基于协同博弈粒子群算法的故障指示器配置优化

doi:10.16182/j.issn1004731x.joss.22-0192

摘要/Abstract

摘要：

为了平衡配电网故障指示器的可靠性与经济性，提出一种多空间协同博弈粒子群算法对其进行优化。基于种群空间分组思想，将种群活动空间自适应分割，子空间中粒子博弈进化，并对粒子进行融合余弦相似反向策略的博弈计算，很好地平衡了算法的收敛性与多样性。仿真结果表明：对种群进行自适应的多空间划分有利于种群跳出局部极值，融合余弦相似反向的博弈计算有利于提升种群收敛精度，该方法具有很好的普适性和有效性。

关键词: 粒子群算法, 故障指示器, 优化配置, 博弈计算, 协同进化

Abstract:

In order to balance the reliability and economy of distribution network fault indicator, a multi-space cooperative game particle swarm optimization algorithm is proposed. Based on the idea of population space grouping, the population activity space is adaptively divided, the particle game evolution in subspace is achieved, and the game calculation of particle fusion cosine similar reverse strategy is carried out, which well balances the convergence and diversity of the algorithm. The simulation results show that the adaptive multi-space division of population is conducive to jumping out of the local extreme value, and the game calculation integrating cosine similar reverse is conducive to improving the precision of population convergence. The method has good universality and effectiveness.

Key words: PSO, fault indicator, optimal configuration, game calculation, co-calculation

中图分类号:

TP301.6

王旭, 季伟东, 周国辉. 基于协同博弈粒子群算法的故障指示器配置优化[J]. 系统仿真学报, 2023, 35(6): 1278-1289.

Xu Wang, Weidong Ji, Guohui Zhou. Fault Indicator Configuration Optimization Based on Cooperative Game Particle Swarm Algorithm[J]. Journal of System Simulation, 2023, 35(6): 1278-1289.

图/表 14

图1

图2

图3

表1

标准测试函数

函数编号	测试函数	解空间	模态
F1	Sphere Function	[-5.12, 5.12] ⁿ	单
F2	Trid Function	[-900, 900] ⁿ	单
F3	Sum of Different Powers Function	[-1, 1] ⁿ	单
F4	Dixon-Price Function	[-10, 10] ⁿ	单
F5	Sum Squares Function	[-5.12, 5.12] ⁿ	单
F6	Zakharov Function	[-10, 10] ⁿ	单
F7	Michalewicz Function	[0, $π$ ] ⁿ	多
F8	Ackley Function	[-32.76, 32.76] ⁿ	多
F9	Rastrigin Function	[-5.12, 5.12] ⁿ	多
F10	Perm Function 0, D, BETA	[-30, 30] ⁿ	多
F11	Levy Function	[-10, 10] ⁿ	多
F12	Griewank Function	[-600, 600] ⁿ	多

表1

表2

其他算法参数

算法名称	算法参数
MCGPSO	$w$ (起始)=0.9， $w$ (终止)=0.4 $c 1$ = $c 2$ =1.49
PSO	$w$ (起始)=0.9， $w$ (终止)=0.4， $c 1$ = $c 2$ =1.49
GA	$P c$ =0.7， $P m$ =1/n
DE	$P c$ =0.8

表2

图4

图5

图6

图7

表3

表4

图8

图9

表5

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测试函数	MCGPSO	PSO	GA	DE
Rank	1.50	2.41	2.75	3.33
F1	0	7.207×10^-2	6.329×10^-1	8.244×10¹
F2	-1.487×10²	-1.488×10²	-1.324×10²	-3.055×10³
F3	0	7.949×10⁴²	2.191×10⁷⁴	1.170×10¹³
F4	9.844×10^-1	7.905×10^-¹	9.675×10^-1	5.820×10⁵
F5	0	1.299×10²	1.977×10²	6.969×10²
F6	1.337	1.571	2.608	8.706×10⁴
F7	-7.359	-9.515	-9.902	-9.143
F8	8.882×10^-16	3.113	3.871	-9.143
F9	0	8.442×10¹	2.001×10²	3.403×10²
F10	4.605×10⁸⁷	3.333×10¹⁰⁶	9.194×10¹⁵⁹	3.127×10⁹⁶
F11	2.649	3.698	4.282	3.404×10⁴
F12	3.039×10^-1	5.414×10^-²	9.717×10^-1	9.869×10^-1

测试函数	MCGPSO	GOPSO	OPSO	FIPS
Rank	1.428	2.250	2.357	3.107
F2	-1.30E×10³	3.19×10⁷	3.26×10⁷	5.27×10⁷
F3	-1.20×10³	6.20×10⁹	4.03×10⁹	3.00×10⁸
F4	-1.10×10³	3.38×10⁴	3.36×10⁴	5.88×10⁴
F5	-9.95×10²	-1.00×10³	-1.00×10³	-1.00×10³
F7	-8.00×10²	-6.84×10²	-6.87×10²	-7.33×10²
F9	-6.00×10²	-5.66×10²	-5.65×10²	-5.64×10²
F10	-5.00×10²	-4.63×10²	-4.85×10²	-4.88×10²
F11	-3.68×10²	-3.46×10²	-3.43×10²	-2.97×10²
F12	-3.00×10²	-1.56×10²	-1.47×10²	-1.02×10²
F13	-2.00×10²	3.31×10¹	2.80×10¹	-1.10×10¹
F14	2.49×10³	1.42×10³	1.53×10³	5.98×10³
F15	1.00×10²	4.79×10³	5.64×10³	7.63×10³
F17	5.27×10²	3.69×10²	3.76×10²	5.02×10²
F18	4.02×10²	6.87×10²	6.57×10²	6.23×10²
F19	5.12×10²	5.06×10²	5.06×10²	5.16×10²
F20	6.00×10²	6.15×10²	6.15×10²	6.15×10²
F21	7.00×10²	1.02×10³	1.12×10³	1.03×10³
F22	3.48×10³	2.85×10³	2.66×10³	7.01×10³
F23	1.00×10³	6.15×10³	5.77×10³	8.73×10³
F27	1.50×10³	2.52×10³	2.52×10³	2.60×10³
F28	1.60×10³	2.49×10³	2.28×10³	4.41×10³

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