计算机科学与探索 ›› 2022, Vol. 16 ›› Issue (12): 2797-2808.DOI: 10.3778/j.issn.1673-9418.2104006
收稿日期:
2021-04-01
修回日期:
2021-06-07
出版日期:
2022-12-01
发布日期:
2021-06-15
通讯作者:
+E-mail: yxm6301@163.com作者简介:
陈达(1997—),男,江苏盐城人,硕士研究生,主要研究方向为智能算法、移动机器人路径规划、嵌入式系统。基金资助:
CHEN Da1, YOU Xiaoming1,+(), LIU Sheng2
Received:
2021-04-01
Revised:
2021-06-07
Online:
2022-12-01
Published:
2021-06-15
About author:
CHEN Da, born in 1997, M.S. candidate. His research interests include intelligent algorithm, path planning of mobile robot and embedded system.Supported by:
摘要:
针对传统蚁群算法在求解旅行商问题(TSP)时存在收敛速度慢、易陷入局部最优等问题,提出一种引入特征迁移学习和匹配学习的双蚁型蚁群算法(BMACS)。首先,将种群动态分级为探索蚁和追踪蚁,其中适应度较高的为探索蚁,较低的为追踪蚁;其次,提出一种局部特征迁移机制,该机制下有两种策略,在特征迁移策略中,将探索蚁公共路径作为局部特征通过局部信息素奖励迁移到信息素矩阵中,进而提高探索蚁的影响力,加快算法收敛速度;在变异学习策略中,追踪蚁跟随探索蚁负责对次优路径的探索,自适应重构探索蚁路径,从而丰富种群多样性;最后,当算法停滞时,利用匹配学习机制将当前最优个体与相似度最高的历史最优个体进行交流学习,重组信息素,增加种群的多样性,进而提高算法跳出局部最优的能力。使用MATLAB对TSPLIB中的多组案例进行仿真实验,结果表明改进后的算法平衡了多样性和收敛速度,有效提高了解的质量。
中图分类号:
陈达, 游晓明, 刘升. 引入特征迁移和匹配学习的双蚁型蚁群算法[J]. 计算机科学与探索, 2022, 16(12): 2797-2808.
CHEN Da, YOU Xiaoming, LIU Sheng. Dual Ant Colony Algorithm Based on Backtracking Migration and Matching Learning[J]. Journal of Frontiers of Computer Science and Technology, 2022, 16(12): 2797-2808.
数据集名称 | 最优解 | 平均误差/% | |
---|---|---|---|
eil51 | 426 | 1 | 0.71 |
2 | 0.52 | ||
3 | 0.23 | ||
4 | 0.41 | ||
5 | 0.53 | ||
6 | 0.66 |
表1 C的取值对精度的影响统计
Table 1 Statistics on influence of value of C on accuracy
数据集名称 | 最优解 | 平均误差/% | |
---|---|---|---|
eil51 | 426 | 1 | 0.71 |
2 | 0.52 | ||
3 | 0.23 | ||
4 | 0.41 | ||
5 | 0.53 | ||
6 | 0.66 |
算法 | 时间复杂度 |
---|---|
BMACS | |
DBA | |
SA-MMAS | |
FWA | |
CFWA | |
ACS |
表2 不同算法复杂度对比
Table 2 Comparison of complexity of different algorithms
算法 | 时间复杂度 |
---|---|
BMACS | |
DBA | |
SA-MMAS | |
FWA | |
CFWA | |
ACS |
Level | |||||
---|---|---|---|---|---|
Level1 | 1 | 1 | 0.1 | 0.1 | 0.6 |
Level2 | 2 | 2 | 0.2 | 0.2 | 0.7 |
Level3 | 3 | 3 | 0.3 | 0.3 | 0.8 |
Level4 | 4 | 4 | 0.4 | 0.4 | 0.9 |
表3 BMACS的实验因素和水平
Table 3 Experimental factors and levels of BMACS
Level | |||||
---|---|---|---|---|---|
Level1 | 1 | 1 | 0.1 | 0.1 | 0.6 |
Level2 | 2 | 2 | 0.2 | 0.2 | 0.7 |
Level3 | 3 | 3 | 0.3 | 0.3 | 0.8 |
Level4 | 4 | 4 | 0.4 | 0.4 | 0.9 |
NO. | Avg | |||||
---|---|---|---|---|---|---|
1 | 1 | 1 | 0.1 | 0.1 | 0.6 | 576.00 |
2 | 1 | 2 | 0.2 | 0.2 | 0.7 | 552.35 |
3 | 1 | 3 | 0.3 | 0.3 | 0.8 | 547.25 |
4 | 1 | 4 | 0.4 | 0.4 | 0.9 | 546.15 |
5 | 2 | 1 | 0.2 | 0.3 | 0.9 | 557.30 |
6 | 2 | 2 | 0.1 | 0.4 | 0.8 | 554.45 |
7 | 2 | 3 | 0.4 | 0.1 | 0.7 | 544.65 |
8 | 2 | 4 | 0.3 | 0.2 | 0.6 | 547.20 |
9 | 3 | 1 | 0.3 | 0.4 | 0.7 | 570.25 |
10 | 3 | 2 | 0.4 | 0.3 | 0.6 | 560.15 |
11 | 3 | 3 | 0.1 | 0.2 | 0.9 | 546.65 |
12 | 3 | 4 | 0.2 | 0.1 | 0.8 | 548.65 |
13 | 4 | 1 | 0.4 | 0.2 | 0.8 | 563.55 |
14 | 4 | 2 | 0.3 | 0.1 | 0.9 | 561.35 |
15 | 4 | 3 | 0.2 | 0.4 | 0.6 | 552.30 |
16 | 4 | 4 | 0.1 | 0.3 | 0.7 | 545.95 |
表4 正交实验方案及BMACS实验结果
Table 4 Orthogonal test scheme and test results of BMACS
NO. | Avg | |||||
---|---|---|---|---|---|---|
1 | 1 | 1 | 0.1 | 0.1 | 0.6 | 576.00 |
2 | 1 | 2 | 0.2 | 0.2 | 0.7 | 552.35 |
3 | 1 | 3 | 0.3 | 0.3 | 0.8 | 547.25 |
4 | 1 | 4 | 0.4 | 0.4 | 0.9 | 546.15 |
5 | 2 | 1 | 0.2 | 0.3 | 0.9 | 557.30 |
6 | 2 | 2 | 0.1 | 0.4 | 0.8 | 554.45 |
7 | 2 | 3 | 0.4 | 0.1 | 0.7 | 544.65 |
8 | 2 | 4 | 0.3 | 0.2 | 0.6 | 547.20 |
9 | 3 | 1 | 0.3 | 0.4 | 0.7 | 570.25 |
10 | 3 | 2 | 0.4 | 0.3 | 0.6 | 560.15 |
11 | 3 | 3 | 0.1 | 0.2 | 0.9 | 546.65 |
12 | 3 | 4 | 0.2 | 0.1 | 0.8 | 548.65 |
13 | 4 | 1 | 0.4 | 0.2 | 0.8 | 563.55 |
14 | 4 | 2 | 0.3 | 0.1 | 0.9 | 561.35 |
15 | 4 | 3 | 0.2 | 0.4 | 0.6 | 552.30 |
16 | 4 | 4 | 0.1 | 0.3 | 0.7 | 545.95 |
参数 | |||||
---|---|---|---|---|---|
2 222.35 | 2 267.70 | 2 223.65 | 2 231.25 | 2 236.25 | |
2 203.60 | 2 228.30 | 2 210.60 | 2 209.75 | 2 213.20 | |
2 225.70 | 2 190.85 | 2 226.05 | 2 210.65 | 2 213.90 | |
2 223.15 | 2 187.95 | 2 214.50 | 2 223.15 | 2 211.45 | |
555.59 | 566.93 | 555.91 | 557.81 | 559.06 | |
550.90 | 557.08 | 552.65 | 552.44 | 553.30 | |
556.43 | 547.71 | 556.51 | 552.66 | 553.48 | |
555.79 | 546.99 | 553.63 | 555.79 | 552.86 | |
556.43 | 566.93 | 556.51 | 557.81 | 559.06 | |
550.90 | 546.99 | 552.65 | 552.44 | 552.86 | |
15.53 | 19.94 | 3.86 | 5.37 | 6.20 | |
Level2 | Level4 | Level2 | Level2 | Level4 |
表5 BMACS测试结果分析
Table 5 Analysis of test results of BMACS
参数 | |||||
---|---|---|---|---|---|
2 222.35 | 2 267.70 | 2 223.65 | 2 231.25 | 2 236.25 | |
2 203.60 | 2 228.30 | 2 210.60 | 2 209.75 | 2 213.20 | |
2 225.70 | 2 190.85 | 2 226.05 | 2 210.65 | 2 213.90 | |
2 223.15 | 2 187.95 | 2 214.50 | 2 223.15 | 2 211.45 | |
555.59 | 566.93 | 555.91 | 557.81 | 559.06 | |
550.90 | 557.08 | 552.65 | 552.44 | 553.30 | |
556.43 | 547.71 | 556.51 | 552.66 | 553.48 | |
555.79 | 546.99 | 553.63 | 555.79 | 552.86 | |
556.43 | 566.93 | 556.51 | 557.81 | 559.06 | |
550.90 | 546.99 | 552.65 | 552.44 | 552.86 | |
15.53 | 19.94 | 3.86 | 5.37 | 6.20 | |
Level2 | Level4 | Level2 | Level2 | Level4 |
TSP实例 | 标准最优解 | 算法 | 最优解 | 最差解 | 平均解 | 误差率/% | 最优迭代数 |
---|---|---|---|---|---|---|---|
eil51 | 426 | BMACS | 426 | 428 | 427 | 0 | 55 |
ACS-3opt | 426 | 429 | 428 | 0 | 83 | ||
ACS | 426 | 435 | 428 | 0 | 309 | ||
eil76 | 538 | BMACS | 538 | 543 | 540 | 0 | 37 |
ACS-3opt | 538 | 547 | 541 | 0 | 175 | ||
ACS | 538 | 549 | 545 | 0 | 1 046 | ||
rat99 | 1 211 | BMACS | 1 211 | 1 221 | 1 215 | 0 | 220 |
ACS-3opt | 1 211 | 1 229 | 1 219 | 0 | 279 | ||
ACS | 1 211 | 1 231 | 1 220 | 0 | 319 | ||
kroA100 | 21 282 | BMACS | 21 282 | 21 734 | 21 313 | 0 | 396 |
ACS-3opt | 21 282 | 21 833 | 21 366 | 0 | 1 231 | ||
ACS | 21 282 | 21 952 | 21 441 | 0 | 1 672 | ||
kroB100 | 22 141 | BMACS | 22 141 | 22 330 | 22 251 | 0 | 1 479 |
ACS-3opt | 22 236 | 22 351 | 22 316 | 0.429 | 960 | ||
ACS | 22 272 | 22 387 | 22 325 | 0.592 | 1 887 | ||
ch130 | 6 110 | BMACS | 6 110 | 6 310 | 6 201 | 0 | 697 |
ACS-3opt | 6 144 | 6 364 | 6 222 | 0.556 | 460 | ||
ACS | 6 148 | 6 389 | 6 227 | 0.622 | 1 920 | ||
kroB150 | 26 130 | BMACS | 26 130 | 26 728 | 26 431 | 0 | 1 287 |
ACS-3opt | 26 154 | 26 809 | 26 471 | 0.092 | 629 | ||
ACS | 26 178 | 26 855 | 26 589 | 0.184 | 1 870 | ||
kroA150 | 26 524 | BMACS | 26 550 | 27 204 | 26 889 | 0.098 | 1 252 |
ACS-3opt | 26 619 | 27 315 | 27 012 | 0.358 | 1 498 | ||
ACS | 26 643 | 27 520 | 27 133 | 0.449 | 1 989 | ||
kroB200 | 29 437 | BMACS | 29 610 | 30 193 | 29 941 | 0.588 | 1 595 |
ACS-3opt | 29 837 | 30 435 | 30 036 | 1.359 | 1 961 | ||
ACS | 29 874 | 30 562 | 30 175 | 1.485 | 1 105 | ||
kroA200 | 29 368 | BMACS | 29 401 | 29 844 | 29 677 | 0.112 | 701 |
ACS-3opt | 29 472 | 29 926 | 29 614 | 0.354 | 1 412 | ||
ACS | 29 498 | 30 049 | 29 501 | 0.443 | 1 231 | ||
tsp225 | 3 916 | BMACS | 3 920 | 4 034 | 3 972 | 0.102 | 309 |
ACS-3opt | 3 935 | 4 065 | 4 011 | 0.485 | 1 775 | ||
ACS | 3 944 | 4 145 | 4 031 | 0.715 | 1 883 | ||
a280 | 2 579 | BMACS | 2 587 | 2 701 | 2 638 | 0.310 | 1 081 |
ACS-3opt | 2 602 | 2 710 | 2 641 | 0.892 | 1 768 | ||
ACS | 2 604 | 2 715 | 2 654 | 0.969 | 1 444 | ||
lin318 | 42 029 | BMACS | 42 361 | 43 573 | 43 065 | 0.790 | 1 736 |
ACS-3opt | 42 939 | 44 094 | 43 634 | 2.165 | 1 291 | ||
ACS | 43 008 | 44 399 | 43 667 | 2.329 | 1 478 | ||
fl417 | 11 861 | BMACS | 11 965 | 12 254 | 12 106 | 0.877 | 1 941 |
ACS-3opt | 12 010 | 12 302 | 12 183 | 1.256 | 1 886 | ||
ACS | 12 057 | 12 347 | 12 213 | 1.652 | 1 877 |
表6 ACS、ACS+3opt、BMACS在不同测试集的性能对比
Table 6 Performance comparison of ACS、ACS+3opt、BMACS in different test sets
TSP实例 | 标准最优解 | 算法 | 最优解 | 最差解 | 平均解 | 误差率/% | 最优迭代数 |
---|---|---|---|---|---|---|---|
eil51 | 426 | BMACS | 426 | 428 | 427 | 0 | 55 |
ACS-3opt | 426 | 429 | 428 | 0 | 83 | ||
ACS | 426 | 435 | 428 | 0 | 309 | ||
eil76 | 538 | BMACS | 538 | 543 | 540 | 0 | 37 |
ACS-3opt | 538 | 547 | 541 | 0 | 175 | ||
ACS | 538 | 549 | 545 | 0 | 1 046 | ||
rat99 | 1 211 | BMACS | 1 211 | 1 221 | 1 215 | 0 | 220 |
ACS-3opt | 1 211 | 1 229 | 1 219 | 0 | 279 | ||
ACS | 1 211 | 1 231 | 1 220 | 0 | 319 | ||
kroA100 | 21 282 | BMACS | 21 282 | 21 734 | 21 313 | 0 | 396 |
ACS-3opt | 21 282 | 21 833 | 21 366 | 0 | 1 231 | ||
ACS | 21 282 | 21 952 | 21 441 | 0 | 1 672 | ||
kroB100 | 22 141 | BMACS | 22 141 | 22 330 | 22 251 | 0 | 1 479 |
ACS-3opt | 22 236 | 22 351 | 22 316 | 0.429 | 960 | ||
ACS | 22 272 | 22 387 | 22 325 | 0.592 | 1 887 | ||
ch130 | 6 110 | BMACS | 6 110 | 6 310 | 6 201 | 0 | 697 |
ACS-3opt | 6 144 | 6 364 | 6 222 | 0.556 | 460 | ||
ACS | 6 148 | 6 389 | 6 227 | 0.622 | 1 920 | ||
kroB150 | 26 130 | BMACS | 26 130 | 26 728 | 26 431 | 0 | 1 287 |
ACS-3opt | 26 154 | 26 809 | 26 471 | 0.092 | 629 | ||
ACS | 26 178 | 26 855 | 26 589 | 0.184 | 1 870 | ||
kroA150 | 26 524 | BMACS | 26 550 | 27 204 | 26 889 | 0.098 | 1 252 |
ACS-3opt | 26 619 | 27 315 | 27 012 | 0.358 | 1 498 | ||
ACS | 26 643 | 27 520 | 27 133 | 0.449 | 1 989 | ||
kroB200 | 29 437 | BMACS | 29 610 | 30 193 | 29 941 | 0.588 | 1 595 |
ACS-3opt | 29 837 | 30 435 | 30 036 | 1.359 | 1 961 | ||
ACS | 29 874 | 30 562 | 30 175 | 1.485 | 1 105 | ||
kroA200 | 29 368 | BMACS | 29 401 | 29 844 | 29 677 | 0.112 | 701 |
ACS-3opt | 29 472 | 29 926 | 29 614 | 0.354 | 1 412 | ||
ACS | 29 498 | 30 049 | 29 501 | 0.443 | 1 231 | ||
tsp225 | 3 916 | BMACS | 3 920 | 4 034 | 3 972 | 0.102 | 309 |
ACS-3opt | 3 935 | 4 065 | 4 011 | 0.485 | 1 775 | ||
ACS | 3 944 | 4 145 | 4 031 | 0.715 | 1 883 | ||
a280 | 2 579 | BMACS | 2 587 | 2 701 | 2 638 | 0.310 | 1 081 |
ACS-3opt | 2 602 | 2 710 | 2 641 | 0.892 | 1 768 | ||
ACS | 2 604 | 2 715 | 2 654 | 0.969 | 1 444 | ||
lin318 | 42 029 | BMACS | 42 361 | 43 573 | 43 065 | 0.790 | 1 736 |
ACS-3opt | 42 939 | 44 094 | 43 634 | 2.165 | 1 291 | ||
ACS | 43 008 | 44 399 | 43 667 | 2.329 | 1 478 | ||
fl417 | 11 861 | BMACS | 11 965 | 12 254 | 12 106 | 0.877 | 1 941 |
ACS-3opt | 12 010 | 12 302 | 12 183 | 1.256 | 1 886 | ||
ACS | 12 057 | 12 347 | 12 213 | 1.652 | 1 877 |
算法 | eil51 | eil76 | kroA100 | kroB150 | kroA200 | lin318 |
---|---|---|---|---|---|---|
BMACS | 426 | 538 | 21 282 | 26 130 | 29 401 | 42 361 |
RBIFWA[ | 426 | — | 21 282 | — | — | — |
SGSAA[ | 426 | 538 | — | — | — | — |
GA-SAC[ | 426 | 538 | 21 282 | — | — | 42 329 |
IADUACO[ | 427 | 538 | — | — | — | — |
PACO-3OPT[ | 426 | 538 | 21 282 | — | 29 533 | — |
EDHACO[ | 426 | 538 | 21 282 | 26 328 | 29 694 | 43 291 |
PCCACO[ | 426 | 538 | 21 282 | 26 130 | 29 393 | 42 461 |
DSMO[ | 426 | 538 | 21 298 | 26 601 | 30 481 | 44 118 |
WWO[ | 427 | 557 | 21 668 | — | 31 064 | — |
表7 BMACS算法与其他算法的对比
Table 7 Comparison between BMACS algorithm and other algorithms
算法 | eil51 | eil76 | kroA100 | kroB150 | kroA200 | lin318 |
---|---|---|---|---|---|---|
BMACS | 426 | 538 | 21 282 | 26 130 | 29 401 | 42 361 |
RBIFWA[ | 426 | — | 21 282 | — | — | — |
SGSAA[ | 426 | 538 | — | — | — | — |
GA-SAC[ | 426 | 538 | 21 282 | — | — | 42 329 |
IADUACO[ | 427 | 538 | — | — | — | — |
PACO-3OPT[ | 426 | 538 | 21 282 | — | 29 533 | — |
EDHACO[ | 426 | 538 | 21 282 | 26 328 | 29 694 | 43 291 |
PCCACO[ | 426 | 538 | 21 282 | 26 130 | 29 393 | 42 461 |
DSMO[ | 426 | 538 | 21 298 | 26 601 | 30 481 | 44 118 |
WWO[ | 427 | 557 | 21 668 | — | 31 064 | — |
TSP实例 | 算法 | 最优解 | 平均解 | 迭代次数 |
---|---|---|---|---|
kroA100 | ACS+迁移 | 21 282 | 21 282 | 396 |
ACS | 22 272 | 1 672 | ||
ACS+迁移 | 21 282 | 21 282 | 500 | |
ACS | 22 236 | 1 231 | ||
ACS+迁移 | 21 282 | 21 282 | 461 | |
ACS | 21 431 | 1 336 |
表8 性能对比
Table 8 Performance comparison
TSP实例 | 算法 | 最优解 | 平均解 | 迭代次数 |
---|---|---|---|---|
kroA100 | ACS+迁移 | 21 282 | 21 282 | 396 |
ACS | 22 272 | 1 672 | ||
ACS+迁移 | 21 282 | 21 282 | 500 | |
ACS | 22 236 | 1 231 | ||
ACS+迁移 | 21 282 | 21 282 | 461 | |
ACS | 21 431 | 1 336 |
TSP实例 | 标准最优解 | 算法 | 平均解 | 平均误差率/% |
---|---|---|---|---|
lin318 | 42 029 | ACS+回溯 | 42 565 | 1.28 |
ACS | 43 008 | 2.30 | ||
fl417 | 11 861 | ACS+回溯 | 11 990 | 1.09 |
ACS | 12 057 | 1.32 |
表9 匹配学习机制的对比分析
Table 9 Contrastive analysis of matching learning mechanism
TSP实例 | 标准最优解 | 算法 | 平均解 | 平均误差率/% |
---|---|---|---|---|
lin318 | 42 029 | ACS+回溯 | 42 565 | 1.28 |
ACS | 43 008 | 2.30 | ||
fl417 | 11 861 | ACS+回溯 | 11 990 | 1.09 |
ACS | 12 057 | 1.32 |
[1] | DORIGO M, MANIEZZO V, COLORNI A. The ant system: optimization by a colony of cooperating agents[J]. IEEE Tran-sactions on Systems, Man, and Cybernetics, Part B: Cyber-netics, 1996, 26(1): 29-41. |
[2] |
DORIGO M, BIRATTARI M, STUTZLE T. Ant colony optimization[J]. IEEE Computational Intelligence Magazine, 2006, 1(4): 28-39.
DOI URL |
[3] |
DORIGO M, GAMBARDELLA L M. Ant colony system: a cooperative learning approach to the traveling salesman pro-blem[J]. IEEE Transactions on Evolutionary Computation, 1997, 1(1): 53-66.
DOI URL |
[4] |
STUTZLE T, HOOS H H. MAX-MIN ant system[J]. Future Generation Computer Systems, 2000, 16(8): 889-914.
DOI URL |
[5] | 周頔. 基于多种群多策略的混合遗传-蚁群算法及应用研究[J]. 计算机与数字工程, 2018, 46(12): 2390-2394. |
ZHOU D. Study on a hybrid genetic-ant colony algorithm based on multi-population and multi-strategy and its appli-cation[J]. Computer and Digital Engineering, 2018, 46(12): 2390-2394. | |
[6] | 高健, 顾垚江. 基于拥挤度的改进蚁群算法[J]. 测控技术, 2019, 38(3): 11-15. |
GAO J, GU Y J. An improved ant colony algorithm based on crowding degree[J]. Measurement and Control Techno-logy, 2019, 38(3): 11-15. | |
[7] |
卜冠南, 刘建华, 姜磊, 等. 一种自适应分组的蚁群算法[J]. 计算机工程与应用, 2021, 57(6): 67-73.
DOI |
BU G N, LIU J H, JIANG L, et al. An adaptive grouping ant colony algorithm[J]. Computer Engineering and Applica-tions, 2021, 57(6): 67-73. | |
[8] |
许凯波, 鲁海燕, 程毕芸, 等. 求解TSP的改进信息素二次更新与局部优化蚁群算法[J]. 计算机应用, 2017, 37(6): 1686-1691.
DOI |
XU K B, LU H Y, CHENG B Y, et al. Ant colony opti-mization algorithm based on improved pheromones double updating and local optimization for solving TSP[J]. Journal of Computer Applications, 2017, 37(6): 1686-1691. | |
[9] | 王铁, 胡泓. 基于K-means信息挥发速率动态调整的改进蚁群算法[J]. 机械与电子, 2020, 38(2): 25-29. |
WANG T, HU H. An improved ant colony algorithm based on K-means and dynamic volatility rate adjustment strategy[J]. Machinery and Electronics, 2020, 38(2): 25-29. | |
[10] | 孟祥萍, 片兆宇, 沈中玉, 等. 基于方向信息素协调的蚁群算法[J]. 控制与决策, 2013, 28(5): 782-786. |
MENG X P, PIAN Z Y, SHEN Z Y, et al. Ant colony algorithm based on directional pheromone coordination[J]. Control and Decision, 2013, 28(5): 782-786. | |
[11] | 尚宝平, 焦建强, 裴杰, 等. 一种求解TSP问题的多策略改进蚁群算法[J]. 数学的实践与认识, 2019, 49(2): 215-224. |
SHANG B P, JIAO J Q, PEI J, et al. Research on an imp-roved multi-strategy ant colony algorithm for TSP problem[J]. Mathematics in Practice and Theory, 2019, 49(2): 215-224. | |
[12] | 吴俊斌, 吴晟, 吴兴蛟. 一种用于求解TSP问题的随机最佳插入烟花算法[J]. 计算机工程与科学, 2020, 42(11): 2080-2087. |
WU J B, WU S, WU X J. A randomized best insertion fire-works algorithm for solving TSP problem[J]. Computer Engi-neering and Science, 2020, 42(11): 2080-2087. | |
[13] | 陈科胜, 鲜思东, 郭鹏. 求解旅行商问题的自适应升温模拟退火算法[J]. 控制理论与应用, 2021, 38(2): 245-254. |
CHEN K S, XIAN S D, GUO P. Adaptive temperature rising simulated annealing algorithm for traveling salesman pro-blem[J]. Control Theory & Applications, 2021, 38(2): 245-254. | |
[14] |
陈斌, 刘卫国. 基于SAC模型的改进遗传算法求解TSP问题[J]. 计算机科学与探索, 2021, 15(9): 1680-1693.
DOI URL |
CHEN B, LIU W G. SAC model based improved genetic algorithm for solving TSP[J]. Journal of Frontiers of Com-puter Science and Technology, 2021, 15(9): 1680-1693. | |
[15] |
陈颖杰, 高茂庭. 基于信息素初始分配和动态更新的蚁群算法[J]. 计算机工程与应用, 2022, 58(2): 95-101.
DOI |
CHEN Y J, GAO M T. Pheromone initialization and dyna-mic update based ant colony algorithm[J]. Computer Enginee-ring and Applications, 2022, 58(2): 95-101. | |
[16] |
GÜlCÜ S, MAHI M, BAYKAN Ö K. et al. A parallel co-operative hybrid method based on ant colony optimization and 3-opt algorithm for solving traveling salesman problem[J]. Soft Computing, 2018, 22(5): 1669-1685.
DOI URL |
[17] |
CHEN J, YOU X M, LIU S, et al. Entropy-based dynamic heterogeneous ant colony optimization[J]. IEEE Access, 2019, 7: 56317-56328.
DOI |
[18] |
ZHU H W, YOU X M, LIU S. Multiple ant colony optimi-zation based on Pearson correlation coefficient[J]. IEEE Access, 2019, 7: 61628-61638.
DOI URL |
[19] |
AKHAND M, AYON S I, SHAHRIYAR S A, et al. Discrete spider monkey optimization for traveling salesman problem[J]. Applied Soft Computing, 2019, 86: 105887.
DOI URL |
[20] | WU X B, LIAO J, WANG Z C. Water wave optimization for the traveling salesman problem[C]// LNCS 9225: Proce-edings of the 11th International Conference on Intelligent Computing Theories and Methodologies, Fuzhou, Aug 20-23, 2015. Cham: Springer, 2015: 137-146. |
[1] | 赵家波, 游晓明, 刘升. 结合价格波动策略与动态回溯机制的蚁群算法[J]. 计算机科学与探索, 2022, 16(6): 1390-1404. |
[2] | 张松灿, 孙力帆, 司彦娜, 普杰信. 单种群自适应异构蚁群算法的机器人路径规划[J]. 计算机科学与探索, 2022, 16(12): 2820-2831. |
[3] | 陈斌, 刘卫国. 基于SAC模型的改进遗传算法求解TSP问题[J]. 计算机科学与探索, 2021, 15(9): 1680-1693. |
[4] | 莫亚东, 游晓明, 刘升. 融合奖惩学习策略的动态分级蚁群算法[J]. 计算机科学与探索, 2021, 15(9): 1703-1716. |
[5] | 刘一凡, 游晓明, 刘升. 基于动态重组和协同交流策略的蚁群优化算法[J]. 计算机科学与探索, 2021, 15(8): 1511-1525. |
[6] | 孟静雯,游晓明,刘升. 结合协同机制与动态调控策略的双蚁群算法[J]. 计算机科学与探索, 2021, 15(11): 2206-2221. |
[7] | 殷绍伟, 彭力, 戴菲菲. 融合改进A*蚁群和滚动窗口法的平滑路径规划[J]. 计算机科学与探索, 2021, 15(10): 1969-1979. |
[8] | 潘晗,游晓明,刘升. 考虑动态导向与邻域交互的双蚁型算法[J]. 计算机科学与探索, 2020, 14(6): 1005-1016. |
[9] | 张德惠,游晓明,刘升. 融合猫群算法的动态分组蚁群算法[J]. 计算机科学与探索, 2020, 14(5): 880-891. |
[10] | 冯志雨,游晓明,刘升. 分层递进的改进聚类蚁群算法解决TSP问题[J]. 计算机科学与探索, 2019, 13(8): 1280-1294. |
[11] | 郭羽含,胡芳霞. 考虑匹配可行性的长期合乘问题建模与求解[J]. 计算机科学与探索, 2019, 13(11): 1894-1910. |
[12] | 朱宏伟,游晓明,刘升. 协同过滤策略的异构双种群蚁群算法[J]. 计算机科学与探索, 2019, 13(10): 1754-1767. |
[13] | 任珂欣,王兴伟,马连博,黄敏. 蚁群分工启发的ICN负载均衡机制[J]. 计算机科学与探索, 2018, 12(7): 1109-1116. |
[14] | 王纯子,郭伟,张斌. 求解非线性混合整数规划的算法设计与仿真[J]. 计算机科学与探索, 2013, 7(9): 854-864. |
[15] | 陈光鹏+, 杨育彬. 利用蚁群算法的记忆式图像检索方法[J]. 计算机科学与探索, 2011, 5(1): 32-37. |
阅读次数 | ||||||
全文 |
|
|||||
摘要 |
|
|||||