基于协方差分析的合作协同进化差分进化算法

doi:10.11959/j.issn.1000-436x.2023005

摘要/Abstract

摘要：

在大规模高维优化问题中，随着决策变量数目的增加，协同进化算法在搜索全局最优解过程中容易陷入局部最优。基于此，提出了一种基于协方差分析的合作协同进化差分进化算法，在根据决策变量之间的相关性对优化问题进行分组之后，针对子组件内部变量之间的相关性会影响种群进化过程的现象，在对子组件优化的过程中，利用协方差计算种群分布的特征向量，通过坐标旋转消除变量之间的相关性，有效避免在种群搜索过程中陷入局部最优，同时加快了算法的寻优速度。在CEC 2014测试函数集上进行了对比实验，实验结果表明，所提算法具有可行性。

关键词: 大规模优化问题, 合作协同进化, 相关性, 协方差分析, 差分进化

Abstract:

With the increase of the number of decision variables, cooperative coevolution algorithm is easy to fall into local optimization in the process of searching the global optimal solution in large-scale high-dimensional optimization problems.Based on this, a cooperative coevolution algorithm with covariance analysis for differential evolution was proposed.After the optimization problems were grouped according to the correlation between the decision variables, the correlation between the internal variables of the subcomponents would affect the population evolution process.In the process of subcomponent optimization, covariance was used to calculate the characteristic vector of population distribution, and the correlation between variables was eliminated through coordinate rotation, which effectively avoided falling into local optimization in the process of population search and speeded up the optimization speed of the algorithm.Comparative experiments were carried out on the CEC 2014 test suite.The experimental results show that the proposed algorithm is feasible.

Key words: large-scale optimization problem, cooperative coevolution, correlation, covariance analysis, differential evo-lution

中图分类号:

TP18

王彬, 任露, 王晓帆, 曹雅娟. 基于协方差分析的合作协同进化差分进化算法[J]. 通信学报, 2023, 44(1): 189-199.

Bin WANG, Lu REN, Xiaofan WANG, Yajuan CAO. Cooperative coevolution algorithm with covariance analysis for differential evolution[J]. Journal on Communications, 2023, 44(1): 189-199.

图/表 10

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表1

8个算法在50维CEC2014上的统计结果（运行50次）"

函数	CCDE	COVDE	DE	ADLADE	CSDE	TVDE	A-CC/COV-DE	CC-COV-DE
F1	8.01+	7.24×10⁵+	1.43×10⁶+	1.40×10⁶+	1.73×10⁶+	6.70×10⁵+	2.50×10^-1+	1.49×10^-4
F2	4.22×10⁶+	1.63×10²-	3.02-	3.63-	1.53×10²-	6.75×10^-9-	3.41×10⁴-	8.88×10⁵
F3	1.71×10¹+	4.44×10^-12-	2.75×10^-1+	4.69×10^-1～	3.06×10^-1+	6.19×10^-6-	1.35×10^-5-	1.27×10^-1
F4	9.34×10¹+	8.24×10¹-	5.78×10¹-	6.27×10¹-	9.66×10¹+	8.96×10¹+	8.13×10¹-	8.80×10¹
F5	2.12×10¹+	2.09×10¹～	2.11×10¹+	2.08×10¹	2.05×10¹-	2.07×10¹-	2.11×10¹+	2.09×10¹
F6	3.99-	4.44×10¹+	1.42-	1.75-	4.94-	6.14×10^-1-	4.13-	5.59
F7	6.79×10^-1+	1.36×10^-13-	1.27×10^-13-	1.48×10^-4-	1.91×10^-13-	1.82×10^-13-	3.80×10^-1-	5.42×10^-1
F8	9.48×10^-13～	1.37×10²+	1.87×10²+	3.63×10¹+	2.03×10¹+	1.40×10¹+	9.35×10^-13～	9.94×10^-13
F9	8.98×10¹+	1.63×10²+	3.53×10²+	5.72×10¹+	5.59×10¹+	4.96×10¹+	8.79×10¹+	4.28×10¹
F10	7.99×10^-3～	6.64×10³+	9.19×10³+	8.56×10²+	9.82×10²+	4.53×10²+	6.50×10^-3+	5.00×10^-3
F11	4.03×10³+	7.50×10³+	1.30×10⁴+	4.63×10³+	5.34×10³+	7.26×10³+	4.07×10³+	2.42×10³
F12	3.42+	1.58～	3.27+	1.50～	6.22×10^-1-	1.08-	1.76+	1.60
F13	5.50×10^-1+	4.02×10^-1-	4.61×10^-1～	3.87×10^-1-	2.36×10^-1-	3.09×10^-1-	5.69×10^-1+	4.77×10^-1
F14	3.62×10^-1+	2.61×10^-1～	3.38×10^-1+	3.64×10^-1+	2.85×10^-1+	3.39×10^-1+	2.79×10^-1～	2.76×10^-1
F15	3.25×10¹+	1.88×10¹～	3.10×10¹+	2.24×10¹+	7.20-	1.29×10¹-	1.87×10¹～	1.87×10¹
F16	2.23×10¹+	2.12×10¹～	2.21×10¹+	2.09×10¹-	2.02×10¹-	1.98×10¹-	2.12×10¹～	2.12×10¹
F17	7.72×10⁴+	1.29×10³-	1.58×10⁴+	1.52×10⁴+	5.04×10⁴+	3.44×10⁴+	1.14×10³-	4.01×10³
F18	1.21×10²+	8.91×10¹+	1.35×10²+	1.46×10²+	1.30×10²+	4.03×10²+	3.30×10¹-	4.72×10¹
F19	6.89-	1.14×10¹+	1.22×10¹+	1.06×10¹+	1.13×10¹+	1.74×10¹+	6.74-	9.42
F20	7.19×10¹+	6.04×10¹+	9.81×10¹+	1.06×10²+	6.74×10¹+	1.02×10²+	3.58×10¹+	3.39×10¹
F21	1.35×10⁴+	1.05×10³+	2.64×10³+	2.71×10³+	1.20×10⁴+	4.24×10⁴+	7.65×10²-	9.32×10²
F22	1.43×10³+	5.54×10²-	7.66×10²-	1.83×10²-	3.27×10²-	3.78×10²-	6.25×10²-	9.49×10²
F23	3.44×10²～	3.44×10²～	3.44×10²～	3.44×10²～	3.44×10²～	3.44×10²～	3.44×10²～	3.44×10²
F24	2.70×10²～	2.70×10²～	2.70×10²～	2.70×10²～	2.62×10²-	2.64×10²-	2.70×10²～	2.70×10²
F25	2.06×10²+	2.05×10²～	2.05×10²～	2.05×10²～	2.07×10²+	2.08×10²+	2.06×10²～	2.06×10²
F26	1.01×10²+	1.02×10²～	1.00×10²+	1.00×10²～	1.00×10²～	1.16×10²+	1.06×10²+	1.00×10²
F27	3.78×10²-	7.89×10²～	3.70×102-	3.71×10²-	3.47×10²-	3.51×10²-	6.89×10²～	6.85×10²
F28	1.07×10³-	1.35×10³～	1.08×10³-	1.08×10³-	1.07×10³-	1.06×10³-	1.36×10³～	1.38×10³
F29	1.20×10³+	7.05×10⁵+	9.40×10²+	9.90×10²+	1.60×10³+	1.47×10³+	6.57×10²+	6.16×10²
F30	8.37×10³～	8.46×10³～	8.25×10³-	8.36×10³～	8.30×10³～	8.59×10³+	8.47×10³～	8.42×10³
+/-/～	21/4/5	11/7/12	18/8/4	13/10/7	15/12/3	16/13/1	10/10/10

表1

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图9

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