Research Article
A Simulated Annealing Heuristic for the Capacitated Green Vehicle Routing Problem
Table 6
SA performance for small CGVRP instances.
| | Sample | CPLEX | SA | | Exact solution | Number of tours | Customers served | Total cost | Number of tours | Customers served | Time | Absolute diff CPLEX | | (miles) | (miles) | (s) | (%) |
| | 20c3sUCAP1 | 1632.01 | 5 | 20 | 1632.02 | 5 | 20 | 12.98 | 0.00 | | 20c3sUCAP2 | 1542.61 | 6 | 20 | 1574.13 | 6 | 20 | 13.67 | 2.04 | | 20c3sUCAP3 | 1624.73 | 6 | 20 | 1624.73 | 6 | 20 | 12.51 | 0.00 | | 20c3sUCAP4 | 1462.89 | 5 | 20 | 1462.89 | 5 | 20 | 11.99 | 0.00 | | 20c3sUCAP5 | 1661.29 | 6 | 20 | 1661.29 | 6 | 20 | 11.88 | 0.00 | | 20c3sUCAP6 | 1537.07 | 5 | 20 | 1537.07 | 5 | 20 | 12.84 | 0.00 | | 20c3sUCAP7 | 1586.42 | 6 | 20 | 1586.42 | 6 | 20 | 12.65 | 0.00 | | 20c3sUCAP8 | 1705.82 | 6 | 20 | 1705.82 | 6 | 20 | 12.14 | 0.00 | | 20c3sUCAP9 | 1708.1 | 6 | 20 | 1708.1 | 6 | 20 | 12.87 | 0.00 | | 20c3sUCAP10 | 1180.86 | 4 | 20 | 1212.24 | 5 | 20 | 12.63 | 2.66 |
| | 20c3sCCAP1 | 1173.09 | 4 | 20 | 1173.1 | 4 | 20 | 12.68 | 0.00 | | 20c3sCCAP2 | 1539.34 | 5 | 19 | 1567.16 | 6 | 19 | 12.84 | 1.81 | | 20c3sCCAP3 | 879.863 | 3 | 12 | 879.862 | 3 | 12 | 9.76 | 0.00 | | 20c3sCCAP4 | 978.428 | 4 | 18 | 978.428 | 4 | 18 | 12.17 | 0.00 | | 20c3sCCAP5 | 2189.77 | 7 | 19 | 2138.69 | 7 | 19 | 12.90 | 2.33 | | 20c3sCCAP6 | 2332.4 | 7 | 17 | 2332.4 | 7 | 17 | 11.83 | 0.00 | | 20c3sCCAP7 | 1054.98 | 3 | 6 | 1054.98 | 3 | 6 | 8.00 | 0.00 | | 20c3sCCAP8 | 3139.92 | 9 | 18 | 3117.55 | 9 | 18 | 13.59 | 0.71 | | 20c3sCCAP9 | 1643.55 | 5 | 19 | 1687.43 | 6 | 19 | 12.27 | 2.67 | | 20c3sCCAP10 | 2583.42 | 8 | 15 | 2571.24 | 9 | 15 | 12.44 | 0.47 |
| | S1_2i6sCAP | 1567.39 | 6 | 20 | 1567.39 | 6 | 20 | 12.52 | 0.00 | | S1_4i6sCAP | 1396.69 | 5 | 20 | 1396.69 | 5 | 20 | 13.42 | 0.00 | | S1_6i6sCAP | 1519.7 | 5 | 20 | 1519.7 | 5 | 20 | 12.93 | 0.00 | | S1_8i6sCAP | 1623.57 | 6 | 20 | 1623.57 | 6 | 20 | 12.68 | 0.00 | | S1_10i6sCAP | 1173.04 | 4 | 20 | 1173.04 | 4 | 20 | 13.05 | 0.00 | | S2_2i6sCAP | 1633.17 | 6 | 20 | 1645.88 | 6 | 20 | 12.73 | 0.78 | | S2_4i6sCAP | 1498.5 | 5 | 19 | 1504.42 | 6 | 19 | 12.74 | 0.40 | | S2_6i6sCAP | 2625.97 | 8 | 20 | 2626.46 | 8 | 20 | 13.54 | 0.02 | | S2_8i6sCAP | 2158.35 | 7 | 16 | 2174.85 | 7 | 16 | 11.26 | 0.76 | | S2_10i6sCAP | 1486.11 | 6 | 16 | 1552.78 | 6 | 16 | 12.35 | 4.49 |
| | S1_4i2sCAP | 1581.56 | 6 | 20 | 1581.56 | 6 | 20 | 12.74 | 0.00 | | S1_4i4sCAP | 1460.09 | 5 | 20 | 1459.49 | 5 | 20 | 12.75 | 0.04 | | S1_4i6sCAP | 1396.69 | 5 | 20 | 1396.69 | 5 | 20 | 12.98 | 0.00 | | S1_4i8sCAP | 1396.69 | 5 | 20 | 1396.69 | 5 | 20 | 12.74 | 0.00 | | S1_4i10sCAP | 1395.46 | 5 | 20 | 1395.16 | 5 | 20 | 12.98 | 0.02 | | S2_4i2sCAP | 978.428 | 4 | 18 | 978.428 | 4 | 18 | 11.96 | 0.00 | | S2_4i4sCAP | 1364.98 | 5 | 19 | 1365.08 | 5 | 19 | 12.88 | 0.01 | | S2_4i6sCAP | 1353.03 | 5 | 20 | 1353.03 | 5 | 20 | 12.22 | 0.00 | | S2_4i8sCAP | 1353.03 | 5 | 20 | 1353.03 | 5 | 20 | 12.65 | 0.00 | | S2_4i10sCAP | 1353.13 | 5 | 20 | 1353.02 | 5 | 20 | 12.30 | 0.01 |
| | Average | | | | | | | 12.45 | 0.48 |
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a indicates a nonoptimal solution because the model is relaxed by determining the number of tours.
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