Research Article
A Problem-Reduction Evolutionary Algorithm for Solving the Capacitated Vehicle Routing Problem
Table 1
Solutions for the CVRPs of Christofides and Eilon [
20].
| Prob. | BKS | IVND1 | ILS-RVND-SP | PREA () | PREA () | Best gap (%) | CPU (s) | Best gap (%) | Avg. gap (%) | CPU (s) | Best gap (%) | Avg. gap (%) | CPU (s) | Best. gap (%) | Avg. gap (%) | CPU (s) |
| C1 (50) | 524.61/5 | 0 | — | 0.00 | 0.00 | 1.5 | 0.00 | 0.00 | 2.6 | 0.00 | 0.00 | 7.7 | C2 (75) | 835.26/10 | 0 | — | 0.00 | 0.00 | 13.5 | 0.00 | 0.07 | 4.9 | 0.00 | 0.00 | 18.2 | C3 (100) | 826.14/8 | 0 | — | 0.00 | 0.00 | 12.5 | 0.00 | 0.28 | 1.6 | 0.00 | 0.17 | 5.3 | C4 (150) | 1028.42/12 | 0 | — | 0.00 | 0.03 | 53.5 | 0.03 | 0.37 | 5.9 | 0.12 | 0.35 | 15.6 | C5 (199) | 1291.29/16 | 0.47 | — | 0.01 | 0.15 | 625.2 | 0.48 | 1.16 | 40.2 | 0.02 | 0.75 | 124.2 | C6 (50) | 555.43/6 | 0 | — | 0.00 | 0.19 | 0.9 | 0.00 | 0.29 | 0.8 | 0.00 | 0.09 | 6.2 | C7 (75) | 909.68/11 | 0 | — | 0.00 | 0.04 | 5.1 | 0.00 | 0.21 | 2.5 | 0.00 | 0.15 | 6.5 | C8 (100) | 865.94/9 | 0 | — | 0.00 | 0.00 | 7.6 | 0.11 | 0.14 | 1.8 | 0.00 | 0.04 | 6.4 | C9 (150) | 1162.55/14 | 0.41 | — | 0.00 | 0.13 | 82.5 | 0.00 | 0.27 | 12.7 | 0.00 | 0.12 | 74.7 | C10 (199) | 1395.85/18 | 0.75 | — | 0.00 | 0.44 | 496.1 | 0.39 | 0.61 | 35.0 | 0.35 | 0.54 | 101.1 | C11 (120) | 1042.11/7 | 0 | — | 0.00 | 0.00 | 20.7 | 0.00 | 1.76 | 6.1 | 0.00 | 0.32 | 15.5 | C12 (100) | 819.56/10 | 0 | — | 0.00 | 0.00 | 5.2 | 0.00 | 0.00 | 0.4 | 0.00 | 0.00 | 0.8 | C13 (120) | 1541.14/11 | 0.12 | — | 0.00 | 0.19 | 80.2 | 0.38 | 1.17 | 5.5 | 0.17 | 0.93 | 28.9 | C14 (100) | 866.37/11 | 0 | — | 0.00 | 0.00 | 7.1 | 0.00 | 0.01 | 0.7 | 0.00 | 0.00 | 2.4 |
| Avg. gap | | 0.13 | | 0.00 | 0.08 | | 0.10 | 0.45 | | 0.05 | 0.25 | | Avg. CPU (s) | | | 65.4 | | | 100.83 | | | 8.82 | | | 29.23 | 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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