Journal of Computer Applications ›› 2024, Vol. 44 ›› Issue (4): 1187-1194.DOI: 10.11772/j.issn.1001-9081.2023101512
Special Issue: 先进计算
• Advanced computing • Previous Articles Next Articles
Received:
2023-11-06
Revised:
2024-01-10
Accepted:
2024-01-12
Online:
2024-04-22
Published:
2024-04-10
Contact:
Zhou HE
About author:
LI Jianqiang, born in 1998, M. S. candidate. His research interests include vehicle path planning, combinatorial optimization.Supported by:
通讯作者:
何舟
作者简介:
李建强(1998—),男,甘肃定西人,硕士研究生,主要研究方向:车辆路径规划、组合优化基金资助:
CLC Number:
Jianqiang LI, Zhou HE. Hybrid NSGA-Ⅱ for vehicle routing problem with multi-trip pickup and delivery[J]. Journal of Computer Applications, 2024, 44(4): 1187-1194.
李建强, 何舟. 面向多行程取送货车辆路径问题的混合NSGA-Ⅱ[J]. 《计算机应用》唯一官方网站, 2024, 44(4): 1187-1194.
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URL: https://www.joca.cn/EN/10.11772/j.issn.1001-9081.2023101512
算例名称 | K | n | 不同算法的距离成本 | ||
---|---|---|---|---|---|
MA | ILS-ANS | 混合NSGA-Ⅱ | |||
1 | 2 | 10 | 133 | 137 | 133 |
2 | 2 | 10 | 157 | 157 | 157 |
3 | 2 | 10 | 158 | 158 | 158 |
4 | 2 | 10 | 155 | 161 | 155 |
5 | 2 | 11 | 137 | 140 | 133 |
6 | 2 | 11 | 148 | 148 | 147 |
7 | 2 | 11 | 162 | 162 | 162 |
8 | 2 | 11 | 134 | 137 | 134 |
9 | 2 | 11 | 159 | 161 | 159 |
10 | 2 | 11 | 184 | 192 | 184 |
11 | 2 | 11 | 156 | 156 | 156 |
12 | 2 | 12 | 146 | 146 | 144 |
13 | 2 | 12 | 150 | 152 | 149 |
14 | 2 | 12 | 142 | 142 | 142 |
15 | 2 | 12 | 151 | 155 | 151 |
16 | 2 | 12 | 200 | 200 | 198 |
17 | 2 | 12 | 160 | 163 | 160 |
18 | 2 | 13 | 142 | 145 | 142 |
19 | 2 | 13 | 136 | 136 | 136 |
20 | 2 | 13 | 139 | 141 | 139 |
21 | 2 | 13 | 155 | 155 | 154 |
22 | 2 | 13 | 155 | 160 | 154 |
23 | 2 | 13 | 139 | 139 | 139 |
24 | 2 | 14 | 124 | 130 | 124 |
25 | 2 | 14 | 124 | 124 | 124 |
26 | 2 | 14 | 139 | 161 | 139 |
27 | 2 | 14 | 156 | 160 | 152 |
28 | 2 | 14 | 121 | 121 | 121 |
29 | 2 | 15 | 137 | 139 | 137 |
30 | 2 | 15 | 138 | 140 | 138 |
Tab. 1 Results of small-scale instances
算例名称 | K | n | 不同算法的距离成本 | ||
---|---|---|---|---|---|
MA | ILS-ANS | 混合NSGA-Ⅱ | |||
1 | 2 | 10 | 133 | 137 | 133 |
2 | 2 | 10 | 157 | 157 | 157 |
3 | 2 | 10 | 158 | 158 | 158 |
4 | 2 | 10 | 155 | 161 | 155 |
5 | 2 | 11 | 137 | 140 | 133 |
6 | 2 | 11 | 148 | 148 | 147 |
7 | 2 | 11 | 162 | 162 | 162 |
8 | 2 | 11 | 134 | 137 | 134 |
9 | 2 | 11 | 159 | 161 | 159 |
10 | 2 | 11 | 184 | 192 | 184 |
11 | 2 | 11 | 156 | 156 | 156 |
12 | 2 | 12 | 146 | 146 | 144 |
13 | 2 | 12 | 150 | 152 | 149 |
14 | 2 | 12 | 142 | 142 | 142 |
15 | 2 | 12 | 151 | 155 | 151 |
16 | 2 | 12 | 200 | 200 | 198 |
17 | 2 | 12 | 160 | 163 | 160 |
18 | 2 | 13 | 142 | 145 | 142 |
19 | 2 | 13 | 136 | 136 | 136 |
20 | 2 | 13 | 139 | 141 | 139 |
21 | 2 | 13 | 155 | 155 | 154 |
22 | 2 | 13 | 155 | 160 | 154 |
23 | 2 | 13 | 139 | 139 | 139 |
24 | 2 | 14 | 124 | 130 | 124 |
25 | 2 | 14 | 124 | 124 | 124 |
26 | 2 | 14 | 139 | 161 | 139 |
27 | 2 | 14 | 156 | 160 | 152 |
28 | 2 | 14 | 121 | 121 | 121 |
29 | 2 | 15 | 137 | 139 | 137 |
30 | 2 | 15 | 138 | 140 | 138 |
算例名称 | K | n | 不同算法的距离成本 | ||
---|---|---|---|---|---|
MA | ILS-ANS | 混合NSGA-Ⅱ | |||
101 | 2 | 29 | 296 | 305 | 281 |
102 | 2 | 32 | 286 | 290 | 267 |
103 | 2 | 37 | 314 | 320 | 280 |
108 | 3 | 50 | 408 | 415 | 398 |
Tab. 2 Results of large-scale instances
算例名称 | K | n | 不同算法的距离成本 | ||
---|---|---|---|---|---|
MA | ILS-ANS | 混合NSGA-Ⅱ | |||
101 | 2 | 29 | 296 | 305 | 281 |
102 | 2 | 32 | 286 | 290 | 267 |
103 | 2 | 37 | 314 | 320 | 280 |
108 | 3 | 50 | 408 | 415 | 398 |
算例 名称 | K | n | NSGA-Ⅱ | NSGA-Ⅱ-ALNS | NSGA-Ⅱ-ANS | 混合NSGA-Ⅱ | ||||
---|---|---|---|---|---|---|---|---|---|---|
距离成本 | CPU运行时间/s | 距离成本 | CPU运行时间/s | 距离成本 | CPU运行时间/s | 距离成本 | CPU运行时间/s | |||
1 | 2 | 10 | 189 | 317.50 | 133 | 10.15 | 133 | 19.17 | 133 | 2.49 |
2 | 2 | 10 | 211 | 132.73 | 157 | 9.48 | 178 | 12.82 | 157 | 4.21 |
3 | 2 | 10 | 223 | 461.30 | 160 | 15.96 | 158 | 19.11 | 158 | 2.39 |
4 | 2 | 10 | 178 | 478.18 | 155 | 13.69 | 155 | 3.97 | 155 | 3.28 |
5 | 2 | 11 | 165 | 223.26 | 133 | 29.88 | 133 | 45.39 | 133 | 5.06 |
6 | 2 | 11 | 223 | 168.30 | 147 | 48.93 | 147 | 36.16 | 147 | 3.78 |
7 | 2 | 11 | 219 | 387.07 | 162 | 16.68 | 162 | 28.86 | 162 | 3.90 |
8 | 2 | 11 | 192 | 403.62 | 142 | 25.36 | 134 | 28.29 | 134 | 4.09 |
9 | 2 | 11 | 251 | 266.20 | 159 | 7.89 | 175 | 54.00 | 159 | 0.75 |
10 | 2 | 11 | 244 | 384.16 | 184 | 25.69 | 184 | 32.42 | 184 | 4.58 |
11 | 2 | 11 | 238 | 519.06 | 161 | 13.95 | 156 | 22.75 | 156 | 4.01 |
12 | 2 | 12 | 172 | 202.14 | 144 | 33.47 | 144 | 34.48 | 144 | 5.09 |
13 | 2 | 12 | 196 | 486.79 | 149 | 38.43 | 165 | 18.57 | 149 | 4.34 |
14 | 2 | 12 | 161 | 492.86 | 143 | 30.75 | 142 | 38.21 | 142 | 4.58 |
15 | 2 | 12 | 206 | 182.43 | 151 | 24.15 | 172 | 19.98 | 151 | 5.44 |
16 | 2 | 12 | 277 | 493.42 | 198 | 19.87 | 221 | 32.05 | 198 | 3.79 |
17 | 2 | 12 | 221 | 210.41 | 160 | 14.95 | 160 | 38.86 | 160 | 5.29 |
18 | 2 | 13 | 197 | 463.42 | 142 | 41.16 | 174 | 20.60 | 142 | 4.21 |
19 | 2 | 13 | 170 | 310.66 | 136 | 2.51 | 136 | 17.09 | 136 | 1.71 |
20 | 2 | 13 | 214 | 287.47 | 139 | 6.01 | 200 | 32.05 | 139 | 3.09 |
21 | 2 | 13 | 179 | 412.47 | 154 | 28.20 | 171 | 49.26 | 154 | 4.33 |
22 | 2 | 13 | 234 | 592.10 | 160 | 26.45 | 161 | 39.63 | 154 | 4.86 |
23 | 2 | 13 | 178 | 248.56 | 139 | 30.49 | 156 | 34.86 | 139 | 3.46 |
24 | 2 | 14 | 134 | 341.21 | 124 | 60.85 | 151 | 36.69 | 124 | 4.82 |
25 | 2 | 14 | 207 | 404.90 | 124 | 16.70 | 154 | 29.96 | 124 | 2.19 |
26 | 2 | 14 | 225 | 410.43 | 139 | 13.30 | 162 | 39.88 | 139 | 6.09 |
27 | 2 | 14 | 248 | 544.61 | 152 | 21.76 | 220 | 47.50 | 152 | 10.71 |
28 | 2 | 14 | 198 | 433.33 | 121 | 12.66 | 121 | 21.59 | 121 | 3.05 |
29 | 2 | 15 | 242 | 345.63 | 137 | 31.50 | 137 | 84.03 | 137 | 7.29 |
30 | 2 | 15 | 277 | 213.21 | 138 | 9.61 | 163 | 33.11 | 138 | 2.39 |
101 | 2 | 29 | — | — | 298 | 1 677.83 | 315 | 818.23 | 280 | 408.16 |
102 | 2 | 32 | — | — | 268 | 1 953.97 | 283 | 946.05 | 267 | 617.52 |
103 | 2 | 37 | — | — | 310 | 2 108.71 | 322 | 1 093.89 | 280 | 441.31 |
108 | 3 | 50 | — | — | 421 | 2 508.71 | 433 | 1 779.71 | 398 | 907.53 |
Tab. 3 Ablation experimental results of hybrid NSGA-Ⅱ
算例 名称 | K | n | NSGA-Ⅱ | NSGA-Ⅱ-ALNS | NSGA-Ⅱ-ANS | 混合NSGA-Ⅱ | ||||
---|---|---|---|---|---|---|---|---|---|---|
距离成本 | CPU运行时间/s | 距离成本 | CPU运行时间/s | 距离成本 | CPU运行时间/s | 距离成本 | CPU运行时间/s | |||
1 | 2 | 10 | 189 | 317.50 | 133 | 10.15 | 133 | 19.17 | 133 | 2.49 |
2 | 2 | 10 | 211 | 132.73 | 157 | 9.48 | 178 | 12.82 | 157 | 4.21 |
3 | 2 | 10 | 223 | 461.30 | 160 | 15.96 | 158 | 19.11 | 158 | 2.39 |
4 | 2 | 10 | 178 | 478.18 | 155 | 13.69 | 155 | 3.97 | 155 | 3.28 |
5 | 2 | 11 | 165 | 223.26 | 133 | 29.88 | 133 | 45.39 | 133 | 5.06 |
6 | 2 | 11 | 223 | 168.30 | 147 | 48.93 | 147 | 36.16 | 147 | 3.78 |
7 | 2 | 11 | 219 | 387.07 | 162 | 16.68 | 162 | 28.86 | 162 | 3.90 |
8 | 2 | 11 | 192 | 403.62 | 142 | 25.36 | 134 | 28.29 | 134 | 4.09 |
9 | 2 | 11 | 251 | 266.20 | 159 | 7.89 | 175 | 54.00 | 159 | 0.75 |
10 | 2 | 11 | 244 | 384.16 | 184 | 25.69 | 184 | 32.42 | 184 | 4.58 |
11 | 2 | 11 | 238 | 519.06 | 161 | 13.95 | 156 | 22.75 | 156 | 4.01 |
12 | 2 | 12 | 172 | 202.14 | 144 | 33.47 | 144 | 34.48 | 144 | 5.09 |
13 | 2 | 12 | 196 | 486.79 | 149 | 38.43 | 165 | 18.57 | 149 | 4.34 |
14 | 2 | 12 | 161 | 492.86 | 143 | 30.75 | 142 | 38.21 | 142 | 4.58 |
15 | 2 | 12 | 206 | 182.43 | 151 | 24.15 | 172 | 19.98 | 151 | 5.44 |
16 | 2 | 12 | 277 | 493.42 | 198 | 19.87 | 221 | 32.05 | 198 | 3.79 |
17 | 2 | 12 | 221 | 210.41 | 160 | 14.95 | 160 | 38.86 | 160 | 5.29 |
18 | 2 | 13 | 197 | 463.42 | 142 | 41.16 | 174 | 20.60 | 142 | 4.21 |
19 | 2 | 13 | 170 | 310.66 | 136 | 2.51 | 136 | 17.09 | 136 | 1.71 |
20 | 2 | 13 | 214 | 287.47 | 139 | 6.01 | 200 | 32.05 | 139 | 3.09 |
21 | 2 | 13 | 179 | 412.47 | 154 | 28.20 | 171 | 49.26 | 154 | 4.33 |
22 | 2 | 13 | 234 | 592.10 | 160 | 26.45 | 161 | 39.63 | 154 | 4.86 |
23 | 2 | 13 | 178 | 248.56 | 139 | 30.49 | 156 | 34.86 | 139 | 3.46 |
24 | 2 | 14 | 134 | 341.21 | 124 | 60.85 | 151 | 36.69 | 124 | 4.82 |
25 | 2 | 14 | 207 | 404.90 | 124 | 16.70 | 154 | 29.96 | 124 | 2.19 |
26 | 2 | 14 | 225 | 410.43 | 139 | 13.30 | 162 | 39.88 | 139 | 6.09 |
27 | 2 | 14 | 248 | 544.61 | 152 | 21.76 | 220 | 47.50 | 152 | 10.71 |
28 | 2 | 14 | 198 | 433.33 | 121 | 12.66 | 121 | 21.59 | 121 | 3.05 |
29 | 2 | 15 | 242 | 345.63 | 137 | 31.50 | 137 | 84.03 | 137 | 7.29 |
30 | 2 | 15 | 277 | 213.21 | 138 | 9.61 | 163 | 33.11 | 138 | 2.39 |
101 | 2 | 29 | — | — | 298 | 1 677.83 | 315 | 818.23 | 280 | 408.16 |
102 | 2 | 32 | — | — | 268 | 1 953.97 | 283 | 946.05 | 267 | 617.52 |
103 | 2 | 37 | — | — | 310 | 2 108.71 | 322 | 1 093.89 | 280 | 441.31 |
108 | 3 | 50 | — | — | 421 | 2 508.71 | 433 | 1 779.71 | 398 | 907.53 |
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