Table 2 Comparison with Mancini/Gansterer

From: The vehicle routing problem with heterogeneous locker boxes

Instance MIP ILS Metaheuristic
  BKS Opt gap (%) gapavg (%) t (s) fbest favg fworst tavg (s) gapbest (%) gapavg (%) gapworst (%)
r25_5_1 161.37 0.00 0.00 1.60 161.37 161.37 161.37 30.5 0.00 0.00 0.00
r25_5_2 166.63 0.00 0.00 6.69 166.63 166.63 166.63 22.6 0.00 0.00 0.00
r25_5_3 146.56 0.00 0.00 7.08 146.56 146.56 146.56 35.8 0.00 0.00 0.00
r25_5_4 161.04 0.00 0.00 62.27 161.04 161.04 161.04 33.1 0.00 0.00 0.00
r25_5_5 157.95 0.00 0.00 2.40 157.95 157.95 157.95 30.1 0.00 0.00 0.00
r25_5_6 160.83 0.00 0.00 4.90 160.83 160.83 160.83 35.9 0.00 0.00 0.00
r25_5_7 152.69 0.00 0.75 30.44 152.69 152.73 152.90 35.4 0.00 0.03 0.14
r25_5_8 165.16 0.00 0.45 60.43 165.16 165.16 165.16 22.0 0.00 0.00 0.00
r25_5_9 151.54 0.00 0.00 4.34 151.54 151.54 151.54 38.5 0.00 0.00 0.00
r25_5_10 151.99 0.00 0.00 5.18 151.99 151.99 151.99 31.1 0.00 0.00 0.00
   Avg. 0.12 18.53     31.5 0.00 0.00 0.01
r50_5_1 266.80 0.00 0.94 263.50 266.80 267.50 267.68 200.1 0.00 0.26 0.33
r50_5_2 267.97 0.00 2.19 224.99 267.97 268.49 269.82 197.3 0.00 0.19 0.69
r50_5_3 273.05 5.29 3.13 352.20 273.05 273.05 273.05 188.4 0.00 0.00 0.00
r50_5_4 268.89 0.00 3.91 171.50 268.89 268.89 268.89 170.8 0.00 0.00 0.00
r50_5_5 271.32 0.00 1.32 303.90 271.32 271.60 272.69 256.3 0.00 0.10 0.51
r50_5_6 268.32 0.00 3.62 293.90 268.32 268.32 268.32 241.4 0.00 0.00 0.00
r50_5_7 253.18 0.00 3.41 145.70 253.18 253.18 253.18 219.5 0.00 0.00 0.00
r50_5_8 266.68 0.00 3.42 350.10 266.68 266.68 266.68 213.9 0.00 0.00 0.00
r50_5_9 267.56 6.81 1.71 328.60 267.56 267.70 268.30 206.5 0.00 0.05 0.28
r50_5_10 273.60 0.00 3.82 332.60 273.60 273.60 273.60 178.1 0.00 0.00 0.00
   Avg. 2.75 276.70     207.2 0.00 0.06 0.18
r75_5_1 362.33 9.70 0.60 647.60 358.50 359.57 361.20 757.8 \(-\) 1.06 \(-\) 0.76 \(-\) 0.31
r75_5_2 383.73 11.10 0.12 660.72 372.52 374.88 377.38 749.4 \(-\) 2.92 \(-\) 2.31 \(-\) 1.65
r75_5_3 377.57 13.55 4.02 804.05 375.72 378.42 380.12 623.8 \(-\) 0.49 0.23 0.68
r75_5_4 395.68 11.79 0.66 840.28 387.94 388.59 391.19 577.3 \(-\) 1.96 \(-\) 1.79 \(-\) 1.13
r75_5_5 410.07 19.23 \(-\) 2.11 911.89 378.09 378.09 378.09 551.7 \(-\) 7.80 \(-\) 7.80 \(-\) 7.80
r75_5_6 386.60 14.20 2.18 1001.57 377.79 380.50 382.32 769.9 \(-\) 2.28 \(-\) 1.58 \(-\) 1.11
r75_5_7 378.68 9.21 2.90 670.05 377.10 378.35 379.44 646.4 \(-\) 0.42 \(-\) 0.09 0.20
r75_5_8 378.07 12.84 2.71 752.47 365.39 366.77 367.96 678.0 \(-\) 3.35 \(-\) 2.99 \(-\) 2.67
r75_5_9 379.16 16.77 2.93 680.17 372.78 373.18 373.45 781.5 \(-\) 1.68 \(-\) 1.58 \(-\) 1.51
r75_5_10 360.79 3.25 3.33 754.99 361.44 361.64 362.11 832.8 0.18 0.24 0.37
   Avg. 1.73 772.38     696.8 \(-\) 2.18 \(-\) 1.84 \(-\) 1.49
   Total avg. 1.53       \(-\) 0.73 \(-\) 0.59 \(-\) 0.43