三元相关性量子行为粒子群优化算法研究

doi:10.11959/j.issn.1000-436x.2015076

Abstract

Abstract:

In order to more effectively utilize existing information and improve QPSO's (quantum-behaved particle swarm optimization) convergence performance, the ternary correlation QPSO (TC-QPSO) algorithm was proposed based on the analysis of the random factors in location formula. The novel algorithm changed the information independent ran-dom processing method of standard QPSO and established internal relations during particles' own experience information, group sharing information and the distance from the particles' current location to the population mean best position using normal copula functions.Then, the method of generating ternary correlation factors was given by using the Cholesky square root formula. The simulation results of the test functions showed that TC-QPSO algorithm outperforms the stan-dard QPSO algorithm in terms of optimization results, given that the negative linear correlation exists betweenu and r1 or u andr2.

Key words: particle swarm optimization (PSO), quantum-behaved particle swarm optimization (QPSO), quantum poten-tial well, normal copula function; convergence

Tao WU,Xi CHEN,Yu-song YAN. Study of the ternary correlation quantum-behaved PSO algorithm[J]. Journal on Communications, 2015, 36(3): 208-215.

Figures/Tables 4

名称	表达式	搜索范围	初始化范围	最优解和最优值
Sphere	$f_{1} (x) = \sum_{i = 1}^{D} x_{i}^{2}$	[-100,100]^D	[-100,50]^D	f ₁(0,0,…,0)=0
Rosenbrock	$f_{2} (x) = [100 {(x_{i + 1} - x_{i}^{2})}^{2} + {(x_{i} - 1)}^{2}]$	[-10,10]^D	[-10,10]^D	f ₂(1,1,…,1)=0

名称	表达式	搜索范围	初始化范围	最优解和最优值
Rastrigin	$f_{3} (x) = \sum_{i = 1}^{D} (x_{i}^{2} - 10 \cos (2 π x_{i}) + 10)$	[-5.12,5.12]^D	[-5.12,2]^D	f ₃(0,0,…,0)=0
Griewank	$f_{4} (x) = \sum_{i = 1}^{D} \frac{x_{i}^{2}}{4000} - \prod_{i = 1}^{D} \cos (\frac{x_{i}}{\sqrt{i}}) + 1$	[-600,600]^D	[-600,200] ^D	f ₄(0,0,…,0)=0
Ackley	$f_{5} (x) = - 20 \exp (- 0.2 \sqrt{\frac{1}{D} \sum_{i = 1}^{D} x_{i}^{2}}) - \exp (\frac{1}{D} \sum_{i = 1}^{D} \cos (2 π x_{i})) + 20 + e$	[-32.786,32.786]^D	[-32.786,16]^D	f ₅(0,0,…,0)=0
Expanded Shaffer	f ₆(X)=g(x₁,x₂)+g(x₂,x₃)+…+g(x_D-1,x_D)+g(x_D,x₁)	[-100,100]^D	[-100,50] ^D	f ₆(0,0,…,0)=0
	$g (x, y) = 0.5 + \frac{{(\sin \sqrt{x^{2} + y^{2}})}^{2} - 0.5}{{(1.0 + 0.001 (\sqrt{x^{2} + y^{2}}))}^{2}}$

References 16

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模型	f₁	f₂	f₃	f₄	f₅	f₆
PTC-QPSO	2.87×10^-206	17.01	19.48	0.48	1.48×10^-13	6.51×10^-8
QPSO	4.24×10^-302	16.55	23.41	0.40	2.66×10^-15	1.91×10^-9
TC-QPSO1	0	16.54	12.80	1.56	2.66×10^-15	0
TC-QPSO2	3.81×10^-205	13.99	15.01	0	6.22×10^-15	4.52×10^-7
TC-QPSO3	0	14.69	11.95	0	1.33×10^-14	2.78×10^-8

Study of the ternary correlation quantum-behaved PSO algorithm

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