基于自适应莱维多样性的改进蚁群算法

doi:10.13229/j.cnki.jdxbgxb.20230372

摘要/Abstract

摘要：

本文提出了一种基于自适应莱维（Lévy）多样性机制的改进蚁群优化（SACO）算法解决算法存在收敛精度差、易陷入局部最优的问题，并将新算法应用到焊接梁工程优化问题中。SACO算法结合该机制随机步长搜索的特点提升种群多样性，使算法避免局部最优。进一步，本文设计了一系列实验测试SACO算法的性能。实验结果显示，该算法在函数实验中表现出更好的收敛性、更高的精度及更强的避免陷入局部最优的能力。最后在工程应用实验结果中，SACO算法在函数优化和焊接梁优化上展现出较强的竞争力，可作为现实工程问题求解的有效工具。

关键词: 群智能算法, 蚁群算法, 工程优化, 莱维多样性机制

Abstract:

The papers proposed an improved ant colony optimization algorithm（SACO） based on the adaptive Lévy diversity mechanism to enhance convergence accuracy and the ability to avoid local optimum. The new algorithm was applied to welded beam engineering optimization problem. SACO combines the mechanism to enhance the population diversity， making the algorithm avoid local optimum. The paper designed a series of experiments to test the performance of SACO. Experimental results show that the algorithm shows better convergence， accuracy， and the ability to avoid local optimization in function experiments. Meanwhile， the proposed algorithm is applied to the welded beam design problem， obtaining significantly better results than other comparison algorithms. SACO shows competitiveness in function optimization and welded beam design optimization， which can be used as an effective tool for solving real-life engineering problems.

Key words: swarm intelligence algorithm, ant colony optimization, engineering optimization, Lévy diversity mechanism

中图分类号:

TP305

杨娇寰,王鹏. 基于自适应莱维多样性的改进蚁群算法[J]. 吉林大学学报(工学版), 2024, 54(10): 2978-2983.

Jiao-huan YANG,Peng WANG. Improved ant colony algorithm based on adaptive Lévy diversity[J]. Journal of Jilin University(Engineering and Technology Edition), 2024, 54(10): 2978-2983.

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算法	+/-/=	均值	排名
SACO	~	1.617	1
DE	9/0/1	2.843	3
WOA	10/0/0	4.877	5
PSO	8/1/1	3.563	4
IGWO	7/1/2	2.430	2
SCADE	10/0/0	5.670	6

算法	F1		F2
算法	AVG	STD	AVG	STD
SACO	5.2444E+08	1.5989E+09	8.291 3E+03	1.227 9E+04
DE	1.560 0E+21	5.881 4E+21	2.036 6E+04	5.919 5E+03
WOA	4.155 5E+23	2.260 9E+24	1.640 8E+05	5.519 0E+04
PSO	3.327 3E+13	3.868 3E+13	6.502 2E+02	5.125 6E+01
IGWO	7.843 2E+13	2.882 5E+14	1.258 0E+03	5.171 7E+02
SCADE	1.817 8E+37	7.773 0E+37	6.044 3E+04	6.326 4E+03
算法	F3		F4
算法	AVG	STD	AVG	STD
SACO	4.734 6E+02	2.592 7E+01	5.8626E+02	1.633 6E+01
DE	4.905 8E+02	9.447 3E+00	6.070 9E+02	7.021 7E+00
WOA	5.448 3E+02	3.986 1E+01	7.909 9E+02	6.029 6E+01
PSO	4.783 5E+02	2.428 8E+01	7.473 6E+02	3.374 0E+01
IGWO	5.030 8E+02	2.804 4E+01	6.115 8E+02	2.446 6E+01
SCADE	3.275 8E+03	9.181 5E+02	8.314 3E+02	1.893 9E+01
算法	F5		F6
算法	AVG	STD	AVG	STD
SACO	8.1792E+02	2.543 2E+01	8.9043E+02	2.482 6E+01
DE	8.464 2E+02	8.661 8E+00	9.079 9E+02	9.104 2E+00
WOA	1.194 7E+03	9.676 6E+01	1.002 1E+03	4.361 3E+01
PSO	9.208 8E+02	1.443 3E+01	9.938 1E+02	3.526 9E+01
IGWO	9.120 4E+02	4.126 1E+01	8.938 7E+02	2.336 5E+01
SCADE	1.171 6E+03	3.120 4E+01	1.085 6E+03	1.561 9E+01
算法	F7		F8
算法	AVG	STD	AVG	STD
SACO	4.176 1E+03	6.099 1E+02	2.397 8E+03	2.886 4E+01
DE	5.798 2E+03	2.406 9E+02	2.412 0E+03	6.8674E+00
WOA	6.028 1E+03	7.392 3E+02	2.575 2E+03	5.649 9E+01
PSO	5.996 0E+03	6.155 2E+02	2.536 8E+03	3.633 2E+01
IGWO	4.634 8E+03	6.653 8E+02	2.399 7E+03	2.563 0E+01
SCADE	8.181 0E+03	2.381 9E+02	2.583 9E+03	2.202 9E+01
算法	F9		F10
算法	AVG	STD	AVG	STD
SACO	2.919 8E+03	2.151 7E+01	3.190 2E+03	7.217 6E+01
DE	2.956 4E+03	1.331 6E+01	3.197 5E+03	5.191 0E+01
WOA	3.153 0E+03	9.208 7E+01	3.346 2E+03	2.515 3E+02
PSO	3.189 2E+03	1.027 4E+02	3.246 4E+03	2.243 9E+01
IGWO	2.942 0E+03	3.177 1E+01	3.251 3E+03	3.140 8E+01
SCADE	3.175 7E+03	2.519 6E+01	4.312 2E+03	2.152 4E+02

算法	变量的最有值				最优成本
算法	h	l	t	b	最优成本
SACO	0.182 00	3.731 00	9.042 39	0.205 70	1.7232 02
RO	0.203 69	3.528 47	9.004 23	0.207 24	1.7353 44
SSA	0.205 70	3.471 40	9.036 60	0.205 70	1.724 910
SSA	0.205 70	3.471 40	9.036 60	0.205 70	1.724 910