Research Article
A Simulated Annealing Heuristic for the Capacitated Green Vehicle Routing Problem
Table 4
Performance comparison on small GVRP instances.
| | Sample | CPLEX | MCWS | DBCA | VNS/TS | SA | | E S (miles) | N | C | N | C | T C | Diff (%) | T C | Diff (%) | T C | N | C | Time | Diff (%) | T C | N | C | Time | Diff | | (miles) | (miles) | (miles) | (s) | (miles) | (s) | (%) |
| | 20c3sU1 | 1632.0 | 5 | 20 | 6 | 20 | 1818.4 | 11.4 | 1797.5 | 10.1 | 1797.5 | 6 | 20 | 41.4 | 10.1 | 1632.02 | 5 | 20 | 11.71 | 0.00 | | 20c3sU2 | 1542.6 | 6 | 20 | 6 | 20 | 1614.2 | 4.6 | 1613.5 | 4.6 | 1574.8 | 6 | 20 | 38.4 | 2.1 | 1574.13 | 6 | 20 | 12.36 | 2.04 | | 20c3sU3 | 1624.7 | 6 | 20 | 7 | 20 | 1969.6 | 21.2 | 1964.6 | 20.9 | 1704.5 | 6 | 20 | 38.4 | 4.9 | 1624.73 | 6 | 20 | 11.63 | 0.00 | | 20c3sU4 | 1462.9 | 5 | 20 | 5 | 20 | 1508.4 | 3.1 | 1487.2 | 1.7 | 1482.0 | 5 | 20 | 39.0 | 1.3 | 1462.89 | 5 | 20 | 11.56 | 0.00 | | 20c3sU5 | 1661.3 | 6 | 20 | 6 | 20 | 1752.7 | 5.5 | 1752.7 | 5.5 | 1689.4 | 6 | 20 | 40.2 | 1.7 | 1661.29 | 6 | 20 | 11.84 | 0.00 | | 20c3sU6 | 1537.1 | 5 | 20 | 6 | 20 | 1668.2 | 8.5 | 1668.2 | 8.5 | 1618.7 | 6 | 20 | 40.2 | 5.3 | 1537.07 | 5 | 20 | 11.74 | 0.00 | | 20c3sU7 | 1586.4 | 6 | 20 | 6 | 20 | 1730.5 | 9.1 | 1730.5 | 9.1 | 1713.7 | 6 | 20 | 38.4 | 8 | 1586.42 | 6 | 20 | 11.84 | 0.00 | | 20c3sU8 | 1705.8 | 6 | 20 | 6 | 20 | 1718.7 | 0.8 | 1718.7 | 0.8 | 1706.5 | 6 | 20 | 40.2 | 0 | 1705.82 | 6 | 20 | 11.50 | 0.00 | | 20c3sU9 | 1708.1 | 6 | 20 | 6 | 20 | 1714.4 | 0.4 | 1714.4 | 0.4 | 1708.8 | 6 | 20 | 39.6 | 0 | 1708.1 | 6 | 20 | 11.96 | 0.00 | | 20c3sU10 | 1180.9 | 4 | 20 | 5 | 20 | 1309.5 | 10.9 | 1309.5 | 10.9 | 1181.3 | 4 | 20 | 38.4 | 0 | 1212.24 | 5 | 20 | 11.75 | 2.65 |
| | 20c3sC1 | 1173.1 | 4 | 20 | 5 | 20 | 1300.6 | 10.9 | 1300.6 | 10.9 | 1173.6 | 4 | 20 | 37.2 | 0 | 1173.1 | 4 | 20 | 11.50 | 0.00 | | 20c3sC2 | 1539.3 | 5 | 19 | 5 | 19 | 1553.5 | 0.9 | 1553.5 | 0.9 | 1540.0 | 5 | 19 | 34.8 | 0 | 1567.16 | 6 | 19 | 12.10 | 1.81 | | 20c3sC3 | 879.9 | 3 | 12 | 4 | 12 | 1083.1 | 23.1 | 1083.1 | 23.1 | 880.2 | 3 | 12 | 15.0 | 0 | 879.862 | 3 | 12 | 9.78 | 0.00 | | 20c3sC4 | 978.4 | 4 | 18 | 5 | 18 | 1135.9 | 16.1 | 1091.8 | 11.6 | 1059.4 | 4 | 18 | 31.8 | 8.3 | 978.428 | 4 | 18 | 11.59 | 0.00 | | 20c3sC5 | 2189.8 | 7 | 19 | 7 | 19 | 2190.7 | 0.0 | 2190.7 | 0.0 | 2156.0 | 7 | 19 | 36.0 | 1.5 | 2138.69 | 7 | 19 | 12.64 | 2.33 | | 20c3sC6 | 2332.4 | 7 | 17 | 9 | 17 | 2883.7 | 23.6 | 2883.7 | 23.6 | 2758.2 | 8 | 17 | 42.6 | 18.3 | 2332.4 | 7 | 17 | 12.10 | 0.00 | | 20c3sC7 | 1055.0 | 3 | 6 | 5 | 6 | 1701.4 | 61.3 | 1701.4 | 61.3 | 1394.0 | 4 | 6 | 10.8 | 32.1 | 1054.98 | 3 | 6 | 8.28 | 0.00 | | 20c3sC8 | 3139.7 | 9 | 18 | 10 | 18 | 3319.7 | 5.7 | 3319.7 | 5.7 | 3139.7 | 9 | 18 | 37.2 | 0 | 3235.57 | 10 | 18 | 12.96 | 3.05 | | 20c3sC9 | 1643.6 | 5 | 19 | 6 | 19 | 1811.1 | 10.2 | 1811.1 | 10.2 | 1799.9 | 6 | 19 | 36.0 | 9.5 | 1687.43 | 6 | 19 | 11.94 | 2.67 | | 20c3sC10 | 2583.4 | 8 | 15 | 8 | 15 | 2648.8 | 2.5 | 2644.1 | 2.4 | 2583.4 | 8 | 15 | 27.0 | 0 | 2571.24 | 9 | 15 | 11.56 | 0.47 |
| | S1_2i6s | 1567.4 | 6 | 20 | 6 | 20 | 1614.2 | 3.0 | 1614.2 | 3.0 | 1578.1 | 6 | 20 | 42.6 | 0.7 | 1567.39 | 6 | 20 | 12.95 | 0.00 | | S1_4i6s | 1396.7 | 5 | 20 | 5 | 20 | 1561.3 | 11.8 | 1541.5 | 10.4 | 1397.3 | 5 | 20 | 45.0 | 0 | 1396.69 | 5 | 20 | 12.05 | 0.00 | | S1_6i6s | 1519.7 | 5 | 20 | 6 | 20 | 1616.2 | 6.4 | 1616.2 | 6.4 | 1560.5 | 5 | 20 | 43.8 | 2.7 | 1519.7 | 5 | 20 | 12.18 | 0.00 | | S1_8i6s | 1623.6 | 6 | 20 | 6 | 20 | 1902.5 | 17.2 | 1882.5 | 16.0 | 1692.3 | 6 | 20 | 44.4 | 4.2 | 1623.57 | 6 | 20 | 12.31 | 0.00 | | S1_10i6s | 1173.0 | 4 | 20 | 5 | 20 | 1309.5 | 11.6 | 1309.5 | 11.6 | 1173.5 | 4 | 20 | 42.6 | 0 | 1173.04 | 4 | 20 | 12.41 | 0.00 | | S2_2i6s | 1633.2 | 6 | 20 | 6 | 20 | 1645.8 | 0.8 | 1645.8 | 0.8 | 1633.1 | 6 | 20 | 45.0 | 0 | 1645.1 | 6 | 20 | 12.28 | 0.73 | | S2_4i6s | 1498.5 | 5 | 19 | 6 | 19 | 1505.1 | 0.4 | 1505.1 | 0.4 | 1533.0 | 5 | 19 | 52.8 | 2.3 | 1504.42 | 6 | 19 | 12.26 | 0.40 | | S2_6i6s | 2626.0 | 8 | 20 | 10 | 20 | 3115.1 | 18.6 | 3115.1 | 18.6 | 2431.3 | 7 | 20 | 46.8 | 7.4 | 2626.46 | 8 | 20 | 12.97 | 0.02 | | S2_8i6s | 2158.4 | 7 | 16 | 9 | 16 | 2722.6 | 26.1 | 2722.6 | 26.1 | 2158.4 | 7 | 16 | 34.2 | 0 | 2174.85 | 7 | 16 | 11.41 | 0.76 | | S2_10i6s | 1486.1 | 6 | 16 | 6 | 16 | 1995.6 | 34.3 | 1995.6 | 34.3 | 1958.5 | 6 | 17 | 36.6 | 31.8 | 1511.38 | 6 | 16 | 11.46 | 1.70 |
| | S1_4i2s | 1581.6 | 6 | 20 | 6 | 20 | 1582.2 | 0.0 | 1582.2 | 0.0 | 1582.2 | 6 | 20 | 37.8 | 0 | 1581.56 | 6 | 20 | 12.23 | 0.00 | | S1_4i4s | 1459.5 | 5 | 20 | 6 | 20 | 1580.5 | 8.3 | 1580.5 | 8.3 | 1460.1 | 5 | 20 | 40.8 | 0 | 1459.49 | 5 | 20 | 12.09 | 0.00 | | S1_4i6s | 1396.7 | 5 | 20 | 5 | 20 | 1561.3 | 11.8 | 1541.5 | 10.4 | 1397.3 | 5 | 20 | 45.0 | 0 | 1396.69 | 5 | 20 | 11.99 | 0.00 | | S1_4i8s | 1396.7 | 5 | 20 | 6 | 20 | 1561.3 | 11.8 | 1561.3 | 11.8 | 1397.3 | 6 | 20 | 49.2 | 0 | 1396.69 | 5 | 20 | 12.33 | 0.00 | | S1_4i10s | 1395.5 | 5 | 20 | 5 | 20 | 1536.0 | 10.1 | 1529.7 | 9.6 | 1396.0 | 5 | 20 | 51.0 | 0 | 1395.16 | 5 | 20 | 12.00 | 0.02 | | S2_4i2s | 978.4 | 4 | 18 | 5 | 18 | 1135.9 | 16.1 | 1117.3 | 14.2 | 1059.4 | 4 | 18 | 30.6 | 8.3 | 978.428 | 4 | 18 | 11.46 | 0.00 | | S2_4i4s | 1365.0 | 5 | 19 | 6 | 19 | 1522.7 | 11.6 | 1522.7 | 11.6 | 1446.1 | 5 | 19 | 36.0 | 5.9 | 1365.08 | 5 | 19 | 12.78 | 0.01 | | S2_4i6s | 1353.0 | 5 | 20 | 6 | 20 | 1786.2 | 32.0 | 1730.5 | 27.9 | 1434.1 | 5 | 20 | 41.4 | 6 | 1353.03 | 5 | 20 | 12.16 | 0.00 | | S2_4i8s | 1353.0 | 5 | 20 | 6 | 20 | 1786.2 | 32.0 | 1786.2 | 32.0 | 1434.1 | 5 | 20 | 45.0 | 6 | 1353.03 | 5 | 20 | 12.13 | 0.00 | | S2_4i10s | 1353.1 | 5 | 20 | 6 | 20 | 1783.6 | 31.8 | 1729.5 | 27.8 | 1413.1 | 5 | 20 | 46.8 | 4.4 | 1353.02 | 5 | 20 | 12.11 | 0.01 |
| | Average | | | | | | | 13.1 | | 12.6 | | | | 39.0 | 4.57 | | | | 11.90 | 0.47 |
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E S = exact solution, N = number of tours, C = customers served, T C = total cost, Diff = absolute difference with CPLEX.
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