Table 17 Objective function values and CPU times of the considered solution approaches (CPLEX, SOAPG, and GA).
From: A multi-objective fuzzy programming model for port tugboat scheduling based on the Stackelberg game
Example(Population size, Iterations’ number) | CPLEX | SOAPG | GA | |||||
|---|---|---|---|---|---|---|---|---|
Objective value | CPU time (seconds) | Objective value | Average value | CPU time (seconds) | Objective value | Average value | CPU time (seconds) | |
1(50,100) | 55,945.80 | 3.38 | 55,945.80 | 56,657.20 | 62.51 | 55,945.80 | 57,547.38 | 56.68 |
2(50,100) | 56,040.66 | 4.04 | 56,040.66 | 58,637.38 | 72.01 | 56,040.66 | 59,543.01 | 63.52 |
3(50,100) | 56,135.52 | 4.71 | 56,135.52 | 58,836.43 | 78.36 | 56,135.52 | 59,638.49 | 69.57 |
4(50,100) | 56,230.38 | 5.37 | 56,230.38 | 58,935.65 | 86.57 | 56,230.38 | 59,865.64 | 75.22 |
5(50,100) | 56,325.24 | 6.03 | 56,325.24 | 59,465.33 | 90.62 | 56,325.24 | 60,475.33 | 81.35 |
6(100,150) | 56,420.10 | 6.70 | 56,420.10 | 60,254.32 | 96.27 | 56,420.10 | 61,354.24 | 87.24 |
7(100,150) | 59,919.15 | 15.59 | 59,919.15 | 61,349.02 | 102.15 | 59,919.15 | 62,267.19 | 94.35 |
8(100,150) | 63,418.20 | 24.48 | 63,418.20 | 64,235.34 | 115.33 | 63,418.20 | 65,258.69 | 106.59 |
9(100,150) | 66,917.25 | 33.37 | 66,917.25 | 67,536.92 | 118.67 | 66,917.25 | 68,741.82 | 109.71 |
10(100,150) | 70,416.30 | 42.27 | 70,416.30 | 72,625.35 | 131.06 | 71,057.12 | 73,159.53 | 120.28 |
11(200,300) | 73,915.35 | 51.16 | 73,915.35 | 75,269.56 | 154.25 | 74,613.02 | 76,752.26 | 137.45 |
12(200,300) | 77,414.40 | 60.05 | 77,414.40 | 79,512.07 | 173.64 | 78,251.33 | 81,236.60 | 159.20 |
13(200,300) | 80,913.45 | 68.94 | 80,913.45 | 82,347.36 | 195.02 | 81,641.37 | 83,068.57 | 180.56 |
14(200,300) | 84,412.50 | 77.83 | 84,412.50 | 86,542.35 | 216.84 | 85,361.22 | 87,940.68 | 203.81 |
15(200,300) | 87,911.55 | 86.72 | 87,911.55 | 89,046.29 | 235.35 | 88,146.54 | 90,248.51 | 224.23 |
16(250,350) | 91,410.60 | 95.62 | 91,410.60 | 92,345.32 | 258.30 | 92,236.07 | 93,753.68 | 245.55 |
17(250,350) | 93,034.38 | 365.09 | 93,034.38 | 95,246.37 | 271.54 | 95,032.71 | 96,657.42 | 259.48 |
18(250,350) | 94,658.16 | 634.56 | 94,658.16 | 96,145.13 | 302.23 | 95,346.98 | 97,862.69 | 284.64 |
19(250,350) | 96,281.94 | 904.03 | 96,281.94 | 98,254.71 | 326.09 | 97,952.63 | 99,861.65 | 309.53 |
20(250,350) | 97,905.72 | 1173.50 | 97,905.72 | 99,694.65 | 350.47 | 98,657.37 | 100,591.88 | 336.52 |
21(300,400) | 99,529.50 | 1442.92 | 99,529.50 | 100,543.52 | 362.64 | 100,475.24 | 101,947.62 | 354.85 |
22(300,400) | 101,153.28 | 1712.44 | 101,243.63 | 103,294.95 | 396.22 | 102,574.68 | 104,133.86 | 371.39 |
23(300,400) | 102,777.06 | 1981.91 | 102,951.26 | 103,876.56 | 420.43 | 103,536.09 | 104,472.48 | 406.08 |
24(300,400) | 104,400.84 | 2251.38 | 104.519.86 | 105,452.68 | 463.24 | 104,946.27 | 106,865.23 | 432.67 |
25(300,400) | 106,024.62 | 2520.85 | 106,237.18 | 108,056.26 | 493.57 | 106,937.36 | 109,342.06 | 470.89 |
26(400,500) | 107,648.40 | 2790.32 | 107,836.17 | 108,951.34 | 512.65 | 108,365.33 | 109,842.37 | 498.21 |
27(400,500) | 109,911.31 | 2815.24 | 110,563.32 | 111,645.55 | 531.03 | 111,124.65 | 112,456.83 | 519.26 |
28(400,500) | 112,174.22 | 2863.37 | 112,537.34 | 113,098.37 | 556.45 | 113,249.74 | 114,254.47 | 535.27 |
29(400,500) | 114,437.13 | 2812.25 | 114,836.27 | 115,297.22 | 573.01 | 115,674.54 | 116,783.49 | 561.85 |
30(400,500) | 116,700.04 | 2954.13 | 116,923.01 | 118,635.42 | 589.62 | 118,357.79 | 119,864.66 | 576.83 |
31(450,600) | 120,304.05 | 2982.51 | 120,476.37 | 121,421.89 | 603.54 | 121,159.59 | 122,498.22 | 593.20 |
32(450,600) | 121,225.86 | 5632.79 | 121,563.51 | 122,489.08 | 621.30 | 122,258.40 | 123,547.82 | 611.16 |
33(450,600) | 123,488.77*(Heuristic still looking.) | 9000+ | 122,826.36 | 123,743.90 | 652.27 | 123,432.74 | 124,574.69 | 639.18 |
34(450,600) | 125,751.68*(Heuristic still looking.) | 9000+ | 124,237.25 | 125,694.72 | 669.26 | 126,327.07 | 127,803.40 | 648.49 |
35(450,600) | 128,014.64*(Heuristic still looking.) | 9000+ | 126,357,22 | 127,364.04 | 685.33 | 127,687.42 | 128,259.82 | 672.30 |
36(500,700) | – | – | 127,261.41 | 128,261.95 | 706.52 | 128,237.91 | 129,382.64 | 686.29 |
37(500,700) | – | – | 127,534.08 | 128,638.68 | 726.11 | 128,864.25 | 129,765.86 | 708.43 |
38(500,700) | – | – | 128,162.30 | 129,236.84 | 735.02 | 129,421.57 | 131,589.31 | 725.29 |
39(500,700) | – | – | 128,637.65 | 129,778.31 | 756.98 | 129,632.04 | 131,625.09 | 735.95 |
40(500,700) | – | – | 129,251.82 | 131,591.69 | 768.32 | 130,234.01 | 132,147.20 | 759.37 |
41(600,900) | – | – | 129,735.21 | 132,547.33 | 784.32 | 130.951.34 | 132,628.55 | 764.65 |
42(600,900) | – | – | 130,235.01 | 133,698.79 | 802.53 | 131,654.21 | 134,320.03 | 783.09 |
43(600,900) | – | – | 131,952.76 | 133,869.26 | 815.43 | 132,684.18 | 134,586.67 | 798.43 |
44(600,900) | – | – | 132,697.32 | 134,694.35 | 839.81 | 133,547.65 | 135,049.40 | 820.85 |
45(600,900) | – | – | 133,246.65 | 135,489.56 | 854.69 | 134,658.49 | 136,852.74 | 842.67 |
