Table 18 Objective function values and CPU times of the considered solution approaches (SOA and SA).
From: A multi-objective fuzzy programming model for port tugboat scheduling based on the Stackelberg game
Example(population size, Iterations’ number) | SOA | SA | ||||
|---|---|---|---|---|---|---|
Objective value | Average value | CPU time (seconds) | Objective value | Average value | CPU time (seconds) | |
1(50,100) | 55,945.80 | 57,726.35 | 59.24 | 55,945.80 | 57,542.33 | 60.57 |
2(50,100) | 56,040.66 | 57,861.42 | 61.58 | 56,040.66 | 57,489.30 | 62.35 |
3(50,100) | 56,135.52 | 58,365.86 | 67.23 | 56,135.52 | 58,567.41 | 68.47 |
4(50,100) | 56,230.38 | 58,751.93 | 73.55 | 56,230.38 | 58,698.75 | 72.57 |
5(50,100) | 56,325.24 | 59,537.23 | 78.29 | 56,325.24 | 59,547.20 | 79.58 |
6(100,150) | 56,420.10 | 59,943.07 | 85.20 | 56,420.10 | 59,846.21 | 87.25 |
7(100,150) | 59,919.15 | 63,679.45 | 92.17 | 59,919.15 | 62,756.05 | 94.33 |
8(100,150) | 63,418.20 | 65,307.59 | 101.34 | 63,418.20 | 65,789.62 | 103.58 |
9(100,150) | 66,917.25 | 68,247.35 | 107.46 | 66,917.25 | 68,574.10 | 108.37 |
10(100,150) | 70,416.30 | 72,354.21 | 116.74 | 73,687.38 | 75,123.60 | 117.22 |
11(200,300) | 74,547.09 | 76,523.46 | 131.08 | 74,869.32 | 75,741.59 | 132.62 |
12(200,300) | 78,258.60 | 80,359.31 | 156.92 | 78,569.27 | 79,482.39 | 157.54 |
13(200,300) | 81,569.54 | 83,497.25 | 177.54 | 81,569.68 | 83,498.62 | 177.84 |
14(200,300) | 85,154.62 | 86,764.59 | 191.95 | 85,476.57 | 87,258.93 | 190.35 |
15(200,300) | 87,637.52 | 89,576.48 | 219.51 | 87,739.51 | 89,328.43 | 218.26 |
16(250,350) | 92,048.75 | 93,597.56 | 236.04 | 92,468.53 | 93,663.42 | 237.08 |
17(250,350) | 94.967.43 | 95,267.24 | 248.16 | 94,246.08 | 96,272.51 | 251.49 |
18(250,350) | 95,241.03 | 96,513.76 | 267.86 | 95,547.21 | 97,635.55 | 270.30 |
19(250,350) | 97,537.89 | 98,421.32 | 296.49 | 97,637.42 | 99,884.21 | 299.57 |
20(250,350) | 98,468.37 | 99.637.21 | 319.43 | 98,787.37 | 100,699.30 | 322.01 |
21(300,400) | 100,257.16 | 101,576.35 | 341.58 | 100,384.65 | 102,587.47 | 345.24 |
22(300,400) | 101,864.45 | 103,468.73 | 359.24 | 101,657,52 | 103,767.66 | 361.35 |
23(300,400) | 103,423.72 | 105,374.68 | 387.41 | 103,423.80 | 105,154.35 | 388.75 |
24(300,400) | 104,819.47 | 105,954.27 | 426.33 | 104,523.14 | 105,928.64 | 428.31 |
25(300,400) | 106,754.80 | 108,469.30 | 462.69 | 106,639.25 | 108,637.20 | 464.78 |
26(400,500) | 109,057.15 | 110,863.47 | 486.26 | 109,394.33 | 110,852.94 | 491.95 |
27(400,500) | 111,967.53 | 112,637.20 | 508.52 | 111,638.32 | 112,264.21 | 512.22 |
28(400,500) | 113,067.64 | 115,563.19 | 524.61 | 113,207.42 | 115,885.43 | 529.25 |
29(400,500) | 116,324.99 | 118,465.17 | 552.03 | 116,389.76 | 118,525.56 | 558.66 |
30(400,500) | 119,384.20 | 120,742.95 | 563.80 | 119,627.20 | 120,541.13 | 569.24 |
31(450,600) | 120,932.26 | 121,649.39 | 589.58 | 121,159.34 | 123,288.95 | 595.19 |
32(450,600) | 122,132.68 | 123,847.46 | 603.39 | 122,415.66 | 124,963.47 | 608.49 |
33(450,600) | 123,256.53 | 125,498.25 | 625.48 | 123,854.57 | 125,227.30 | 628.65 |
34(450,600) | 126,568.32 | 127,864.59 | 636.05 | 126,837.62 | 127,626.08 | 640.09 |
35(450,600) | 127,820.60 | 128,657.34 | 659.83 | 128,687.04 | 130,212,32 | 662.43 |
36(500,700) | 129,104.37 | 130,378.92 | 670.54 | 129,563.18 | 131,545.17 | 672.62 |
37(500,700) | 129,634.90 | 132,156.36 | 695.71 | 130,691.36 | 132,682.66 | 701.31 |
38(500,700) | 131,196.84 | 133,468.37 | 716.43 | 131,257.86 | 133,236.52 | 715.60 |
39(500,700) | 131,541.22 | 133,835.96 | 723.28 | 131,630.54 | 133,894.54 | 726.42 |
40(500,700) | 131,935.70 | 133,579.63 | 742.60 | 132,045.75 | 134,427.70 | 748.05 |
41(600,900) | 132,309.08 | 134,549.05 | 754.26 | 132,952.34 | 134,853.64 | 756.35 |
42(600,900) | 133,865.24 | 134,687.54 | 772.13 | 133,985.47 | 135,527.41 | 786.20 |
43(600,900) | 134,286.12 | 136,579.58 | 785.02 | 135,204.55 | 137,152.86 | 793.84 |
44(600,900) | 134,683.07 | 136,289.67 | 811.24 | 135,810.21 | 137,656.28 | 816.32 |
45(600,900) | 136,335.68 | 138,479.53 | 836.37 | 137,023.68 | 139,726.01 | 839.33 |
