一种自适应模拟退火粒子群优化算法

doi:10.19665/j.issn1001-2400.2021.04.016

Abstract

Abstract:

Particle swarm optimization is widely used in various fields because of the few parameters to be set and the simple calculation structure.In order to improve the optimization speed and accuracy of the PSO,and to avoid falling into the local optimal solution,an adaptive simulated annealing PSO is proposed,which uses the hyperbolic tangent function to control the inertia weight factor for nonlinear adaptive changes,uses linear change strategies to control 2 learning factors,introduces the simulation annealing operation,set a temperature according to the initial state of the population,guide the population to accept the difference solution with a certain probability according to the Metropolis criterion,and ensure the ability to jump out of the local optimal solution.To verify the effect of the algorithm proposed in this paper,7 typical test functions and 5 algorithms proposed in the literature are selected for comparison and testing.According to the average value,standard deviation and number of iterations of the optimization results,the algorithm proposed in this paper has greatly improved the iteration accuracy,convergence speed and stability so as to overcome the shortcomings of particle swarm optimization.

Key words: particle swarm optimization, simulated annealing, inertia weight factor, self-adaptive adjust tactics

CLC Number:

TP301.6

YAN Qunmin,MA Ruiqing,MA Yongxiang,WANG Junjie. Adaptive simulated annealing particle swarm optimization algorithm[J].Journal of Xidian University, 2021, 48(4): 120-127.

Figures/Tables 8

函数	函数表达式	搜索空间
Sphere	f₁= $∑ i = 1 D x i 2$	[-100,100]
Levy	f₂=sin²(πω_i)+ $∑ i = 1 D - 1$ (ω_i-1)²[1+10sin²(πω_i+1)]+ (ω_D-1)²[1+sin²(2πω_D)], ω_i=1+(x_i-1)/4	[-10,10]
Ackley	f₃=-20exp $- 0.2 1 / D ∑ i = 1 D x i 2 1 / 2$ -exp((1/D) $∑ i = 1 D$ cos(2π $x i 2$ ))+20+e	[-30,30]
Griewank	f₄= $∑ i = 1 D x i 2 4000$ - $∏ i = 1 D$ cos $x 1 i$ +1	[-600,600]
Rastrigin	f₅= $∑ i = 1 D$ [ $x i 2$ -10cos(2πx_i)+10]	[-5.12,5.12]
Rosenbrock	f₆= $∑ i = 1 D - 1$ [100( $x i 2$ -x_i+1)²+(x_i-1)²]	[-2.408,2.408]
Schwefel	f₇=418.982 9D- $∑ i = 1 D$ x_isin\|x_i\|^1/2	[-500,500]

References 16

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函数	准则	MSMPSO	RPPSO	PSO-DAC	NDPSO	APSO-DA	文中算法
f₁	avg	2.48×10^-2	8.24×10	5.72×10²	4.24×10^-2	2.14×10^-4	0.00
	std	4.16×10^-2	8.99×10	3.65×10²	8.67×10^-2	1.14×10^-3	0.00
f₂	avg	3.91×10^-1	1.36	2.47	3.87×10^-2	8.56×10^-2	3.70×10^-2
	std	6.88×10^-1	1.23	1.80	9.86×10^-2	1.01×10^-1	4.34×10^-2
f₃	avg	1.78	4.87	7.90	3.89×10^-1	8.88×10^-16	8.88×10^-16
	std	9.44×10^-1	2.02	1.99	5.12×10^-1	9.86×10^-32	9.86×10^-32
f₄	avg	3.10×10^-1	2.17	7.05	1.67×10^-1	3.36×10^-3	0.00
	std	1.70×10^-1	2.25	4.65	2.05×10^-1	1.78×10^-2	0.00
f₅	avg	9.76	2.14×10	2.19×10	2.47	1.33×10^-1	0.00
	std	5.38	9.54	8.32	5.11	7.03×10^-1	0.00
f₆	avg	6.92	1.56×10	5.58×10	7.14	7.41	6.81
	std	1.76	1.30×10	3.41×10	1.65	2.60	3.17
f₇	avg	9.38×10²	1.58×10³	1.72×10³	8.81×10²	8.30×10²	8.22×10²
	std	2.87×10²	4.25×10²	3.07×10²	4.05×10²	2.86×10²	3.50×10²

函数	准则	MSMPSO	RPPSO	PSO-DAC	NDPSO	APSO-DA	文中算法
f₁	avg	1.93×10³	6.46×10³	9.74×10³	7.86×10²	2.04	0.00
	std	9.43×10²	2.48×10³	2.79×10³	2.53×10³	7.13	0.00
f₂	avg	8.68	2.05×10	2.55×10	1.10×10	2.16	2.04
	std	3.48	6.89	9.43	7.70	2.48	2.31
f₃	avg	8.74	1.30×10	1.44×10	6.32	1.83×10^-1	8.88×10^-16
	std	1.88	1.05	1.07	5.63	5.16×10^-1	5.07×10^-22
f₄	avg	1.85×10	5.82×10	9.99×10	1.92×10	6.47×10^-2	4.83×10^-2
	std	8.19	1.79×10	3.71×10	4.97×10	2.47×10^-1	2.64×10^-1
f₅	avg	1.05×10²	1.49×10²	1.72×10²	7.98×10	1.16×10	3.63
	std	2.06×10	2.49×10	2.77×10	3.86×10	1.70×10	8.68
f₆	avg	1.55×10²	4.54×10²	6.58×10²	4.05×10	2.87×10	2.87×10
	std	7.72×10	1.95×10²	1.96×10²	2.41×10	2.13×10^-1	4.03×10^-1
f₇	avg	4.74×10³	6.78×10³	7.65×10³	4.40×10³	4.13×10³	4.05×10³
	std	9.14×10²	5.80×10²	6.10×10²	1.02×10³	7.36×10²	6.62×10²

Adaptive simulated annealing particle swarm optimization algorithm

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