基于种群状态信息的自适应差分进化算法

doi:10.11959/j.issn.1000-436x.2023113

Abstract

Abstract:

The local optimum and stagnation state information of the population seriously affects the performance of differential evolution (DE) algorithm.An advanced DE algorithm with population state processing measures was proposed to address the above two issues.When the population falled into the local optimum, the individuals in the population were learned randomly by LBFGS method to improve the global quality of the solution, and Gaussian mutation was employed to trigger new individuals to jump out of local optimum.As for the stagnation state, the covariance matrix of the population was applied to reorganize the target individuals based on the rotation of the spatial coordinates to suppress the stagnation state of the population and enhance the global search ability of the algorithm.In addition, a new selection strategy was designed, which built an external archive to store abandoned individuals after greedy selection.When the trial individual was inferior to the target individual, the algorithm no longer generated the next generation with greedy selection strategy, but made reasonable intelligent selection around the external archive to ensure that the algorithm converges to the global optimum.Compared with eight state-of-the-art DE algorithms on 29 benchmark functions, the experimental results show that the proposed algorithm has better performance in terms of the solution accuracy and convergence speed.

Key words: differential evolution, selection strategy, population status information, covariance matrix, external archive

CLC Number:

TP18

Weijie MAI, Weili LIU, Jinghui ZHONG. Self-adaptive differential evolution algorithm based on population state information[J]. Journal on Communications, 2023, 44(6): 34-46.

Figures/Tables 7

函数	量度	CODE		SADE		SinDE		RankDE		AEPDE-JADE		MPEDE		CSDE		ADEDE		NSPSDE
f₁	mean	2.84×10^-30	-	4.06×10^-39	-	4.36×10^-58	-	1.18×10^-31	-	4.16×10^-163	-	1.93×10^-60	-	2.01×10^-58	-	2.9×10^-34	-	5.21×10^-278
	std	2.39×10^-30		5.79×10^-39		2.40×10^-58		7.78×10^-32		0		4.21×10^-60		2.66×10^-58		1.65×10^-34		0
f₂	mean	8.77×10^-27	-	1.41×10^-36	-	1.30×10^-55	-	1.72×10^-28	-	2.03×10^-159	-	4.10×10^-56	-	2.42×10^-57	-	1.47×10^-30	-	2.33×10^-238
	std	6.62×10^-27		1.15×10^-36		1.05×10^-55		1.45×10^-28		4.54×10^-159		5.45×10^-56		3.33×10^-57		1.09×10^-30		0
f₃	mean	4.99×10^-24	-	5.53×10^-34	-	1.23×10^-52	-	4.13×10^-25	-	5.17×10^-150	-	1.63×10^-54	-	6.96×10^-54	-	2.65×10^-28	-	2.45×10^-279
	std	5.19×10^-24		4.66×10^-34		6.81×10^-53		7.41×10^-25		1.16×10^-149		2.04×10^-54		1.25×10^-53		1.45×10^-28		0
f₄	mean	3.19×10^-7	-	1.11×10^-4	-	6.65×10⁰	-	5.85×10^-7	-	1.86×10^-21	-	3.19×10^-39	-	3.30×10^-5	-	8.74×10^-2	-	1.21×10^-200
	std	4.61×10^-7		1.16×10^-4		2.31×10⁰		1.62×10^-7		4.16×10^-21		5.55×10^-39		3.17×10^-5		5.56×10^-2		0
f₅	mean	4.54×10^-15	-	2.76×10^-21	-	2.51×10^-32	-	9.07×10^-15	-	1.82×10^-78	-	4.79×10^-27	-	5.34×10^-28	-	8.37×10^-20	-	7.00×10^-149
	std	2.68×10^-15		1.66×10^-21		1.18×10^-32		5.10×10^-15		3.12×10^-78		4.71×10^-27		1.17×10^-27		2.35×10^-20		3.79×10^-148
f₆	mean	2.50×10^-7	-	2.69×10^-4	-	5.12×10^-7	-	2.39×10^-4	-	4.80×10^-3	-	7.27×10^-23	-	4.51×10^-10	-	4.50×10^-2	-	8.97×10^-137
	std	2.13×10^-7		5.43×10^-4		4.50×10^-7		1.59×10^-4		5.81×10^-3		8.64×10^-23		3.39×10^-10		9.65×10^-2		7.91×10^-137
f₇	mean	1.11×10^-27	-	1.82×10^-38	-	5.89×10^-57	-	3.39×10^-30	-	1.18×10^-159	-	1.41×10^-57	-	8.75×10^-56	-	4.64×10^-33	-	1.80×10^-277
	std	2.21×10^-27		3.31×10^-38		6.99×10^-57		2.68×10^-30		2.41×10^-159		2.69×10^-57		1.42×10^-55		2.96×10^-33		0
f₈	mean	8.37×10^-30	-	5.33×10^-39	-	7.63×10^-59	-	1.94×10^-31	-	3.33×10^-164	-	3.15×10^-60	-	1.90×10^-56	-	8.66×10^-34	-	2.49×10^-277
	std	7.58×10^-30		7.40×10^-39		5.24×10^-59		1.78×10^-31		0		4.33×10^-60		3.32×10^-56		5.95×10^-34		0
f₉	mean	5.03×10^-26	-	5.57×10^-33	-	1.12×10^-52	-	2.27×10^-27	-	1.72×10^-130	+	3.82×10^-41	-	2.41×10^-46	-	3.12×10^-31	-	7.40×10^-97
	std	6.28×10^-26		2.77×10^-33		3.94×10^-53		2.80×10^-27		3.28×10^-130		6.84×10^-41		4.53×10^-46		9.70×10^-32		2.07×10^-98
f₁₀	mean	-1.00×10⁰	≈	-1.00×10⁰	≈	-1.00×10⁰	≈	-1.00×10⁰	-	-1.00×10⁰	-	-1.00×10⁰	≈	-1.00×10⁰	≈	-1.00×10⁰	≈	-1.00×10⁰
	std	0		0		0		1.57×10^-16		1.57×10^-16		0		0		0		0
f₁₁	mean	7.22×10^-28	-	9.36×10^-34	-	1.95×10^-45	-	4.86×10^-29	-	3.21×10^-144	-	7.08×10^-63	-	3.07×10^-48	-	2.49×10^-26	-	1.72×10^-253
	std	5.98×10^-28		1.07×10^-33		1.28×10^-45		1.84×10^-29		7.19×10^-144		1.42×10^-62		4.18×10^-48		2.10×10^-26		0
f₁₂	mean	0	≈	0	≈	0	≈	0	≈	0	≈	0	≈	0	≈	0	≈	0
	std	0		0		0		0		0		0		0		0		0
f₁₃	mean	6.16×10^-3	+	8.38×10^-3	+	5.12×10^-3	+	5.70×10^-3	+	4.81×10^-3	+	1.25×10^-3	+	3.34×10^-2	+	9.43×10^-3	+	6.21×10^-2
	std	2.18×10^-3		2.52×10^-3		8.26×10^-4		1.57×10^-3		1.72×10^-3		3.24×10^-4		6.23×10^-3		1.43×10^-3		2.32×10^-2
f₁₄	mean	0	≈	0	≈	0	≈	0	≈	0	≈	0	≈	0	≈	0	≈	0
	std	0		0		0		0		0		0		0		0		0
f₁₅	mean	2.04×10^-6	-	4.62×10^-15	-	9.94×10¹	-	1.20×10²	-	0	≈	0	≈	0	≈	0	≈	0
	std	2.01×10^-6		6.36×10^-15		3.44×10⁰		3.88×10¹		0		0		0		0		0
f₁₆	mean	4.23×10^-3	-	8.94×10^-6	-	9.81×10^-3	-	2.65×10^-9	-	4.44×10^-17	-	2.75×10^-7	-	1.44×10^-7	-	5.51×10^-5	-	2.70×10^-147
	std	2.03×10^-3		7.01×10^-6		4.33×10^-3		5.53×10^-9		9.93×10^-17		4.07×10^-7		2.72×10^-7		5.82×10^-5		4.05×10^-147
f₁₇	mean	0	≈	0	≈	0	≈	0	≈	0	≈	0	≈	2.22×10^-17	-	0	≈	0
	std	0		0		0		0		0		0		4.97×10^-17		0		0
f₁₈	mean	1.99×10^-1	-	1.60×10^-1	-	1.99×10^-1	-	1.99×10^-1	-	1.99×10^-1	-	1.19×10^-1	-	1.99×10^-1	-	1.99×10^-1	-	1.06×10^-133
	std	1.13×10^-9		5.47×10^-2		7.71×10^-10		3.68×10^-9		1.69×10^-9		4.47×10^-2		3.10×10^-13		1.36×10^-10		4.94×10^-134
f₁₉	mean	2.77×10⁰	-	3.63×10⁰	-	1.52×10¹	-	1.99×10¹	-	2.45×10^-1	-	3.59×10^-1	-	3.78×10^-1	-	4.29×10⁰	-	2.45×10^-80
	std	1.57×10⁰		6.48×10^-1		1.02×10⁰		2.28×10⁰		4.48×10^-2		1.71×10^-1		3.40×10^-1		9.99×10^-1		0
f₂₀	mean	5.51×10^-15	-	2.66×10^-15	-	3.38×10^-15	-	4.09×10^-15	-	6.22×10^-15	-	2.66×10^-15	-	2.04×10^-14	-	2.66×10^-15	-	8.88×10^-16
	std	1.59×10^-15		0		1.59×10^-15		1.95×10^-15		0		0		2.15×10^-14		0		0
f₂₁	mean	1.78×10⁰	-	1.52×10¹	-	2.68×10¹	-	3.75×10¹	-	1.09×10^-1	-	2.02×10^-1	-	8.79×10⁰	-	1.33×10¹	-	0
	Std	2.47×10^-1		4.05×10^-1		1.32×10⁰		2.07×10⁰		8.16×10^-2		4.91×10^-2		1.94×10⁰		9.85×10^-1		0
f₂₂	mean	1.61×10^-3	-	1.11×10^-1	-	3.33×10^-1	-	1.55×10⁰	-	2.65×10^-5	-	1.75×10^-4	-	3.09×10^-2	-	1.17×10^-1	-	0
	std	2.51×10^-4		1.24×10^-2		5.18×10^-2		2.14×10^-1		5.40×10^-5		7.55×10^-5		4.90×10^-3		2.58×10^-2		0
f₂₃	mean	3.15×10^-1	+	3.59×10^-1	+	3.54×10^-1	+	3.76×10^-1	+	2.37×10^-1	+	2.30×10^-1	+	2.18×10^-1	+	3.39×10^-1	+	6.82×10^-1
	std	6.92×10^-2		5.81×10^-2		3.43×10^-2		5.74×10^-2		1.56×10^-2		1.71×10^-2		2.90×10^-2		2.24×10^-2		5.74×10^-1
f₂₄	mean	2.77×10^-1	≈	3.64×10^-1	≈	3.13×10^-1	≈	3.80×10^-1	≈	2.13×10^-1	≈	3.62×10^-1	≈	4.39×10^-1	≈	3.50×10^-1	≈	5.00×10^-1
	std	5.31×10^-2		3.50×10^-2		5.07×10^-2		1.63×10^-1		4.73×10^-2		9.12×10^-2		1.67×10^-1		6.77×10^-3		0
f₂₅	mean	1.55×10⁰	-	1.71×10⁰	-	4.02×10⁰	-	6.57×10⁰	-	5.16×10^-1	-	7.57×10^-1	-	5.76×10^-1	-	2.09×10⁰	-	0
	std	3.55×10^-1		2.24×10^-1		6.89×10^-1		2.84×10^-1		5.26×10^-2		6.37×10^-2		1.10×10^-1		2.81×10^-1		0
f₂₆	mean	1.25×10⁰	-	1.71×10⁰	-	4.21×10⁰	-	6.57×10⁰	-	5.16×10^-1	-	6.96×10^-1	-	4.47×10^-1	-	2.01×10⁰	-	0
	std	3.16×10^-1		1.29×10^-1		4.03×10^-1		4.01×10^-1		5.26×10^-2		6.01×10^-2		1.09×10^-1		2.60×10^-1		0
f₂₇	mean	9.85×10⁰	-	3.32×10^-9	-	5.84×10¹	-	9.98×10¹	-	0	≈	0	≈	4.60×10⁰	-	0	≈	0
	std	4.07×10⁰		3.99×10^-9		6.11×10⁰		2.20×10¹		0		0		1.52×10⁰		0		0
f₂₈	mean	1.32×10^-31	-	1.57×10^-32	≈	1.57×10^-32	≈	2.01×10^-32	-	1.57×10^-32	≈	1.57×10^-32	≈	4.38×10^-31	-	1.57×10^-32	≈	1.57×10^-32
	std	1.09×10^-31		0		0		8.44×10^-33		0		0		3.05×10^-31		0		0
f₂₉	mean	9.57×10^-30	-	1.35×10^-31	≈	1.35×10^-31	≈	4.03×10^-31	-	1.35×10^-31	≈	1.35×10^-31	≈	1.35×10^-31	≈	1.35×10^-31	≈	1.35×10^-31
	std	9.19×10^-30		0		0		2.20×10^-31		0		0		0		0		0
+、-、=的数目		2、23、4		2、21、6		2、21、6		2、23、4		3、19、7		2、19、8		2、23、4		2、20、7		—
最优解数目		4		6		6		3		8		9		5		8		25

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算法	等级	排名
CODE	6.379 3	8
SADE	5.620 7	5
SinDE	5.672 4	6
RankDE	7.172 4	9
AEPDE-JADE	3.206 9	2
MPEDE	3.465 5	3
CSDE	4.982 8	4
ADEDE	6.034 5	7
NSPSDE	2.465 5	1

对比算法	R⁺	R^-	p	α=0.05
CODE	383.0	52.0	1.39×10^-4	Yes
SADE	376.5	58.5	2.84×10^-4	Yes
SinDE	383.5	51.5	1.36×10^-4	Yes
RankDE	388.0	47.0	7.73×10^-5	Yes
AEPDE-JADE	347.0	88.0	4.10×10^-3	Yes
MPEDE	342.0	93.0	5.99×10^-3	Yes
CSDE	354.0	52.0	2.74×10^-4	Yes
ADEDE	369.0	66.0	6.07×10^-4	Yes

Self-adaptive differential evolution algorithm based on population state information

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