Journal of Computer Applications ›› 2023, Vol. 43 ›› Issue (7): 2248-2254.DOI: 10.11772/j.issn.1001-9081.2022060812
• Advanced computing • Previous Articles Next Articles
Jian LIN1(), Jingxuan YE1, Wenwen LIU1,2, Xiaowen SHAO1,3
Received:
2022-06-06
Revised:
2022-08-29
Accepted:
2022-09-01
Online:
2023-07-20
Published:
2023-07-10
Contact:
Jian LIN
About author:
LIN Jian, born in 1983, Ph. D., professor. His research interests include scheduling, intelligent computation, intelligent logistics.Supported by:
通讯作者:
林剑
作者简介:
林剑(1983—),男,浙江温州人,教授,博士,CCF会员,主要研究方向:调度、智能计算、智慧物流;基金资助:
CLC Number:
Jian LIN, Jingxuan YE, Wenwen LIU, Xiaowen SHAO. Multimodal differential evolution algorithm for solving capacitated vehicle routing problem[J]. Journal of Computer Applications, 2023, 43(7): 2248-2254.
林剑, 叶璟轩, 刘雯雯, 邵晓雯. 求解带容量约束车辆路径问题的多模态差分进化算法[J]. 《计算机应用》唯一官方网站, 2023, 43(7): 2248-2254.
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URL: https://www.joca.cn/EN/10.11772/j.issn.1001-9081.2022060812
实例 | 真实值 | MDE | ||
---|---|---|---|---|
Best | Num | Best | Num | |
n5-k2-1 | 250 | 4 | 250 | 4 |
n5-k2-2 | 752 | 4 | 752 | 4 |
n5-k2-3 | 747 | 4 | 747 | 4 |
n5-k2-4 | 1 706 | 2 | 1 706 | 2 |
n5-k2-5 | 540 | 2 | 540 | 2 |
n6-k2-1 | 1 239 | 2 | 1 239 | 2 |
n6-k2-2 | 1 205 | 4 | 1 205 | 4 |
n6-k2-3 | 2 230 | 2 | 2 230 | 2 |
n6-k2-4 | 2 400 | 2 | 2 400 | 2 |
n6-k2-5 | 854 | 2 | 854 | 2 |
Tab. 1 Comparison of results obtained by MDE algorithm and real values
实例 | 真实值 | MDE | ||
---|---|---|---|---|
Best | Num | Best | Num | |
n5-k2-1 | 250 | 4 | 250 | 4 |
n5-k2-2 | 752 | 4 | 752 | 4 |
n5-k2-3 | 747 | 4 | 747 | 4 |
n5-k2-4 | 1 706 | 2 | 1 706 | 2 |
n5-k2-5 | 540 | 2 | 540 | 2 |
n6-k2-1 | 1 239 | 2 | 1 239 | 2 |
n6-k2-2 | 1 205 | 4 | 1 205 | 4 |
n6-k2-3 | 2 230 | 2 | 2 230 | 2 |
n6-k2-4 | 2 400 | 2 | 2 400 | 2 |
n6-k2-5 | 854 | 2 | 854 | 2 |
实例集 | 实例 | Best | Num | MDE | DE | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Avg | Dev | MaxNum | MinNum | AvgNum | Avg | Dev | MaxNum | MinNum | AvgNum | ||||
A | A-n32-k5 | 784 | 5 | 784.0 | 0.00 | 3 | 1 | 2.4 | 784.0 | 0.00 | 3 | 1 | 2.0 |
A-n33-k5 | 661 | 6 | 661.0 | 0.00 | 4 | 2 | 3.4 | 661.0 | 0.00 | 3 | 1 | 1.8 | |
A-n33-k6 | 742 | 6 | 742.0 | 0.00 | 4 | 1 | 2.2 | 742.0 | 0.00 | 5 | 1 | 2.0 | |
A-n34-k5 | 778 | 5 | 778.0 | 0.00 | 2 | 1 | 1.4 | 782.6 | 0.59 | 1 | 0 | 0.4 | |
A-n36-k5 | 799 | 5 | 799.0 | 0.00 | 3 | 1 | 1.8 | 812.4 | 1.68 | 0 | 0 | 0.0 | |
A-n37-k5 | 669 | 5 | 669.0 | 0.00 | 3 | 2 | 2.8 | 670.8 | 0.27 | 3 | 0 | 1.8 | |
A-n37-k6 | 949 | 3 | 949.6 | 0.06 | 1 | 0 | 1.0 | 963.0 | 1.48 | 1 | 0 | 0.2 | |
A-n38-k5 | 730 | 5 | 730.2 | 0.03 | 4 | 0 | 2.0 | 739.2 | 1.26 | 1 | 0 | 0.2 | |
A-n39-k5 | 822 | 4 | 822.6 | 0.07 | 1 | 0 | 1.0 | 827.4 | 0.66 | 0 | 0 | 0.0 | |
A-n39-k6 | 831 | 3 | 831.8 | 0.10 | 2 | 0 | 1.2 | 833.0 | 0.24 | 2 | 0 | 0.4 | |
A-n44-k6 | 937 | 3 | 939.6 | 0.28 | 2 | 0 | 1.2 | 959.0 | 2.35 | 0 | 0 | 0.0 | |
A-n45-k7 | 1 146 | 5 | 1 146.0 | 0.00 | 3 | 2 | 2.2 | 1 147.2 | 0.10 | 1 | 0 | 0.8 | |
A-n46-k7 | 914 | 5 | 914.0 | 0.00 | 2 | 1 | 1.4 | 914.0 | 0.00 | 1 | 1 | 1.0 | |
A-n48-k7 | 1 073 | 5 | 1 073.0 | 0.00 | 3 | 1 | 2.0 | 1 075.6 | 0.24 | 2 | 0 | 1.0 | |
A-n54-k7 | 1 167 | 5 | 1 167.0 | 0.00 | 2 | 1 | 1.2 | 1 203.0 | 3.08 | 0 | 0 | 0.0 | |
A-n55-k9 | 1 073 | 4 | 1 073.4 | 0.04 | 2 | 1 | 1.4 | 1 077.2 | 0.39 | 1 | 0 | 0.2 | |
B | B-n31-k5 | 672 | 3 | 672.8 | 0.12 | 1 | 0 | 0.6 | 674.8 | 0.42 | 0 | 0 | 0.0 |
B-n34-k5 | 788 | 5 | 788.0 | 0.00 | 4 | 2 | 4.0 | 788.0 | 0.00 | 2 | 1 | 1.2 | |
B-n35-k5 | 955 | 5 | 955.0 | 0.00 | 2 | 1 | 1.0 | 955.0 | 0.00 | 1 | 1 | 1.0 | |
B-n38-k6 | 781 | 4 | 781.0 | 0.00 | 2 | 1 | 1.3 | 781.4 | 0.05 | 1 | 0 | 0.6 | |
B-n39-k5 | 549 | 5 | 549.0 | 0.00 | 1 | 1 | 1.0 | 549.6 | 0.11 | 1 | 0 | 0.6 | |
B-n43-k6 | 742 | 5 | 742.0 | 0.00 | 2 | 1 | 1.3 | 744.0 | 0.27 | 2 | 0 | 0.4 | |
B-n44-k7 | 909 | 5 | 909.0 | 0.00 | 2 | 1 | 1.5 | 917.0 | 0.88 | 0 | 0 | 0.0 | |
B-n45-k5 | 751 | 2 | 754.0 | 0.40 | 1 | 0 | 0.2 | 762.2 | 1.49 | 0 | 0 | 0.0 | |
B-n50-k7 | 741 | 5 | 741.0 | 0.00 | 5 | 2 | 3.8 | 741.0 | 0.00 | 5 | 2 | 2.8 | |
B-n52-k7 | 747 | 5 | 747.0 | 0.00 | 4 | 2 | 3.0 | 747.4 | 0.05 | 2 | 0 | 0.8 | |
P | P-n16-k8 | 450 | 5 | 450.0 | 0.00 | 5 | 2 | 2.6 | 450.0 | 0.00 | 3 | 2 | 2.4 |
P-n19-k2 | 201 | 4 | 201.0 | 0.00 | 1 | 1 | 1.0 | 209.4 | 4.18 | 1 | 0 | 0.2 | |
P-n20-k2 | 216 | 5 | 216.0 | 0.00 | 3 | 2 | 2.2 | 216.0 | 0.00 | 2 | 1 | 1.8 | |
P-n21-k2 | 211 | 5 | 211.0 | 0.00 | 1 | 1 | 1.0 | 211.0 | 0.00 | 1 | 1 | 1.0 | |
P-n22-k2 | 216 | 5 | 216.0 | 0.00 | 2 | 1 | 1.4 | 218.4 | 1.11 | 1 | 0 | 0.6 | |
P-n22-k8 | 603 | 5 | 603.0 | 0.00 | 3 | 2 | 2.6 | 603.0 | 0.00 | 5 | 2 | 3.2 | |
P-n23-k8 | 529 | 5 | 529.0 | 0.00 | 2 | 1 | 1.4 | 532.2 | 0.60 | 1 | 0 | 0.8 | |
P-n40-k5 | 458 | 5 | 458.0 | 0.00 | 2 | 1 | 1.2 | 458.0 | 0.00 | 2 | 1 | 1.2 | |
P-n45-k5 | 510 | 5 | 510.0 | 0.00 | 2 | 2 | 2.0 | 512.6 | 0.51 | 1 | 0 | 0.4 | |
P-n50-k7 | 554 | 5 | 554.0 | 0.00 | 2 | 1 | 1.6 | 555.8 | 0.32 | 1 | 0 | 0.4 | |
P-n55-k7 | 568 | 3 | 568.6 | 0.11 | 2 | 1 | 1.4 | 573.2 | 0.92 | 1 | 0 | 0.2 |
Tab. 2 Running results of different algorithms on instance set A, B and P
实例集 | 实例 | Best | Num | MDE | DE | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Avg | Dev | MaxNum | MinNum | AvgNum | Avg | Dev | MaxNum | MinNum | AvgNum | ||||
A | A-n32-k5 | 784 | 5 | 784.0 | 0.00 | 3 | 1 | 2.4 | 784.0 | 0.00 | 3 | 1 | 2.0 |
A-n33-k5 | 661 | 6 | 661.0 | 0.00 | 4 | 2 | 3.4 | 661.0 | 0.00 | 3 | 1 | 1.8 | |
A-n33-k6 | 742 | 6 | 742.0 | 0.00 | 4 | 1 | 2.2 | 742.0 | 0.00 | 5 | 1 | 2.0 | |
A-n34-k5 | 778 | 5 | 778.0 | 0.00 | 2 | 1 | 1.4 | 782.6 | 0.59 | 1 | 0 | 0.4 | |
A-n36-k5 | 799 | 5 | 799.0 | 0.00 | 3 | 1 | 1.8 | 812.4 | 1.68 | 0 | 0 | 0.0 | |
A-n37-k5 | 669 | 5 | 669.0 | 0.00 | 3 | 2 | 2.8 | 670.8 | 0.27 | 3 | 0 | 1.8 | |
A-n37-k6 | 949 | 3 | 949.6 | 0.06 | 1 | 0 | 1.0 | 963.0 | 1.48 | 1 | 0 | 0.2 | |
A-n38-k5 | 730 | 5 | 730.2 | 0.03 | 4 | 0 | 2.0 | 739.2 | 1.26 | 1 | 0 | 0.2 | |
A-n39-k5 | 822 | 4 | 822.6 | 0.07 | 1 | 0 | 1.0 | 827.4 | 0.66 | 0 | 0 | 0.0 | |
A-n39-k6 | 831 | 3 | 831.8 | 0.10 | 2 | 0 | 1.2 | 833.0 | 0.24 | 2 | 0 | 0.4 | |
A-n44-k6 | 937 | 3 | 939.6 | 0.28 | 2 | 0 | 1.2 | 959.0 | 2.35 | 0 | 0 | 0.0 | |
A-n45-k7 | 1 146 | 5 | 1 146.0 | 0.00 | 3 | 2 | 2.2 | 1 147.2 | 0.10 | 1 | 0 | 0.8 | |
A-n46-k7 | 914 | 5 | 914.0 | 0.00 | 2 | 1 | 1.4 | 914.0 | 0.00 | 1 | 1 | 1.0 | |
A-n48-k7 | 1 073 | 5 | 1 073.0 | 0.00 | 3 | 1 | 2.0 | 1 075.6 | 0.24 | 2 | 0 | 1.0 | |
A-n54-k7 | 1 167 | 5 | 1 167.0 | 0.00 | 2 | 1 | 1.2 | 1 203.0 | 3.08 | 0 | 0 | 0.0 | |
A-n55-k9 | 1 073 | 4 | 1 073.4 | 0.04 | 2 | 1 | 1.4 | 1 077.2 | 0.39 | 1 | 0 | 0.2 | |
B | B-n31-k5 | 672 | 3 | 672.8 | 0.12 | 1 | 0 | 0.6 | 674.8 | 0.42 | 0 | 0 | 0.0 |
B-n34-k5 | 788 | 5 | 788.0 | 0.00 | 4 | 2 | 4.0 | 788.0 | 0.00 | 2 | 1 | 1.2 | |
B-n35-k5 | 955 | 5 | 955.0 | 0.00 | 2 | 1 | 1.0 | 955.0 | 0.00 | 1 | 1 | 1.0 | |
B-n38-k6 | 781 | 4 | 781.0 | 0.00 | 2 | 1 | 1.3 | 781.4 | 0.05 | 1 | 0 | 0.6 | |
B-n39-k5 | 549 | 5 | 549.0 | 0.00 | 1 | 1 | 1.0 | 549.6 | 0.11 | 1 | 0 | 0.6 | |
B-n43-k6 | 742 | 5 | 742.0 | 0.00 | 2 | 1 | 1.3 | 744.0 | 0.27 | 2 | 0 | 0.4 | |
B-n44-k7 | 909 | 5 | 909.0 | 0.00 | 2 | 1 | 1.5 | 917.0 | 0.88 | 0 | 0 | 0.0 | |
B-n45-k5 | 751 | 2 | 754.0 | 0.40 | 1 | 0 | 0.2 | 762.2 | 1.49 | 0 | 0 | 0.0 | |
B-n50-k7 | 741 | 5 | 741.0 | 0.00 | 5 | 2 | 3.8 | 741.0 | 0.00 | 5 | 2 | 2.8 | |
B-n52-k7 | 747 | 5 | 747.0 | 0.00 | 4 | 2 | 3.0 | 747.4 | 0.05 | 2 | 0 | 0.8 | |
P | P-n16-k8 | 450 | 5 | 450.0 | 0.00 | 5 | 2 | 2.6 | 450.0 | 0.00 | 3 | 2 | 2.4 |
P-n19-k2 | 201 | 4 | 201.0 | 0.00 | 1 | 1 | 1.0 | 209.4 | 4.18 | 1 | 0 | 0.2 | |
P-n20-k2 | 216 | 5 | 216.0 | 0.00 | 3 | 2 | 2.2 | 216.0 | 0.00 | 2 | 1 | 1.8 | |
P-n21-k2 | 211 | 5 | 211.0 | 0.00 | 1 | 1 | 1.0 | 211.0 | 0.00 | 1 | 1 | 1.0 | |
P-n22-k2 | 216 | 5 | 216.0 | 0.00 | 2 | 1 | 1.4 | 218.4 | 1.11 | 1 | 0 | 0.6 | |
P-n22-k8 | 603 | 5 | 603.0 | 0.00 | 3 | 2 | 2.6 | 603.0 | 0.00 | 5 | 2 | 3.2 | |
P-n23-k8 | 529 | 5 | 529.0 | 0.00 | 2 | 1 | 1.4 | 532.2 | 0.60 | 1 | 0 | 0.8 | |
P-n40-k5 | 458 | 5 | 458.0 | 0.00 | 2 | 1 | 1.2 | 458.0 | 0.00 | 2 | 1 | 1.2 | |
P-n45-k5 | 510 | 5 | 510.0 | 0.00 | 2 | 2 | 2.0 | 512.6 | 0.51 | 1 | 0 | 0.4 | |
P-n50-k7 | 554 | 5 | 554.0 | 0.00 | 2 | 1 | 1.6 | 555.8 | 0.32 | 1 | 0 | 0.4 | |
P-n55-k7 | 568 | 3 | 568.6 | 0.11 | 2 | 1 | 1.4 | 573.2 | 0.92 | 1 | 0 | 0.2 |
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