基于竞争式协同进化的混合变量粒子群优化算法

doi:10.16182/j.issn1004731x.joss.22-1466

系统仿真学报 ›› 2024, Vol. 36 ›› Issue (4): 844-858.doi: 10.16182/j.issn1004731x.joss.22-1466

基于竞争式协同进化的混合变量粒子群优化算法

张虎¹(), 张衡², 黄子路², 王喆², 付青坡², 彭瑾³, 王峰²()

^1.中国航天科工集团有限公司第三研究院体系对抗与智能信息系统总体部, 北京 100074
^2.武汉大学计算机学院, 武汉 430072
^3.海军装备部北京局驻北京地区第三军事代表室, 北京 100074

收稿日期:2022-12-07 修回日期:2023-03-13 出版日期:2024-04-15 发布日期:2024-04-18
通讯作者: 王峰 E-mail:jxzhanghu@126.com;fengwang@whu.edu.cn
第一作者简介:张虎(1986-)，男，研究员，博士，研究方向为作战概念设计仿真、体系需求开发、体系设计仿真。E-mail：jxzhanghu@126.com
基金资助:
国家自然科学基金(62173258);国防基础科研项目(JCKY2019204A007)

Mixed-variable Particle Swarm Optimization Algorithm Based on Competitive Coevolution

Zhang Hu¹(), Zhang Heng², Huang Zilu², Wang Zhe², Fu Qingpo², Peng Jin³, Wang Feng²()

^1.Department of System Confrontation and Intelligent Information System, the Third Research Institute of CASIC, Beijing 100074, China
^2.School of Computer Science, Wuhan University, Wuhan 430072, China
^3.The Third Military Representative Office of the Beijing Bureau of the Naval Armament Department in the Beijing Area, Beijing 100074, China

Received:2022-12-07 Revised:2023-03-13 Online:2024-04-15 Published:2024-04-18
Contact: Wang Feng E-mail:jxzhanghu@126.com;fengwang@whu.edu.cn

摘要/Abstract

摘要：

现实工业生产应用中存在大量的混合变量优化问题，这类问题的决策变量既包含连续变量，又包含离散变量。由于决策变量为混合类型，导致问题的决策空间变得不规则，采用已有的方法很难进行有效求解。引入协同进化策略，提出一种基于竞争式协同进化的混合变量粒子群优化算法(competitive coevolution based PSO，CCPSO)。设计基于容忍度的搜索方向调整机制来判断粒子的进化状态，从而自适应地调整粒子的搜索方向，避免陷入局部最优，平衡了种群的收敛性和多样性；引入基于竞争式协同进化的学习对象生成机制，在检测到粒子进化停滞时为每个粒子生成新的学习对象，从而推动粒子的进一步搜索，提高了种群的多样性；采用基于竞争学习的预测策略为粒子选择合适的学习对象，充分利用了新旧学习对象的学习潜力，保证了算法的收敛速度。实验结果表明：相比其他主流的混合变量优化算法，CCPSO可以获得更优的结果。

关键词: 混合变量优化, 协同策略, 进化算法, 粒子群

Abstract:

For the current algorithm, it is difficult to obtain the available solution due to the irregularity of problem decision space caused by the numerous mixed variable optimization problems during real industrial applications. The coevolution strategy is introduced and a mixed variable particle swarm optimization algorithm(CCPSO) based on competitive coevolution is proposed. The search direction adjustment mechanism based on tolerance is designed to judge the evolution state of particles, adaptively adjust the search direction of particles, avoid falling into local optimum, and balance the convergence and diversity of the population.The learning object generation mechanism is adopted for each particle to generate new learning objects when particle evolution stagnation is detected to promote the evolution of particles and improve the diversity of the population. The prediction strategy based on competitive learning is applied to select the appropriate learning objects for particles, which makes full use of the learning potential of new and old learning objects and ensures the convergence speed of the algorithm. Experimental results show that, CCPSO can obtain the better results compared with the other main mixed variable optimization algorithms.

Key words: mixed variable optimization, coevolution strategy, evolutionary algorithm, particle swarm

中图分类号:

TP273

张虎,张衡,黄子路等 . 基于竞争式协同进化的混合变量粒子群优化算法[J]. 系统仿真学报, 2024, 36(4): 844-858.

Zhang Hu,Zhang Heng,Huang Zilu,et al . Mixed-variable Particle Swarm Optimization Algorithm Based on Competitive Coevolution[J]. Journal of System Simulation, 2024, 36(4): 844-858.

图/表 12

图1

图2

图3

图4

图5

图6

表1

算法参数设置

算法名称	算法参数设置
GPSO	$N = 20$ ， $w = 0.4$ ， $c 1 = c 2 = 2$ ， $I m a x$ =10 000
CLPSO^[8]	$N = 20$ ， $w ∈ [0.4,0.9]$ ， $c = 1.494 45$ ， $m = 7$ ， $I m a x$ =10 000
AEDA^[17]	$N = 20$ ， $N P b e s t = 0.45$ ， $g p = 0.5$ ， $I m a x$ =10 000
SLPSO^[10]	$N = 20$ ， $α = 0.5$ ， $β = 0.01$ ， $I m a x$ =10 000
DEmv^[18]	$N = 20$ ， $F = R = 0.2$ ， $I m a x$ =10 000
CCPSO	$N = 20$ ， $w = 0.4$ ， $c = 2$ ， $T = 5$ ， $I m a x$ =10 000

表1

表2

表3

实验数值统计结果

函数类型	函数		GPSO	CLPSO	AEDA	SLPSO	DEmv	CCPSO
单峰	f1	误差均值	1.87E+01	2.57E-01	3.89E-02	3.60E+02	4.31E+03	2.36E-07
	f1	误差方差	1.15E+02	2.42E+00	9.83E-01	1.44E+03	3.62E+03	2.16E-06
	f2	误差均值	6.25E+06	5.78E+06	8.60E+07	2.18E+07	1.64E+08	5.38E+06
	f2	误差方差	1.57E+07	1.06E+07	2.99E+08	4.30E+07	1.34E+08	6.61E+06
	f3	误差均值	1.25E+09	1.16E+08	6.33E+08	1.20E+10	7.34E+10	3.26E+08
	f3	误差方差	6.69E+09	6.46E+08	2.36E+09	2.23E+10	7.92E+10	6.04E+08
	f4	误差均值	1.12E+03	6.13E+03	4.80E+04	4.41E+04	9.18E+04	3.86E+03
	f4	误差方差	4.26E+03	7.02E+03	3.08E+04	4.81E+04	4.71E+04	1.37E+03
	f5	误差均值	1.35E+01	1.10E+00	3.69E-01	2.10E+02	7.43E+02	3.68E-06
	f5	误差方差	1.28E+02	7.74E+00	2.33E+00	7.73E+02	4.51E+02	1.98E-05
多峰	f6	误差均值	1.29E+02	1.09E+02	2.10E+02	2.56E+02	6.73E+02	7.31E+01
	f6	误差方差	4.10E+02	1.67E+02	2.12E+02	2.81E+02	4.59E+02	1.07E+02
	f7	误差均值	5.69E+01	2.47E+01	2.55E+01	6.92E+01	1.88E+02	4.32E+01
	f7	误差方差	8.91E+01	4.97E+01	3.21E+01	7.38E+01	1.18E+02	3.08E+01
多峰	f8	误差均值	2.11E+01	2.11E+01	2.13E+01	2.11E+01	2.13E+01	2.11E+01
	f8	误差方差	2.22E-01	2.39E-01	1.71E-01	3.28E-01	2.47E-01	1.62E-01
	f9	误差均值	4.30E+01	2.08E+01	6.40E+01	3.54E+01	6.58E+01	3.27E+01
	f9	误差方差	4.67E+01	2.73E+01	1.11E+02	2.43E+01	9.55E+00	3.11E+01
	f10	误差均值	3.20E+01	4.65E+00	2.77E+01	2.18E+02	1.46E+03	2.75E+00
	f10	误差方差	1.37E+02	1.92E+01	7.31E+01	3.53E+02	8.86E+02	1.24E+00
	f11	误差均值	8.50E+01	4.90E+01	1.57E+02	1.38E+02	3.82E+02	4.40E+01
	f11	误差方差	1.09E+02	1.12E+02	1.11E+02	1.34E+02	1.15E+02	3.64E+01
	f12	误差均值	2.16E+02	2.64E+02	5.70E+02	2.05E+02	6.23E+02	1.66E+02
	f12	误差方差	2.17E+02	2.87E+02	1.01E+02	1.94E+02	1.49E+02	1.60E+02
	f13	误差均值	2.95E+02	3.37E+02	3.71E+02	3.22E+02	6.34E+02	3.12E+02
	f13	误差方差	3.31E+02	2.37E+02	7.72E+01	2.71E+02	1.61E+02	1.04E+02
	f14	误差均值	2.41E+03	4.54E+03	6.47E+03	4.43E+03	6.24E+03	1.27E+03
	f14	误差方差	4.14E+03	1.20E+04	1.68E+03	5.02E+03	1.44E+03	1.28E+03
	f15	误差均值	8.59E+03	1.31E+04	1.36E+04	7.02E+03	1.31E+04	6.97E+03
	f15	误差方差	8.30E+03	3.68E+03	2.04E+03	4.58E+03	1.94E+03	3.55E+03
	f16	误差均值	3.27E+00	3.51E+00	3.73E+00	1.50E+00	3.75E+00	3.15E+00
	f16	误差方差	2.24E+00	1.38E+00	1.27E+00	2.95E+00	2.08E+00	1.03E+00
	f17	误差均值	1.19E+02	9.64E+01	1.69E+02	2.17E+02	6.28E+02	4.72E+01
	f17	误差方差	1.81E+02	2.55E+02	7.76E+01	3.18E+02	2.23E+02	2.70E+01
	f18	误差均值	1.07E+02	4.86E+01	1.76E+02	2.16E+02	6.40E+02	4.65E+01
	f18	误差方差	1.62E+02	1.88E+02	3.62E+02	2.93E+02	1.91E+02	3.65E+01
	f19	误差均值	1.21E+01	2.11E+01	1.62E+01	6.14E+01	3.71E+01	7.42E+00
	f19	误差方差	3.98E+01	1.75E+01	1.15E+01	1.90E+02	6.69E+02	2.93E+00
	f20	误差均值	1.96E+01	2.04E+01	2.16E+01	1.87E+01	2.18E+01	1.85E+01
	f20	误差方差	5.31E+00	2.46E+00	1.32E+00	4.52E+00	1.22E+00	4.54E+00
复合	f21	误差均值	2.01E+02	2.00E+02	2.01E+02	2.37E+02	4.78E+02	2.00E+02
	f21	误差方差	1.11E+01	3.36E-01	1.71E-01	1.02E+02	1.84E+02	6.64E-09
	f22	误差均值	2.56E+03	5.31E+03	6.61E+03	4.72E+03	6.39E+03	1.42E+03
	f22	误差方差	2.95E+03	1.14E+04	1.68E+03	4.39E+03	1.43E+03	1.70E+03
	f23	误差均值	1.29E+04	1.54E+04	1.64E+04	1.21E+04	1.62E+04	1.20E+04
	f23	误差方差	5.56E+03	2.70E+03	9.06E+02	3.43E+03	1.50E+03	4.90E+03
	f24	误差均值	1.05E+03	1.19E+03	1.43E+03	9.93E+02	1.74E+03	9.14E+02
	f24	误差方差	4.93E+02	7.32E+02	2.96E+02	4.93E+02	2.75E+02	3.94E+02
	f25	误差均值	4.72E+02	5.00E+02	5.36E+02	4.65E+02	6.14E+02	4.47E+02
	f25	误差方差	8.24E+01	1.24E+02	6.83E+01	1.15E+02	5.44E+01	7.89E+01
	f26	误差均值	1.20E+03	7.94E+02	7.70E+02	1.65E+03	2.05E+03	1.05E+03
	f26	误差方差	1.15E+03	8.89E+02	8.39E+02	1.60E+03	2.33E+03	5.63E+02
	f27	误差均值	5.35E+03	4.91E+03	5.08E+03	5.49E+03	5.34E+03	5.01E+03
	f27	误差方差	8.66E+02	5.59E+02	5.83E+02	7.93E+02	2.19E+02	3.04E+02
	f28	误差均值	8.56E+03	9.94E+03	1.15E+04	7.68E+03	1.05E+04	7.56E+03
	f28	误差方差	4.27E+03	7.47E+03	1.18E+03	3.56E+03	1.45E+03	2.97E+03

表3

图7

表4

策略对比实验结果

函数类型	函数		CCPSO-CLP	CCPSO-CCLOG	CCPSO
单峰	f1	误差均值	8.19E+01	1.04E+02	2.36E-07
		误差方差	1.04E+03	1.14E+03	2.16E-06
	f2	误差均值	7.28E+06	1.22E+08	5.38E+06
		误差方差	2.22E+07	3.84E+08	6.61E+06
	f3	误差均值	1.06E+09	2.61E+10	3.26E+08
		误差方差	6.80E+09	4.39E+10	6.04E+08
	f4	误差均值	2.65E+04	3.32E+04	3.86E+03
		误差方差	2.56E+04	1.51E+04	1.37E+03
	f5	误差均值	1.63E+01	1.81E+01	3.68E-06
		误差方差	1.31E+02	1.18E+02	1.98E-05
多峰	f6	误差均值	2.34E+02	3.01E+02	7.31E+01
		误差方差	3.84E+02	5.74E+02	1.07E+02
	f7	误差均值	2.97E+01	1.11E+02	4.32E+01
		误差方差	8.70E+01	6.27E+01	3.08E+01
	f8	误差均值	2.12E+01	2.12E+01	2.11E+01
		误差方差	2.44E-01	1.82E-01	1.62E-01
	f9	误差均值	4.07E+01	5.62E+01	3.27E+01
		误差方差	4.21E+01	2.31E+01	3.11E+01
	f10	误差均值	5.20E+01	2.35E+02	2.75E+00
		误差方差	2.68E+02	1.22E+03	1.24E+00
	f11	误差均值	1.56E+02	2.24E+02	4.40E+01
		误差方差	2.22E+02	4.58E+02	3.64E+01
	f12	误差均值	3.25E+02	5.09E+02	1.66E+02
		误差方差	5.04E+02	2.14E+02	1.60E+02
	f13	误差均值	3.99E+02	5.28E+02	3.12E+02
		误差方差	1.13E+02	9.92E+01	1.04E+02
多峰	f14	误差均值	3.99E+03	9.68E+03	1.27E+03
		误差方差	4.44E+03	1.59E+04	1.28E+03
	f15	误差均值	1.27E+04	1.31E+04	6.97E+03
		误差方差	3.40E+03	2.03E+03	3.55E+03
	f16	误差均值	3.49E+00	3.63E+00	3.15E+00
		误差方差	2.27E+00	2.04E+00	1.03E+00
	f17	误差均值	2.04E+02	3.44E+02	4.72E+01
		误差方差	4.70E+02	7.52E+02	2.70E+01
	f18	误差均值	2.45E+02	3.23E+02	4.65E+01
		误差方差	6.17E+02	8.31E+02	3.65E+01
	f19	误差均值	1.57E+01	7.46E+01	7.42E+00
		误差方差	3.04E+01	6.62E+02	2.93E+00
	f20	误差均值	2.07E+01	2.09E+01	1.85E+01
复合		误差方差	1.79E+00	1.44E+00	4.54E+00
	f21	误差均值	2.06E+02	2.04E+02	2.00E+02
		误差方差	6.15E+01	5.79E+01	6.64E-09
	f22	误差均值	4.07E+03	8.68E+03	1.42E+03
		误差方差	4.51E+03	1.57E+04	1.70E+03
	f23	误差均值	1.57E+04	1.59E+04	1.20E+04
		误差方差	2.40E+03	9.87E+02	4.90E+03
	f24	误差均值	1.45E+03	1.56E+03	9.14E+02
		误差方差	3.55E+02	2.27E+02	3.94E+02
	f25	误差均值	5.33E+02	5.66E+02	4.47E+02
		误差方差	5.40E+01	6.21E+01	7.89E+01
	f26	误差均值	1.57E+03	1.91E+03	1.05E+03
		误差方差	1.99E+03	2.91E+03	5.63E+02
	f27	误差均值	5.31E+03	5.64E+03	5.01E+03
		误差方差	7.39E+02	8.60E+02	3.04E+02
	f28	误差均值	1.08E+04	1.14E+04	7.56E+03
		误差方差	3.86E+03	1.22E+03	2.97E+03

表4

表5

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函数类型	编号	函数名称	最优解
单峰	f1	Sphere Function	-1 400
	f2	Rotated High Conditioned Elliptic Function	-1 300
	f3	Rotated Bent Cigar Function	-1 200
	f4	Rotated Discus Function	-1 100
	f5	Different Powers Function	-1 000
多峰	f6	Rotated Rosenbrocks Function	-900
	f7	Rotated Schaffers f7 Function	-800
	f8	Rotated Ackleys Function	-700
	f9	Rotated Weierstrass Function	-600
	f10	Rotated Griewanks Function	-500
	f11	Rastrigins Function	-400
	f12	Rotated Rastrigins Function	-300
	f13	Non-Continuous Rotated Rastrigins Function	-200
	f14	Schwefel’s Function	-100
	f15	Rotated Schwefel’s Function	100
	f16	Rotated Katsuura Function	200
	f17	Lunacek-Bi-Rastrigin Function	300
	f18	Rotated Lunacek Bi-Rastrigin Function	400
	f19	Expanded Griewanks plus Rosenbrocks Function	500
	f20	Expanded Scaffers f6 Function	600
复合	f21	Composition Function 1 (n=5, Rotated)	700
	f22	Composition Function 2 (n=3, Unrotated)	800
	f23	Composition Function 3 (n=3, Rotated)	900
	f24	Composition Function 4 (n=3, Rotated)	1 000
	f25	Composition Function 5 (n=3, Rotated)	1 100
	f26	Composition Function 6 (n=5, Rotated)	1 200
	f27	Composition Function 7 (n=5, Rotated)	1 300
	f28	Composition Function 8 (n=5, Rotated)	1 400

算法	最优	最差	平均	方差
GPSO	2.658 55	3.487 27	3.128 16	2.2492E+00
CLPSO	2.628 52	2.628 56	2.628 54	4.8647E-15
AEDA	2.628 52	11.357 50	4.686 63	1.0079E+01
DEmv	2.658 55	2.800 16	2.673 12	2.3224E-01
SLPSO	2.658 55	3.487 27	3.321 53	1.8156E+01
CCPSO	2.628 52	2.628 52	2.628 52	0

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基于竞争式协同进化的混合变量粒子群优化算法

Mixed-variable Particle Swarm Optimization Algorithm Based on Competitive Coevolution

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