Table 1 Comparison between MIP and metaheuristic

From: The vehicle routing problem with heterogeneous locker boxes

Instance MIP BKS Opt gap (%) topt (s) fbest favg fworst gapbest (%) gapavg (%) gapworst (%) tavg (s)
10_1_1 163.14 0.00 0.70 163.14 163.14 163.14 0.00 0.00 0.00 0.23
10_1_2 164.19 0.00 0.46 164.19 164.19 164.19 0.00 0.00 0.00 0.27
10_1_3 166.87 0.00 3.15 166.87 166.87 166.87 0.00 0.00 0.00 0.34
10_1_4 231.60 0.00 0.38 231.60 231.60 231.60 0.00 0.00 0.00 0.31
10_1_5 250.53 0.00 7.14 250.53 250.53 250.53 0.00 0.00 0.00 0.40
10_2_1 218.82 0.00 21.45 218.82 218.82 218.82 0.00 0.00 0.00 0.88
10_2_2 231.29 0.00 9.64 231.29 231.29 231.29 0.00 0.00 0.00 0.66
10_2_3 227.28 0.00 2.63 227.28 227.28 227.28 0.00 0.00 0.00 0.51
10_2_4 207.41 0.00 6.77 207.41 207.41 207.41 0.00 0.00 0.00 0.58
10_2_5 148.28 0.00 2.90 148.28 148.28 148.28 0.00 0.00 0.00 0.64
14_1_1 256.41 0.00 7.51 256.41 256.41 256.41 0.00 0.00 0.00 1.14
14_1_2 253.28 0.00 6.26 253.28 253.28 253.28 0.00 0.00 0.00 0.60
14_1_3 311.09 0.00 7.96 311.09 311.09 311.09 0.00 0.00 0.00 1.09
14_1_4 216.93 0.00 49.57 216.93 216.93 216.93 0.00 0.00 0.00 0.89
14_1_5 156.78 0.00 1.20 156.78 156.78 156.78 0.00 0.00 0.00 0.98
14_2_1 239.39 0.00 40.62 239.39 239.39 239.39 0.00 0.00 0.00 1.59
14_2_2 288.75 0.00 100.83 288.75 288.75 288.75 0.00 0.00 0.00 1.24
14_2_3 220.68 0.00 14.63 220.68 220.68 220.68 0.00 0.00 0.00 1.61
14_2_4 229.48 0.00 8.02 229.48 229.92 231.00 0.00 0.19 0.66 2.09
14_2_5 242.01 0.00 48.31 242.01 242.01 242.01 0.00 0.00 0.00 1.82
18_1_1 242.54 0.00 11.07 242.54 242.54 242.54 0.00 0.00 0.00 2.25
18_1_2 399.59 0.00 1775.82 399.59 399.59 399.59 0.00 0.00 0.00 1.21
18_1_3 331.69 0.00 83.06 331.69 331.69 331.69 0.00 0.00 0.00 1.73
18_1_4 446.82 0.00 570.15 446.82 446.82 446.82 0.00 0.00 0.00 2.32
18_1_5 259.62 0.00 7.66 259.62 259.62 259.62 0.00 0.00 0.00 1.79
18_2_1 429.60 9.46 Time limit 429.60 429.60 429.60 0.00 0.00 0.00 1.59
18_2_2 271.74 0.00 2460.15 271.74 271.74 271.74 0.00 0.00 0.00 2.12
18_2_3 252.90 0.00 9.57 252.90 252.90 252.90 0.00 0.00 0.00 1.67
18_2_4 281.61 0.00 982.36 281.61 282.92 283.79 0.00 0.46 0.77 2.58
18_2_5 345.47 0.00 89.40 345.47 345.47 345.47 0.00 0.00 0.00 2.32
22_2_1 386.71 0.00 2508.39 386.71 386.71 386.71 0.00 0.00 0.00 2.61
22_2_2 349.82 0.00 151.52 349.82 350.36 352.54 0.00 0.16 0.78 3.86
22_2_3 255.58 0.00 30.14 255.58 255.58 255.58 0.00 0.00 0.00 2.68
22_2_4 303.80 0.00 1245.01 303.80 303.80 303.80 0.00 0.00 0.00 3.22
22_2_5 360.86 0.00 11,804.50 360.86 360.86 360.86 0.00 0.00 0.00 3.72
23_2_1 330.46 6.42 Time limit 330.46 330.46 330.46 0.00 0.00 0.00 3.35
23_2_2 302.26 0.00 27,855.10 302.26 302.26 302.26 0.00 0.00 0.00 4.79
23_2_3 306.97 11.30 Time limit 297.96 297.96 297.96 \(-\) 2.93 \(-\) 2.93 \(-\) 2.93 4.86
23_2_4 447.65 0.00 15,276.30 447.65 447.65 447.65 0.00 0.00 0.00 5.28
23_2_5 297.46 0.00 551.76 297.46 297.46 297.46 0.00 0.00 0.00 3.22
24_2_1 323.65 0.00 18,005.70 323.65 323.65 323.65 0.00 0.00 0.00 4.07
24_2_2 340.98 0.00 399.08 340.98 340.98 340.98 0.00 0.00 0.00 4.63
24_2_3 321.50 0.00 1002.77 321.50 321.50 321.50 0.00 0.00 0.00 4.40
24_2_4 369.35 0.00 492.02 369.35 369.35 369.35 0.00 0.00 0.00 3.94
24_2_5 396.29 3.77 Time limit 396.15 396.15 396.15 \(-\) 0.03 \(-\) 0.03 \(-\) 0.03 3.12
25_2_1 455.76 22.70 Time limit 432.39 432.39 432.39 \(-\) 5.13 \(-\) 5.13 \(-\) 5.13 3.81
25_2_2 354.90 0.00 21,099.80 354.90 354.90 354.90 0.00 0.00 0.00 11.48
25_2_3 338.60 0.00 4417.50 338.60 338.60 338.60 0.00 0.00 0.00 3.90
25_2_4 429.63 0.00 14,348.60 429.63 429.63 429.63 0.00 0.00 0.00 4.16
25_2_5 302.61 0.00 11,454.60 302.61 302.61 302.61 0.00 0.00 0.00 4.23
    3043.83 292.56 292.61 292.69 \(-\) 0.16 \(-\) 0.15 \(-\) 0.12 2.46