Dual Ant Colony Algorithm Based on Backtracking Migration and Matching Learning

doi:10.3778/j.issn.1673-9418.2104006

Journal of Frontiers of Computer Science and Technology ›› 2022, Vol. 16 ›› Issue (12): 2797-2808.DOI: 10.3778/j.issn.1673-9418.2104006

• Artificial Intelligence • Previous Articles Next Articles

Dual Ant Colony Algorithm Based on Backtracking Migration and Matching Learning

CHEN Da¹, YOU Xiaoming¹^,⁺(), LIU Sheng²

1. School of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Shanghai 201620,;China
2. School of Management, Shanghai University of Engineering Science, Shanghai 201620, China

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.
YOU Xiaoming, born in 1963, Ph.D., professor, M.S. supervisor. Her research interests include swarm intelligent systems, distributed parallel processing and evolutionary computing.
LIU Sheng, born in 1966, Ph.D., professor, M.S. supervisor. His research interests include quantum inspired evolutionary computation, distributed parallel processing and evolutionary computing.
Supported by:
National Natural Science Foundation of China(61673258);National Natural Science Foundation of China(61075115)

引入特征迁移和匹配学习的双蚁型蚁群算法

陈达¹, 游晓明¹^,⁺(), 刘升²

1.上海工程技术大学电子电气工程学院，上海 201620
2.上海工程技术大学管理学院，上海 201620

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。
游晓明（1963—），女，江苏兴化人，博士，教授，硕士生导师，主要研究方向为群智能系统、分布式并行处理、进化算法。
刘升（1966—），男，湖北大冶人，博士，教授，硕士生导师，主要研究方向为量子启发式进化算法、分布式并行处理、进化算法。
基金资助:
国家自然科学基金(61673258);国家自然科学基金(61075115)

Abstract

Abstract:

In order to solve the problems of slow convergence speed and easy to fall into local optimum of tradi-tional ant colony algorithm in solving traveling salesman problem (TSP), the dual ant colony algorithm based on backtracking migration and matching learning (BMACS) is proposed. Firstly, the population is dynamically graded into exploration ants and tracking ants. The ants with higher fitness are exploration ants and the ones with lower fitness are tracking ants. Secondly, a local feature transfer mechanism is proposed, in which there are two strategies: in the feature transfer strategy, the pheromone on the common path of exploration ants is rewarded, and this path is transferred into the pheromone matrix as a local feature, so as to improve the influence of exploration ants and acce-lerate the convergence speed of the algorithm; in the mutation learning strategy, the tracking ants are responsible for exploring the suboptimal path, and adaptively reconstruct the path of exploration ants to enrich the diversity of the population. Finally, when the algorithm stagnates, the matching learning mechanism is used to communicate and learn between the current optimal individual and the historical optimal individual with the highest similarity, and the pheromone is reorganized to increase the diversity of the population, thus improving the ability of the algorithm to jump out of the local optimal. Simulation experiments are carried out with MATLAB for multiple sets of cases in TSPLIB, and the results show that the improved algorithm balances diversity and convergence speed, and effecti-vely improves the quality of solution.

Key words: ant colony algorithm, traveling salesman problem (TSP), local feature migration, matching learning, dyna-mic classification

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。

关键词: 蚁群算法, 旅行商问题（TSP）, 局部特征迁移, 匹配学习, 动态分级

CLC Number:

TP18

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.

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.

Figures/Tables 20

Fig.1 Communication between exploration and tracking ants

Table 1 Statistics on influence of value of C on accuracy

数据集名称	最优解	$C$ 取值	平均误差/%
eil51	426	1	0.71
		2	0.52
		3	0.23
		4	0.41
		5	0.53
		6	0.66

Table 1 Statistics on influence of value of C on accuracy

数据集名称	最优解	$C$ 取值	平均误差/%
eil51	426	1	0.71
		2	0.52
		3	0.23
		4	0.41
		5	0.53
		6	0.66

Fig.2 Distribution process of tracking ants

Fig.3 Common feature selection

Fig.4 Feature migration process

Fig.5 Mutation learning process

Table 2 Comparison of complexity of different algorithms

算法	时间复杂度 $O$
BMACS	$N c ∙ m ∙ n c i t y$
DBA	$N c ∙ m ∙ n c i t y$
SA-MMAS	$N c ∙ m ∙ n c i t y$
FWA	$N c ∙ m ∙ n c i t y$
CFWA	$N c ∙ m ∙ n c i t y$
ACS	$N c ∙ m ∙ n c i t y$

Table 2 Comparison of complexity of different algorithms

算法	时间复杂度 $O$
BMACS	$N c ∙ m ∙ n c i t y$
DBA	$N c ∙ m ∙ n c i t y$
SA-MMAS	$N c ∙ m ∙ n c i t y$
FWA	$N c ∙ m ∙ n c i t y$
CFWA	$N c ∙ m ∙ n c i t y$
ACS	$N c ∙ m ∙ n c i t y$

Table 3 Experimental factors and levels of BMACS

Level	$α$	$β$	$ρ$	$ξ$	$q 0$
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

Table 3 Experimental factors and levels of BMACS

Level	$α$	$β$	$ρ$	$ξ$	$q 0$
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

Table 4 Orthogonal test scheme and test results of BMACS

NO.	$α$	$β$	$ρ$	$ξ$	$q 0$	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

Table 4 Orthogonal test scheme and test results of BMACS

NO.	$α$	$β$	$ρ$	$ξ$	$q 0$	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

Table 5 Analysis of test results of BMACS

参数	$α$	$β$	$ρ$	$ξ$	$q 0$
$T 1$	2 222.35	2 267.70	2 223.65	2 231.25	2 236.25
$T 2$	2 203.60	2 228.30	2 210.60	2 209.75	2 213.20
$T 3$	2 225.70	2 190.85	2 226.05	2 210.65	2 213.90
$T 4$	2 223.15	2 187.95	2 214.50	2 223.15	2 211.45
$t 1$	555.59	566.93	555.91	557.81	559.06
$t 2$	550.90	557.08	552.65	552.44	553.30
$t 3$	556.43	547.71	556.51	552.66	553.48
$t 4$	555.79	546.99	553.63	555.79	552.86
$m a x$	556.43	566.93	556.51	557.81	559.06
$m i n$	550.90	546.99	552.65	552.44	552.86
$r a n g e$	15.53	19.94	3.86	5.37	6.20
$s c h e m e$	Level2	Level4	Level2	Level2	Level4

Table 5 Analysis of test results of BMACS

参数	$α$	$β$	$ρ$	$ξ$	$q 0$
$T 1$	2 222.35	2 267.70	2 223.65	2 231.25	2 236.25
$T 2$	2 203.60	2 228.30	2 210.60	2 209.75	2 213.20
$T 3$	2 225.70	2 190.85	2 226.05	2 210.65	2 213.90
$T 4$	2 223.15	2 187.95	2 214.50	2 223.15	2 211.45
$t 1$	555.59	566.93	555.91	557.81	559.06
$t 2$	550.90	557.08	552.65	552.44	553.30
$t 3$	556.43	547.71	556.51	552.66	553.48
$t 4$	555.79	546.99	553.63	555.79	552.86
$m a x$	556.43	566.93	556.51	557.81	559.06
$m i n$	550.90	546.99	552.65	552.44	552.86
$r a n g e$	15.53	19.94	3.86	5.37	6.20
$s c h e m e$	Level2	Level4	Level2	Level2	Level4

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

Fig.6 Optimum path maps

Fig.7 Comparison of rat99 test set

Fig.8 Comparison of kroA150 test set

Fig.9 Comparison of kroA200 test set

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^[12]	426	—	21 282	—	—	—
SGSAA^[13]	426	538	—	—	—	—
GA-SAC^[14]	426	538	21 282	—	—	42 329
IADUACO^[15]	427	538	—	—	—	—
PACO-3OPT^[16]	426	538	21 282	—	29 533	—
EDHACO^[17]	426	538	21 282	26 328	29 694	43 291
PCCACO^[18]	426	538	21 282	26 130	29 393	42 461
DSMO^[19]	426	538	21 298	26 601	30 481	44 118
WWO^[20]	427	557	21 668	—	31 064	—

Fig.10 Individual distribution map

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

Fig.11 Comparison between variant learning and original algorithm on eil51

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
lin318	42 029	ACS	43 008	2.30
fl417	11 861	ACS+回溯	11 990	1.09
fl417	11 861	ACS	12 057	1.32

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Dual Ant Colony Algorithm Based on Backtracking Migration and Matching Learning

引入特征迁移和匹配学习的双蚁型蚁群算法

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[4]	LIU Yifan, YOU Xiaoming, LIU Sheng. Ant Colony Optimization Algorithm Based on Dynamic Recombination and Co- operative Communication Strategy [J]. Journal of Frontiers of Computer Science and Technology, 2021, 15(8): 1511-1525.
[5]	MENG Jingwen, YOU Xiaoming, LIU Sheng. Double Ant Colony Algorithm Based on Collaborative Mechanism and Dynamic Regulation Strategy [J]. Journal of Frontiers of Computer Science and Technology, 2021, 15(11): 2206-2221.
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