100 983 926 5.8 1.3 899 8.5 1.3 937.6 4.6 117.2 923 6.1 9.2
RC208-100 1057 1037 1.9 2.3 1015 4.0 2.3 1041.0 1.5 34.0 1008 4.6 13.3
Avg 3.6 1.6   5.5 1.6   1.8 107.4   4.9 9.0
PR11-48 353 330 6.5 0.3 339 4.0 0.3 351 0.6 0.7
PR12-96 442 431 2.5 0.9 432 2.3 0.9 427 3.4 2.1
PR13-144 467 450 3.6 1.9 424 9.2 1.9 436 6.6 2.7
PR14-192 567 482 15.0 1.1 499 12.0 1.1 479 15.5 6.0
PR15-240 708 638 9.9 5.3 613 13.4 5.3 616 13.0 16.4
PR16-288 674 559 17.1 4.1 562 16.6 4.1 582 13.6 13.3
PR17-72 362 346 4.4 0.2 335 7.5 0.2 363 −0.3 1.0
PR18-144 539 479 11.1 0.8 477 11.5 0.8 459 14.8 4.1
PR19-216 562 499 11.2 2.7 501 10.9 2.7 479 14.8 6.2
PR20-288 667 570 14.5 2.5 568 14.8 2.5 588 11.8 10.2
Avg 9.6 2.0   10.2 2.0      9.4 6.3
Instance-n BKS GA
Profit Gap (%) CPU (s)
C101-100 320 317 0.9 0.3
C102-100 360 360 0.0 0.3
C103-100 400 389 2.8 0.4
C104-100 420 403 4.0 0.4
C105-100 340 340 0.0 0.3
C106-100 340 340 0.0 0.3
C107-100 370 362 2.2 0.3
C108-100 370 370 0.0 0.3
C109-100 380 380 0.0 0.3
Avg 1.1 0.3
R101-100 198 189 4.5 0.2
R102-100 286 286 0.0 0.3
R103-100 293 290 1.0 0.3
R104-100 303 297 2.0 0.3
R105-100 247 244 1.2 0.2
R106-100 293 292 0.3 0.3
R107-100 299 292 2.3 0.4
R108-100 308 300 2.6 0.3
R109-100 277 270 2.5 0.3
R110-100 284 277 2.5 0.3
R111-100 297 293 1.3 0.4
R112-100 298 293 1.7 0.4
Avg 1.8 0.3
RC101-100 219 216 1.4 0.2
RC102-100 266 261 1.9 0.3
RC103-100 266 262 1.5 0.3
RC104-100 301 294 2.3 0.4
RC105-100 244 236 3.3 0.3
RC106-100 252 245 2.8 0.3
RC107-100 277 269 2.9 0.3
RC108-100 298 289 3.0 0.3
Avg 2.4 0.3
C201-100 870 848 2.5 0.8
C202-100 930 901 3.1 1.0
C203-100 960 931 3.0 1.1
C204-100 980 952 2.9 1.5
C205-100 910 893 1.9 1.0
C206-100 930 905 2.7 1.0
C207-100 930 910 2.2 1.0
C208-100 950 931 2.0 1.0
Avg 2.5 1.0
R201-100 797 760 4.6 1.2
R202-100 930 867 6.8 1.8
R203-100 1028 954 7.2 2.2
R204-100 1093 1018 6.9 2.5
R205-100 953 876 8.1 1.6
R206-100 1032 954 7.6 2.0
R207-100 1077 986 8.4 2.1
R208-100 1117 1042 6.7 2.4
R209-100 959 897 6.5 1.7
R210-100 991 915 7.7 1.8
R211-100 1051 967 8.0 2.4
Avg 7.1 2.0
RC201-100 795 768 3.4 1.3
RC202-100 938 866 7.7 1.3
RC203-100 1003 866 13.7 1.3
RC204-100 1140 1044 8.4 2.0
RC205-100 859 808 5.9 1.3
RC206-100 899 850 5.5 1.3
RC207-100 983 896 8.9 1.7
RC208-100 1057 976 7.7 1.4
Avg 7.6 1.5
Instance-n Opt VAN VNS HILS
Profit CPU (s) Profit CPU (s) Worst Best Avg CPU (s) Best Worst Avg CPU (s)
C101-50 270 0.0 270 0.3 270 270 270 44.5 270 270 270 0.2
C102-50 300 1.1 300 0.3 300 300 300 65.4 290 290 290 0.2
C103-50 320 23.0 320 0.3 320 320 320 69.0 310 310 310 0.4
C104-50 340 81.4 340 0.3 330 340 340 80.7 340 340 340 0.4
C105-50 300 0.0 300 0.3 300 300 300 45.2 300 300 300 0.2
C106-50 280 0.0 280 0.2 280 280 280 39.7 280 280 280 0.2
C107-50 310 0.0 310 0.2 310 310 310 53.8 310 310 310 0.2
C108-50 320 0.2 320 0.3 320 320 320 42.7 320 320 320 0.2
C109-50 340 0.9 340 0.2 340 340 340 41.7 340 340 340 0.3
Avg CPU (s)   11.8   0.3     53.6     0.3
Adjusted CPU (s)   0.1     <11.8     0.1
R101-50 126 0.0 126 0.1 126 126 126 13.6 126 126 126 0.1
R102-50 198 0.7 195 0.2 198 198 198 24.5 195 195 195 0.2
R103-50 214 30.0 210 0.2 214 214 214 26.5 214 214 214 0.2
R104-50 227 152.7 227 0.3 227 227 227 29.3 227 227 227 0.3
R105-50 159 0.0 159 0.1 159 159 159 16.1 159 159 159 0.2
R106-50 208 0.6 203 0.2 208 208 208 24.8 203 203 203 0.1
R107-50 220 9.8 220 0.3 219 220 219.9 32.5 219 219 219 0.2
R108-50 227 410.6 223 0.2 227 227 227 28.2 227 227 227 0.2
R109-50 192 0.2 192 0.2 192 192 192 20.1 192 192 192 0.3
R110-50 208 1.6 208 0.2 208 208 208 23.4 208 208 208 0.2
R111-50 223 1.8 223 0.2 223 223 223 25.2 223 223 223 0.3
R112-50 226 3.1 226 0.2 226 226 226 26.0 226 226 226 0.3
Avg CPU (s)   50.9   0.2     24.2     0.2
Adjusted CPU (s)   0.0     <5.3     0.0
RC101-50 180 0.0 180 0.1 180 180 180 30.8 180 180 180 0.1
RC102-50 230 0.7 230 0.2 230 230 230 32.8 230 230 230 0.1
RC103-50 240 2.2 240 0.2 240 240 240 32.5 230 230 230 0.1
RC104-50 270 6.1 270 0.2 260 270 266 38.3 250 250 250 0.2
RC105-50 210 0.7 200 0.2 210 210 210 22.2 210 210 210 0.1
RC106-50 210 0.8 200 0.2 210 210 210 33.9 200 200 200 0.1
RC107-50 240 3.4 230 0.1 240 240 240 31.1 220 220 220 0.2
RC108-50 250 9.3 240 0.2 250 250 250 33.8 240 240 240 0.2
Avg CPU (s)   2.9   0.2     31.9     0.1
Adjusted CPU (s)   0.0     <7.0     0.0
  1. The new best solutions obtained by HILS algorithm are presented as italics numbers