《计算机应用》唯一官方网站 ›› 2024, Vol. 44 ›› Issue (4): 1187-1194.DOI: 10.11772/j.issn.1001-9081.2023101512
• 先进计算 • 上一篇
收稿日期:
2023-11-06
修回日期:
2024-01-10
接受日期:
2024-01-12
发布日期:
2024-04-22
出版日期:
2024-04-10
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:
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:
摘要:
针对多行程取送货车辆路径问题(VRP)收敛性与多样性相互制约的问题,提出一种融合自适应大邻域搜索(ALNS)算法和自适应邻域选择(ANS)的混合快速非支配排序遗传算法(NSGA-Ⅱ-ALNS-ANS)。首先,考虑初始解对算法收敛速度的影响,提出一种改进的后悔插入法以获得高质量初始解;其次,结合取送货问题特性,设计多组破坏和修复算子,以及多种邻域结构,提高算法的全局搜索能力和局部搜索能力;最后,设计基于随机采样的最佳拟合下降(BFD)算法与高效的可行解评价标准,生成路径分配方案。采用不同规模的标准公开算例进行仿真实验,与模因算法(MA)相比,所提算法的最优解质量提升了27%。实验结果表明,所提算法可快速得到满足多重约束的高质量车辆多行程路径分配方案,并在收敛性与多样性上优于对比算法。
中图分类号:
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, 2024, 44(4): 1187-1194.
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.
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 |
表1 小规模算例结果
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 |
表2 大规模算例结果
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 |
表3 混合NSGA-Ⅱ消融实验结果
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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