Research Article
Comparative Study of Swarm-Based Algorithms for Location-Allocation Optimization of Express Depots
Table 5
The averaged optimal costs and standard deviations with various numbers of DCs and DPs.
| | Number of DCs | Algorithm | Encoding scheme | Number of DPs | | #DP = 10 | #DP = 20 | #DP = 30 | #DP = 40 | #DP = 50 |
| | #DC = 2 | PSO | RPK | 9.75 (0.2) | 17.71 (1.1) | 28.93 (0.9) | 63.35 (1.1) | 100.94 (0.9) | | TES | 10.00 (0.6) | 19.14 (0.8) | 31.29 (1.1) | 66.06 (1.3) | 104.53 (1.6) | | DE | RPK | 9.79 (0.0) | 16.18 (0.4) | 27.11 (0.3) | 60.78 (0.3) | 97.12 (0.6) | | TES | 9.17 (0.3) | 16.65 (0.6) | 27.39 (0.5) | 61.36 (0.7) | 102.68 (3.7) | | ABC | RPK | 9.00 (0.2) | 15.94 (0.0) | 27.07 (0.2) | 60.52 (0.1) | 97.19 (0.2) | | TES | 9.16 (0.3) | 16.76 (0.4) | 28.22 (0.6) | 62.24 (0.7) | 99.26 (0.9) | | LDES | RPK | 9.76 (0.2) | 15.94 (0.0) | 27.04 (0.3) | 60.90 (0.3) | 97.11 (0.3) | | TES | 8.87 (0.1) | 16.12 (0.2) | 28.47 (0.7) | 63.70 (0.9) | 102.22 (1.0) |
| | #DC = 4 | PSO | RPK | 9.74 (0.2) | 17.20 (0.9) | 25.67 (1.1) | 36.72 (1.7) | 46.76 (1.7) | | TES | 12.38 (0.8) | 21.14 (1.3) | 29.44 (1.9) | 42.22 (1.6) | 54.54 (2.1) | | DE | RPK | 9.79 (0.0) | 15.95 (0.0) | 21.69 (0.7) | 34.98 (2.5) | 44.31 (2.1) | | TES | 12.09 (0.5) | 17.95 (0.4) | 24.19 (1.3) | 37.95 (2.6) | 48.81 (3.4) | | ABC | RPK | 8.94 (0.2) | 15.59 (0.3) | 21.43 (0.4) | 30.07 (0.6) | 38.86 (0.6) | | TES | 10.85 (0.3) | 16.68 (0.5) | 22.56 (0.6) | 32.68 (0.9) | 42.24 (1.3) | | LDES | RPK | 9.75 (0.1) | 15.94 (0.0) | 22.01 (0.4) | 31.75 (1.3) | 41.42 (1.4) | | TES | 10.99 (0.3) | 17.74 (0.5) | 24.52 (1.0) | 35.54 (1.5) | 46.47 (1.6) |
| | #DC = 6 | PSO | RPK | 9.76 (0.1) | 17.74 (0.9) | 25.53 (1.2) | 36.94 (1.5) | 45.41 (1.6) | | TES | 15.42 (1.2) | 23.72 (1.6) | 33.20 (1.9) | 44.28 (2.5) | 53.08 (2.3) | | DE | RPK | 9.79 (0.0) | 15.94 (0.0) | 21.44 (0.5) | 34.33 (2.7) | 41.59 (3.0) | | TES | 14.25 (0.8) | 20.49 (0.6) | 26.99 (1.4) | 40.48 (3.5) | 51.23 (5.3) | | ABC | RPK | 8.92 (0.2) | 15.53 (0.4) | 21.55 (0.4) | 30.11 (0.6) | 36.45 (1.1) | | TES | 12.72 (0.2) | 18.46 (0.4) | 23.88 (0.5) | 31.47 (0.8) | 37.29 (1.0) | | LDES | RPK | 9.79 (0.0) | 15.94 (0.0) | 22.21 (0.7) | 31.52 (1.6) | 39.23 (2.4) | | TES | 13.19 (0.5) | 20.39 (0.9) | 26.53 (1.1) | 35.21 (1.3) | 41.94 (2.1) |
| | #DC = 8 | PSO | RPK | 9.73 (0.2) | 17.31 (0.9) | 25.66 (1.3) | 37.13 (1.5) | 45.11 (1.8) | | TES | 17.94 (1.2) | 27.92 (1.9) | 37.98 (2.1) | 48.02 (3.0) | 56.36 (3.3) | | DE | RPK | 9.78 (0.0) | 15.96 (0.0) | 23.17 (1.1) | 34.54 (1.9) | 43.21 (3.8) | | TES | 15.37 (0.5) | 22.49 (0.5) | 36.58 (2.5) | 48.52 (10.8) | 58.75 (15.8) | | ABC | RPK | 8.94 (0.2) | 15.54 (0.4) | 21.49 (0.4) | 30.32 (0.5) | 36.47 (0.7) | | TES | 14.76 (0.2) | 20.41 (0.4) | 25.98 (0.5) | 32.75 (0.6) | 37.29 (0.8) | | LDES | RPK | 9.79 (0.0) | 15.96 (0.1) | 22.27 (0.7) | 31.10 (1.5) | 38.72 (2.7) | | TES | 15.73 (0.7) | 22.22 (0.8) | 29.23 (2.2) | 36.24 (1.3) | 42.00 (2.1) |
| | #DC = 10 | PSO | RPK | 9.76 (0.1) | 17.86 (1.1) | 25.67 (1.7) | 36.81 (1.3) | 45.10 (1.8) | | TES | 22.21 (1.9) | 31.67 (3.0) | 41.91 (3.3) | 52.69 (3.1) | 60.96 (3.4) | | DE | RPK | 9.78 (0.1) | 17.02 (0.7) | 24.45 (1.3) | 33.70 (2.0) | 40.60 (3.1) | | TES | 17.60 (0.7) | 24.81 (0.8) | 39.60 (3.1) | 57.69 (14.9) | 82.14 (27.3) | | ABC | RPK | 9.07 (0.2) | 15.47 (0.4) | 21.66 (0.7) | 30.33 (0.7) | 36.75 (0.9) | | TES | 16.74 (0.2) | 22.40 (0.5) | 27.97 (0.5) | 34.60 (0.5) | 39.06 (0.8) | | LDES | RPK | 9.69 (0.3) | 15.95 (0.0) | 22.62 (0.9) | 31.09 (1.9) | 38.77 (2.5) | | TES | 17.40 (0.5) | 23.96 (0.9) | 31.38 (2.5) | 38.13 (1.3) | 45.89 (4.5) |
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