Research Article
A Problem-Reduction Evolutionary Algorithm for Solving the Capacitated Vehicle Routing Problem
Table 2
Solutions for the CVRPs of Golden et al. [
21].
| | Problem data | IVND1 | ILS-RVND-SP | PREA () | PREA () | | Prob. | BKS | Best
gap (%) | CPU (s) | Best
gap (%) | Avg.
gap (%) | CPU (s) | Best
gap (%) | Avg.
gap (%) | CPU (s) | Best
gap (%) | Avg.
gap (%) | CPU (s) |
| | G1 (240) | 5623.47/9 | 0.64 | — | 0.61 | 0.86 | 994.6 | 0.26 | 1.35 | 74.6 | 0.23 | 0.32 | 410.29 | | G2 (320) | 8404.61/10 | 0.72 | — | 0.52 | 0.54 | 2659.7 | 0.52 | 0.61 | 185.5 | 0.52 | 0.52 | 613.93 | | G3 (400) | 11036.22/10 | 0.21 | — | 0.00 | 0.00 | 6065.0 | 0.00 | 0.02 | 131.6 | 0.00 | 0.00 | 380.02 | | G4 (480) | 13592.88/10 | 0.23 | — | 0.23 | 0.23 | 10644.5 | 0.23 | 0.24 | 162.0 | 0.23 | 0.23 | 510.43 | | G5 (200) | 6460.98/5 | 0.00 | — | 0.00 | 0.00 | 978.7 | 0.00 | 0.00 | 6.5 | 0.00 | 0.00 | 17.08 | | G6 (280) | 8404.26/7 | 0.10 | — | 0.10 | 0.10 | 2455.6 | 0.10 | 0.11 | 18.5 | 0.10 | 0.10 | 68.10 | | G7 (360) | 10102.7/9 | 1.63 | — | 0.92 | 0.92 | 4410.8 | 0.92 | 0.92 | 121.5 | 0.92 | 0.92 | 237.79 | | G8 (440) | 11635.3/10 | 1.22 | — | 0.65 | 1.20 | 7541.8 | 1.59 | 1.71 | 433.6 | 1.27 | 1.45 | 1450.41 | | G9 (255) | 579.71/14 | 0.95 | — | 0.61 | 0.95 | 1720.8 | 0.56 | 0.80 | 92.8 | 0.26 | 0.58 | 284.01 | | G10 (323) | 736.26/16 | 1.26 | — | 0.77 | 1.07 | 3229.4 | 0.28 | 0.64 | 251.3 | 0.32 | 0.44 | 531.94 | | G11 (399) | 912.84/18 | 1.13 | — | 0.94 | 1.11 | 5979.0 | 0.22 | 0.33 | 874.0 | 0.13 | 0.22 | 1865.32 | | G12 (483) | 1102.69/19 | 1.38 | — | 0.96 | 1.25 | 10410.7 | 0.19 | 0.37 | 1901.6 | 0.15 | 0.27 | 2896.87 | | G13 (252) | 857.19/26 | 0.52 | — | 0.00 | 0.33 | 910.4 | 0.33 | 0.48 | 176.7 | 0.00 | 0.10 | 622.49 | | G14 (320) | 1080.55/30 | 0.77 | — | 0.00 | 0.15 | 1513.3 | 0.00 | 0.24 | 228.0 | 0.00 | 0.03 | 1363.32 | | G15 (396) | 1337.92/33 | 1.38 | — | 0.69 | 0.85 | 3265.7 | 0.29 | 0.42 | 1072.5 | 0.07 | 0.27 | 4742.69 | | G16 (480) | 1612.5/37 | 1.53 | — | 0.75 | 0.95 | 4835.1 | 0.45 | 0.60 | 1746.0 | −0.03 | 0.29 | 4441.63 | | G17 (240) | 707.76/22 | 0.16 |
— | 0.00 | 0.01 | 937.6 | <0.01 | 0.08 | 142.5 | <0.01 | 0.02 | 602.65 | | G18 (300) | 995.13/27 | 1.55 | — | 0.05 | 0.27 | 2297.6 | 1.15 | 1.30 | 250.4 | 0.29 | 0.79 | 1430.09 | | G19 (360) | 1365.6/33 | 1.25 | — | 0.05 | 0.12 | 2917.3 | 0.09 | 0.19 | 755.7 | 0.03 | 0.10 | 2418.39 | | G20 (420) | 1818.32/38 | 1.19 | — | 0.16 | 0.29 | 4997.3 | 0.14 | 0.23 | 2758.6 | 0.01 | 0.11 | 6290.95 |
| | Avg. gap | | 0.89 | | 0.40 | 0.56 | | 0.37 | 0.53 | | 0.23 | 0.34 | | | Avg. CPU (s) | | | 1706.40 | | | 3938.23 | | | 569.19 | | | 1558.92 | | Computer | | Pentium IV 2.93 G | Intel Core i7 2.93 GHz | Intel Core E7500 2.93 GHz |
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The average running time and average solution for each problem are not provided.
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