基于群体早熟程度和非线性周期振荡策略的改进粒子群算法

doi:10.3969/j.issn.1000-436x.2014.02.022

摘要/Abstract

摘要：

提出了一种新的粒子群优化算法——基于群体早熟收敛程度和非线性周期振荡策略的自适应混沌粒子群优化算法。利用混沌的遍历特性初始化粒子的速度和位置，根据种群的早熟收敛程度和粒子的适应度值自适应地调整惯性权重；学习因子则采用非线性周期振荡策略，模拟鸟类觅食过程中交替出现的分散和重组现象。基准测试函数的仿真结果表明，所提出的算法不仅收敛速度快、寻优质量高，而且具有良好的稳定性。

关键词: 粒子群算法, 早熟程度, 非线性周期振荡策略, 自适应, 混沌

Abstract:

A novel particle swarm optimization algorithm was proposed, which was adaptive chaos particle swarm opti-mization algorithm based on swarm premature convergence degree and nonlinear periodic oscillating strategy. The er-godic of chaos was used for initializing the velocities and positions of the particles. The inertia weights were adjusted adaptively according to the swarm's premature convergence degree and the particles' fitnesses, and the nonlinear periodic oscillating strategy was used for the learning coefficients, which simulates the decentralization and regroup of the birds when they were foraging. The simulation results on benchmark functions show that the proposed algorithm not only has fast convergent rate and high quality of optimization, but also has good stability.

Key words: PSO algorithm, prematurity degree, nonlinear periodic oscillating strategy, adaptive, chaos

朱喜华,李颖晖,李宁,范炳奎. 基于群体早熟程度和非线性周期振荡策略的改进粒子群算法[J]. 通信学报, 2014, 35(2): 182-189.

Xi-hua ZHU,Ying-hui LI,Ning LI,Bing-kui FAN. Improved PSO algorithm based on swarm prematurely degree and nonlinear periodic oscillating strategy[J]. Journal on Communications, 2014, 35(2): 182-189.

图/表 4

图1

表1

基准测试函数及其参数设置"

函数名称	数学表达式	全局最优值	非对称初始化区间	[x_min, x_max]
Sphere	$f (x) = \sum_{i = 1}^{n} x_{i}^{2}$	(0,…,0)	(50, 100)ⁿ	[-100, 100]
Rosenbrock	$f (x) = \sum_{i = 1}^{n - 1} [100 {(x_{i + 1} - x_{i}^{2})}^{2} + {(x_{i} - 1)}^{2}]$	(1,…,1)	(50, 100)ⁿ	[-100, 100]
Rastrigrin	$f (x) = \sum_{i = 1}^{n} [x_{i}^{2} - 10 \cos (2 π x_{i}) + 10]$	(0,…,0)	(5, 10)ⁿ	[-10, 10]
Griewank	$f (x) = \frac{1}{4000} \sum_{i = 1}^{n} x_{i}^{2} - \prod_{i = 1}^{n} \cos (x_{i} / \sqrt{i}) + 1$	(0,…,0)	(50, 100)ⁿ	[-600, 600]

表1

图2

表2

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函数	L-PSO		N-PSO		C-PSO		PD-PSO		PDNPO-PSO
函数	平均值	标准差	平均值	标准差	平均值	标准差	平均值	标准差	平均值	标准差
Sphere	0.060 0	1.939 6	0.045 0	1.246 6	0.032 4	1.229 7	0.016 9	1.228 0	0.006 4	0.351 3
Rosenbrock	-0.115 0	2.043 4	0.011 7	1.732 7	0.027 3	1.553 1	-0.032 3	2.588 1	-0.001 5	0.760 0
Rastrigrin	0.317 6	6.242 0	0.267 0	4.675 2	-0.181 2	4.215 4	0.201 6	4.763 4	0.134 0	2.266 5
Griewank	-0.125 4	2.609 6	0.172 5	1.972 6	0.038 6	1.324 5	0.048 3	0.824 6	0.056 3	1.534 7