系统仿真学报 ›› 2024, Vol. 36 ›› Issue (6): 1475-1492.doi: 10.16182/j.issn1004731x.joss.23-0524
收稿日期:
2023-05-06
修回日期:
2023-08-06
出版日期:
2024-06-28
发布日期:
2024-06-19
通讯作者:
游晓明
E-mail:Wyj13942013593@163.com;Yxm7520253@163.com
第一作者简介:
王育洁(2000-),女,硕士生,研究方向为智能算法、移动机器人路径规划。E-mail:Wyj13942013593@163.com
基金资助:
Wang Yujie(), You Xiaoming(
), Liu Sheng
Received:
2023-05-06
Revised:
2023-08-06
Online:
2024-06-28
Published:
2024-06-19
Contact:
You Xiaoming
E-mail:Wyj13942013593@163.com;Yxm7520253@163.com
摘要:
针对蚁群算法在求解旅行商问题中出现收敛速度慢以及易陷入局部最优等问题,提出一种结合评估奖惩机制和邻域动态退化的协同蚁群算法。根据路径评估值将路径划分为活跃路径和舍弃路径,以路径评估值作为权重对两类路径采取不同的信息素奖惩策略,加快算法的收敛速度。采用邻域动态退化策略,利用邻域半径将城市集分为探索区和退化区,自适应缩小蚂蚁的搜索范围,通过保留概率动态保留部分退化区中的城市,结合探索区中的城市一并计算状态转移概率,平衡算法的收敛速度和种群的多样性。采取种间协同进化机制,根据Tanimoto相关系数确定种群间的交互周期,并在算法的不同阶段选择合适的交互方式帮助算法跳出局部最优,提高算法的求解精度,达到种群间有效交流的目的。
中图分类号:
王育洁,游晓明,刘升 . 结合评估奖惩机制和邻域动态退化的协同蚁群算法[J]. 系统仿真学报, 2024, 36(6): 1475-1492.
Wang Yujie,You Xiaoming,Liu Sheng . Cooperative Ant Colony Algorithm Combining Evaluation Reward and Punishment Mechanism and Neighborhood Dynamic Degradation[J]. Journal of System Simulation, 2024, 36(6): 1475-1492.
表4
3种城市集中不同阈值θ组合的结果
TSP | 标准最优解 | 阈值 | 最优解 | 平均解 | 误差率% | 迭代次数 |
---|---|---|---|---|---|---|
eil51 | 426 | A | 426 | 426.9 | 0 | 422 |
B | 426 | 427.5 | 0 | 416 | ||
C | 426 | 426.8 | 0 | 60 | ||
D | 426 | 427.3 | 0 | 63 | ||
kroB150 | 26 130 | A | 26 249 | 26 324.3 | 0.46 | 1 634 |
B | 26 193 | 26 342.8 | 0.24 | 1 151 | ||
C | 26 130 | 26 296.9 | 0 | 867 | ||
D | 26 178 | 26 336.2 | 0.18 | 1 074 | ||
lin318 | 42 029 | A | 42 425 | 42 962.0 | 0.94 | 1 631 |
B | 42 634 | 43 013.1 | 1.44 | 1 635 | ||
C | 42 236 | 42 793.5 | 0.49 | 1 864 | ||
D | 42 342 | 42 949.9 | 0.74 | 1 628 |
表7
ENCACO与经典算法ACS和MMAS在不同测试集下的性能对比
TSP | 标准最优解 | 算法 | 最优解 | 平均解 | 误差率/% | 迭代次数 |
---|---|---|---|---|---|---|
eil51 | 426 | ACS | 426 | 428.1 | 0 | 964 |
MMAS | 426 | 429.8 | 0 | 870 | ||
ENCACO | 426 | 426.8 | 0 | 60 | ||
eil76 | 538 | ACS | 538 | 543.3 | 0 | 285 |
MMAS | 538 | 544.3 | 0 | 1 813 | ||
ENCACO | 538 | 538.7 | 0 | 267 | ||
kroA100 | 21 282 | ACS | 21 282 | 21 476.1 | 0 | 1 436 |
MMAS | 21 356 | 21 845.4 | 0.35 | 1 235 | ||
ENCACO | 21 282 | 21 397.8 | 0 | 589 | ||
kroB100 | 22 141 | ACS | 22 237 | 22 351.5 | 0.43 | 1 565 |
MMAS | 22 304 | 22 381.2 | 0.74 | 1 393 | ||
ENCACO | 22 141 | 22 289.9 | 0 | 820 | ||
ch130 | 6 110 | ACS | 6 156 | 6 218.5 | 0.75 | 1 089 |
MMAS | 6 197 | 6 234.0 | 1.42 | 1 250 | ||
ENCACO | 6 110 | 6 198.5 | 0 | 535 | ||
kroA150 | 26 524 | ACS | 26 761 | 27 199.9 | 0.89 | 1 460 |
MMAS | 26 877 | 27 223.1 | 1.33 | 1 665 | ||
ENCACO | 26 525 | 26 781.7 | 0 | 820 | ||
kroB150 | 26 130 | ACS | 26 248 | 26 715.8 | 0.45 | 1 892 |
MMAS | 26 289 | 26 826.4 | 0.61 | 1 750 | ||
ENCACO | 26 130 | 26 296.9 | 0 | 867 | ||
ch150 | 6 528 | ACS | 6 547 | 6 626.9 | 0.29 | 1 465 |
MMAS | 6 533 | 6 585.7 | 0.08 | 894 | ||
ENCACO | 6 528 | 6 554.5 | 0 | 549 | ||
kroA200 | 29 368 | ACS | 29 528 | 29 901.7 | 0.54 | 1 516 |
MMAS | 29 450 | 29 862.1 | 0.28 | 1 219 | ||
ENCACO | 29 368 | 29 673.4 | 0 | 1 498 | ||
kroB200 | 29 437 | ACS | 29 751 | 30 333.3 | 1.07 | 1 960 |
MMAS | 29 838 | 30 207.4 | 1.36 | 1 648 | ||
ENCACO | 29 437 | 29 815.9 | 0 | 1 115 | ||
tsp225 | 3 916 | ACS | 3 934 | 3 998.7 | 0.46 | 1 470 |
MMAS | 3 978 | 4 093.0 | 1.58 | 1 195 | ||
ENCACO | 3 916 | 3 965.3 | 0 | 1 235 | ||
a280 | 2 579 | ACS | 2 583 | 2 713.8 | 0.16 | 1 862 |
MMAS | 2 590 | 2 632.2 | 0.43 | 570 | ||
ENCACO | 2 579 | 2 613.1 | 0 | 1 039 | ||
lin318 | 42 029 | ACS | 42 708 | 43322.2 | 1.62 | 1 818 |
MMAS | 43 111 | 44 640.5 | 2.57 | 1 643 | ||
ENCACO | 42 236 | 42 793.5 | 0.49 | 1 864 | ||
fl417 | 11 861 | ACS | 12 005 | 12 105.4 | 1.21 | 1 919 |
MMAS | 12 189 | 12 359.8 | 2.77 | 1 970 | ||
ENCACO | 11 963 | 12 059.2 | 0.86 | 1 478 | ||
pr439 | 107 217 | ACS | 108 711 | 110 501.8 | 1.39 | 1 816 |
MMAS | 108 857 | 110 614.5 | 1.53 | 1 850 | ||
ENCACO | 107 961 | 109 329.6 | 0.69 | 1 233 | ||
rat575 | 6 773 | ACS | 7 093 | 7 350.4 | 4.72 | 1 907 |
MMAS | 7 101 | 7 366.3 | 4.84 | 1 878 | ||
ENCACO | 6 922 | 7 009.8 | 2.20 | 1 676 | ||
p654 | 34 643 | ACS | 35 445 | 36 564.4 | 2.32 | 1 924 |
MMAS | 35 912 | 36 944.5 | 3.66 | 1 895 | ||
ENCACO | 34 793 | 35 147.4 | 0.43 | 1 692 | ||
u724 | 41 910 | ACS | 43 598 | 44 200.7 | 4.03 | 1 945 |
MMAS | 43 654 | 44 967.2 | 4.16 | 1 957 | ||
ENCACO | 42 895 | 43 377.7 | 2.35 | 1 900 |
表8
ENCACO与其他改进算法比较
TSP | 标准解 | ENCACO | 误差率/% | DChOA | 误差率/% | PBACO | 误差率/% |
---|---|---|---|---|---|---|---|
eil76 | 538 | 538 | 0 | 538 | 0 | 538 | 0 |
kroA150 | 265 24 | 26 525 | 0 | 27 231 | 2.67 | 26 605 | 0.30 |
ch150 | 6 528 | 6 528 | 0 | 6 715 | 2.86 | 6 533 | 0.07 |
kroA200 | 29 368 | 29 368 | 0 | 29 565 | 0.67 | 29 383 | 0.05 |
tsp225 | 3 916 | 3 916 | 0 | 3 997 | 2.07 | 3 923 | 0.17 |
lin318 | 42 029 | 42 236 | 0.49 | 44 136 | 5.01 | 42 384 | 0.84 |
pr439 | 107 217 | 107 954 | 0.69 | 111 262 | 3.77 | — | — |
表9
ENCACO与NBACO比较
TSP | 标准解 | ENCACO | NBACO | ||||
---|---|---|---|---|---|---|---|
最优解 | 误差率/% | 平均解 | 最优解 | 误差率/% | 平均解 | ||
eil51 | 426 | 426 | 0 | 426.8 | 426 | 0 | 428 |
kroA150 | 26 524 | 26 525 | 0 | 26 781.7 | 26 528 | 0.02 | 26 989 |
tsp225 | 3 916 | 3 916 | 0 | 3 965.3 | 3 924 | 0.20 | 3 992 |
a280 | 2 579 | 2 579 | 0 | 2 613.1 | 2 581 | 0.07 | 2 630 |
lin318 | 42 029 | 42 236 | 0.49 | 42 793.5 | 42 370 | 0.81 | 43 222 |
fl417 | 11 861 | 11 963 | 0.86 | 12 059.2 | 11 967 | 0.89 | 12 097 |
pr439 | 107 217 | 107 961 | 0.69 | 109 329.6 | 107 842 | 0.58 | 110 684 |
表10
ENCACO与SOS-ACO比较
TSP | 标准解 | ENCACO | SOS-ACO | ||||
---|---|---|---|---|---|---|---|
最优解 | 误差率/% | 平均解 | 最优解 | 误差率/% | 平均解 | ||
eil51 | 426 | 426 | 0 | 426.8 | 426 | 0 | 428.1 |
eil76 | 538 | 538 | 0 | 538.7 | 538 | 0 | 541.7 |
kroA100 | 21 282 | 21 282 | 0 | 21 397.8 | 21 282 | 0 | 21 290.1 |
ch150 | 6 528 | 6 528 | 0 | 6 554.5 | 6 558 | 0.46 | 6 571.2 |
kroA200 | 29 368 | 29 368 | 0 | 29 673.4 | 29 413 | 0.15 | 29 520.2 |
lin318 | 42 029 | 42 236 | 0.49 | 42 793.5 | 42 473 | 1.05 | 42 762.7 |
pr439 | 107 217 | 107 961 | 0.69 | 109 329.6 | 107 978 | 0.71 | 108 873.8 |
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