Table 2.
The results of the total traveled distance for Solomon’s 100 customers set Problems.
| No. | Problem | Best-Known Solution | Genetic | PSO | ACO | The Proposed Algorithm | |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Best | Average | Best | Average | Best | Average | Best | Average | ||||||||||||
| TD | NV | TD | NV | TD | NV | TD | NV | TD | NV | TD | NV | TD | NV | TD | NV | TD | NV | ||
| 1 | C101 | 828.94 | 10 | 828.94 | 10 | 856.26 | 10.20 | 828.94 | 10 | 842.60 | 10.10 | 828.94 | 10 | 842.60 | 10.10 | 828.94 | 10 | 842.60 | 10.10 |
| 2 | C102 | 828.94 | 10 | 828.94 | 10 | 828.94 | 10.00 | 828.94 | 10 | 828.94 | 10.00 | 828.94 | 10 | 857.82 | 10.10 | 828.94 | 10 | 828.94 | 10.00 |
| 3 | C103 | 828.06 | 10 | 828.06 | 10 | 859.88 | 10.00 | 828.06 | 10 | 828.06 | 10.00 | 828.06 | 10 | 828.06 | 10.00 | 828.06 | 10 | 828.06 | 10.00 |
| 4 | C104 | 824.78 | 10 | 824.78 | 10 | 824.78 | 10.00 | 824.78 | 10 | 824.78 | 10.00 | 824.78 | 10 | 849.79 | 10.10 | 824.78 | 10 | 824.78 | 10.00 |
| 5 | C105 | 828.94 | 10 | 828.94 | 10 | 854.25 | 10.20 | 828.94 | 10 | 866.91 | 10.30 | 828.94 | 10 | 904.88 | 10.60 | 828.94 | 10 | 841.60 | 10.10 |
| 6 | C106 | 828.94 | 10 | 828.94 | 10 | 851.78 | 10.10 | 828.94 | 10 | 897.46 | 10.30 | 828.94 | 10 | 943.14 | 10.50 | 828.94 | 10 | 874.62 | 10.20 |
| 7 | C107 | 828.94 | 10 | 828.94 | 10 | 856.47 | 10.20 | 828.94 | 10 | 842.70 | 10.10 | 828.94 | 10 | 870.23 | 10.30 | 828.94 | 10 | 842.70 | 10.10 |
| 8 | C108 | 828.94 | 10 | 828.94 | 10 | 865.99 | 10.00 | 828.94 | 10 | 841.29 | 10.00 | 828.94 | 10 | 853.64 | 10.00 | 828.94 | 10 | 841.29 | 10.00 |
| 9 | C109 | 828.94 | 10 | 828.94 | 10 | 910.27 | 10.30 | 828.94 | 10 | 856.05 | 10.10 | 828.94 | 10 | 883.16 | 10.20 | 828.94 | 10 | 828.94 | 10.00 |
| 10 | C201 | 591.56 | 3 | 591.56 | 3 | 602.53 | 3.30 | 591.56 | 3 | 606.18 | 3.40 | 591.56 | 3 | 609.84 | 3.50 | 591.56 | 3 | 598.87 | 3.20 |
| 11 | C202 | 591.56 | 3 | 591.56 | 3 | 656.01 | 3.20 | 591.56 | 3 | 623.78 | 3.10 | 591.56 | 3 | 623.78 | 3.10 | 591.56 | 3 | 591.56 | 3.00 |
| 12 | C203 | 591.17 | 3 | 591.17 | 3 | 606.19 | 3.00 | 591.17 | 3 | 604.69 | 3.00 | 591.17 | 3 | 618.20 | 3.00 | 591.17 | 3 | 604.69 | 3.00 |
| 13 | C204 | 590.60 | 3 | 590.60 | 3 | 704.28 | 3.30 | 590.60 | 3 | 666.39 | 3.20 | 590.60 | 3 | 742.17 | 3.40 | 590.60 | 3 | 628.49 | 3.10 |
| 14 | C205 | 588.88 | 3 | 588.88 | 3 | 619.27 | 3.30 | 588.88 | 3 | 599.01 | 3.10 | 588.88 | 3 | 609.14 | 3.20 | 588.88 | 3 | 599.01 | 3.10 |
| 15 | C206 | 588.49 | 3 | 588.49 | 3 | 620.28 | 3.20 | 588.49 | 3 | 604.38 | 3.10 | 588.49 | 3 | 636.17 | 3.30 | 588.49 | 3 | 588.49 | 3.00 |
| 16 | C207 | 588.29 | 3 | 588.29 | 3 | 610.49 | 3.00 | 588.29 | 3 | 632.69 | 3.00 | 588.29 | 3 | 621.59 | 3.00 | 588.29 | 3 | 599.39 | 3.00 |
| 17 | C208 | 588.32 | 3 | 588.32 | 3 | 622.73 | 3.00 | 588.32 | 3 | 599.79 | 3.00 | 588.32 | 3 | 611.26 | 3.00 | 588.32 | 3 | 599.79 | 3.00 |
| 18 | R101 | 1483.57 | 16 | 1642.87 | 20 | 1645.83 | 19.50 | 1642.87 | 20 | 1645.33 | 19.50 | 1645.79 | 19 | 1647.29 | 19.00 | 1642.87 | 20 | 1645.83 | 19.50 |
| 19 | R102 | 1355.93 | 14 | 1482.74 | 18 | 1483.75 | 17.70 | 1472.62 | 18 | 1477.95 | 17.80 | 1480.73 | 18 | 1482.21 | 17.80 | 1472.62 | 18 | 1477.14 | 17.80 |
| 20 | R103 | 1133.35 | 12 | 1292.85 | 15 | 1248.88 | 14.40 | 1213.62 | 14 | 1239.30 | 14.40 | 1213.62 | 14 | 1247.22 | 14.30 | 1213.62 | 14 | 1239.01 | 13.80 |
| 21 | R104 | 968.28 | 10 | 982.01 | 10 | 995.05 | 9.60 | 1007.24 | 9 | 1007.30 | 9.00 | 982.01 | 10 | 1000.11 | 9.40 | 982.01 | 10 | 992.52 | 9.70 |
| 22 | R105 | 1262.53 | 12 | 1360.78 | 15 | 1366.87 | 14.80 | 1360.78 | 15 | 1374.14 | 14.70 | 1360.78 | 15 | 1369.99 | 15.30 | 1360.78 | 15 | 1366.42 | 15.00 |
| 23 | R106 | 1201.78 | 12 | 1249.40 | 13 | 1251.48 | 12.20 | 1241.52 | 13 | 1249.39 | 12.40 | 1251.98 | 12 | 1252.00 | 12.00 | 1241.52 | 13 | 1247.29 | 12.60 |
| 24 | R107 | 1051.92 | 11 | 1076.13 | 11 | 1094.18 | 10.70 | 1076.13 | 11 | 1094.19 | 10.50 | 1076.13 | 11 | 1096.08 | 10.70 | 1076.13 | 11 | 1088.49 | 10.70 |
| 25 | R108 | 948.57 | 10 | 963.99 | 9 | 965.42 | 9.90 | 963.99 | 9 | 965.10 | 9.70 | 948.57 | 10 | 960.92 | 9.60 | 948.57 | 10 | 955.82 | 9.60 |
| 26 | R109 | 1110.40 | 12 | 1151.84 | 13 | 1181.86 | 11.60 | 1151.84 | 13 | 1186.15 | 11.40 | 1151.84 | 13 | 1190.44 | 11.20 | 1151.84 | 13 | 1164.71 | 12.40 |
| 27 | R110 | 1080.36 | 11 | 1080.36 | 11 | 1112.79 | 10.30 | 1080.36 | 11 | 1105.14 | 10.50 | 1080.36 | 11 | 1107.72 | 10.50 | 1080.36 | 11 | 1098.14 | 10.70 |
| 28 | R111 | 987.80 | 10 | 1053.50 | 12 | 1086.43 | 10.80 | 1053.50 | 12 | 1083.13 | 11.60 | 1088.48 | 12 | 1095.07 | 10.40 | 1053.50 | 12 | 1069.14 | 11.60 |
| 29 | R112 | 953.63 | 10 | 982.14 | 9 | 995.33 | 10.80 | 953.63 | 10 | 965.03 | 10.00 | 953.63 | 10 | 987.40 | 10.60 | 960.68 | 10 | 968.58 | 9.90 |
| 30 | R201 | 1148.48 | 9 | 1148.48 | 9 | 1208.94 | 7.70 | 1179.79 | 9 | 1231.20 | 5.50 | 1148.48 | 9 | 1212.51 | 7.30 | 1148.48 | 9 | 1178.39 | 8.40 |
| 31 | R202 | 1049.74 | 7 | 1049.74 | 7 | 1086.62 | 5.70 | 1049.74 | 7 | 1100.68 | 5.00 | 1079.36 | 6 | 1142.69 | 4.10 | 1049.74 | 7 | 1081.57 | 5.70 |
| 32 | R203 | 900.08 | 5 | 900.08 | 5 | 930.23 | 4.60 | 932.76 | 7 | 939.72 | 3.80 | 939.54 | 3 | 941.70 | 3.00 | 900.08 | 5 | 922.71 | 4.60 |
| 33 | R204 | 772.33 | 4 | 807.38 | 4 | 828.06 | 2.40 | 772.33 | 4 | 817.42 | 2.80 | 772.33 | 4 | 823.17 | 2.80 | 772.33 | 4 | 801.47 | 3.40 |
| 34 | R205 | 959.74 | 4 | 970.89 | 6 | 982.66 | 4.50 | 970.89 | 6 | 980.30 | 4.80 | 970.89 | 6 | 989.71 | 3.60 | 970.89 | 6 | 977.95 | 5.10 |
| 35 | R206 | 898.91 | 5 | 898.91 | 5 | 906.06 | 3.40 | 906.14 | 3 | 910.24 | 3.00 | 906.14 | 3 | 912.29 | 3.00 | 898.91 | 5 | 903.89 | 4.00 |
| 36 | R207 | 814.78 | 3 | 814.78 | 3 | 844.73 | 3.40 | 814.78 | 3 | 868.25 | 2.60 | 814.78 | 3 | 876.51 | 2.60 | 814.78 | 3 | 836.67 | 3.00 |
| 37 | R208 | 715.37 | 3 | 725.75 | 2 | 726.61 | 2.00 | 725.42 | 4 | 725.77 | 3.20 | 725.75 | 2 | 726.71 | 2.00 | 723.61 | 3 | 725.50 | 2.50 |
| 38 | R209 | 879.53 | 6 | 879.53 | 6 | 892.08 | 5.40 | 879.53 | 6 | 891.00 | 5.40 | 879.53 | 6 | 903.21 | 4.20 | 879.53 | 6 | 891.82 | 5.10 |
| 39 | R210 | 932.89 | 7 | 954.12 | 3 | 955.06 | 6.60 | 954.12 | 3 | 954.64 | 5.00 | 939.34 | 3 | 952.94 | 4.78 | 932.89 | 7 | 937.89 | 6.20 |
| 40 | R211 | 761.10 | 4 | 885.71 | 2 | 892.31 | 2.30 | 885.71 | 2 | 889.53 | 4.40 | 888.73 | 5 | 867.07 | 2.90 | 808.56 | 4 | 824.99 | 3.90 |
| 41 | RC101 | 1481.27 | 13 | 1660.10 | 16 | 1689.57 | 14.40 | 1623.58 | 15 | 1658.18 | 15.10 | 1639.97 | 16 | 1687.56 | 14.40 | 1623.58 | 15 | 1645.18 | 15.10 |
| 42 | RC102 | 1395.25 | 13 | 1466.84 | 14 | 1493.53 | 13.50 | 1482.91 | 14 | 1497.28 | 13.60 | 1477.54 | 13 | 1539.85 | 12.30 | 1466.84 | 14 | 1487.10 | 13.50 |
| 43 | RC103 | 1221.53 | 10 | 1261.67 | 11 | 1263.56 | 11.00 | 1262.02 | 11 | 1262.29 | 11.00 | 1262.02 | 11 | 1264.17 | 11.00 | 1261.67 | 11 | 1262.04 | 11.00 |
| 44 | RC104 | 1135.48 | 10 | 1135.48 | 10 | 1135.50 | 10.00 | 1135.48 | 10 | 1135.50 | 10.00 | 1135.48 | 10 | 1135.51 | 10.00 | 1135.48 | 10 | 1135.49 | 10.00 |
| 45 | RC105 | 1354.20 | 12 | 1518.60 | 16 | 1601.17 | 15.40 | 1518.60 | 16 | 1593.35 | 14.80 | 1629.44 | 13 | 1633.29 | 13.00 | 1618.55 | 16 | 1621.16 | 15.40 |
| 46 | RC106 | 1226.62 | 11 | 1377.35 | 13 | 1396.59 | 11.80 | 1384.92 | 12 | 1417.25 | 11.20 | 1377.35 | 13 | 1416.49 | 11.30 | 1377.35 | 13 | 1392.80 | 12.30 |
| 47 | RC107 | 1150.99 | 10 | 1230.48 | 11 | 1254.98 | 12.60 | 1212.83 | 12 | 1240.50 | 12.30 | 1230.48 | 11 | 1258.04 | 12.80 | 1212.83 | 12 | 1226.01 | 12.00 |
| 48 | RC108 | 1076.81 | 10 | 1117.53 | 11 | 1135.32 | 10.30 | 1117.53 | 11 | 1127.41 | 10.90 | 1117.53 | 11 | 1128.55 | 10.80 | 1117.53 | 11 | 1126.40 | 10.70 |
| 49 | RC201 | 1134.91 | 6 | 1406.91 | 4 | 1391.43 | 7.20 | 1406.91 | 4 | 1406.91 | 4.00 | 1286.83 | 9 | 1397.23 | 6.00 | 1387.55 | 8 | 1391.43 | 7.20 |
| 50 | RC202 | 1113.53 | 8 | 1365.57 | 4 | 1250.18 | 3.60 | 1113.53 | 8 | 1162.75 | 7.60 | 1113.53 | 8 | 1204.86 | 6.30 | 1148.84 | 9 | 1173.34 | 7.90 |
| 51 | RC203 | 945.96 | 5 | 945.96 | 5 | 1034.30 | 3.40 | 945.96 | 5 | 1032.14 | 3.40 | 1049.62 | 3 | 1052.87 | 3.00 | 945.96 | 5 | 990.67 | 4.20 |
| 52 | RC204 | 796.11 | 4 | 798.41 | 3 | 798.69 | 3.20 | 798.41 | 3 | 799.18 | 3.60 | 798.46 | 3 | 799.43 | 3.80 | 798.41 | 3 | 798.67 | 3.20 |
| 53 | RC205 | 1168.22 | 8 | 1270.69 | 7 | 1276.08 | 6.40 | 1168.22 | 8 | 1282.01 | 4.70 | 1168.22 | 8 | 1263.14 | 6.80 | 1161.81 | 7 | 1187.56 | 6.90 |
| 54 | RC206 | 1059.89 | 7 | 1059.89 | 7 | 1105.75 | 5.80 | 1084.30 | 8 | 1139.24 | 4.00 | 1059.89 | 7 | 1135.44 | 4.00 | 1059.89 | 7 | 1092.22 | 6.00 |
| 55 | RC207 | 976.40 | 7 | 999.26 | 6 | 1060.37 | 3.60 | 976.40 | 7 | 1011.75 | 5.70 | 1053.58 | 6 | 1064.28 | 3.90 | 976.40 | 7 | 995.65 | 6.40 |
| 56 | RC208 | 785.93 | 4 | 816.10 | 5 | 824.93 | 3.60 | 816.10 | 5 | 822.41 | 4.00 | 806.87 | 5 | 819.64 | 4.00 | 795.39 | 5 | 807.27 | 4.78 |