多种群协方差学习差分进化算法

杜永兆; 范宇凌; 柳培忠; 唐加能; 骆炎民

doi:10.11999/JEIT180670

引用本文: 杜永兆, 范宇凌, 柳培忠, 唐加能, 骆炎民. 多种群协方差学习差分进化算法[J]. 电子与信息学报, 2019, 41(6): 1488-1495. doi: 10.11999/JEIT180670 shu

Citation: Yongzhao DU, Yuling FAN, Peizhong LIU, Jianeng TANG, Yanmin LUO. Multi-populations Covariance Learning Differential Evolution Algorithm[J]. Journal of Electronics and Information Technology, 2019, 41(6): 1488-1495. doi: 10.11999/JEIT180670 shu

多种群协方差学习差分进化算法

1.
华侨大学工学院泉州 362021
2.
华侨大学机电及自动化学院厦门 361021
3.
华侨大学计算机科学与技术学院厦门 361021

作者简介: 杜永兆: 男，1985年生，副教授，博士，研究方向为智能计算、光学成像优化、医学图像处理;
范宇凌: 男，1995年生，硕士生，研究方向为智能计算、图像处理;
柳培忠: 男，1976年生，副教授，博士，研究方向为智能计算、视觉媒体检索、深度学习、信息安全;
唐加能: 男，1983年生，副教授，博士，研究方向为智能计算、混沌同步和控制、网络同步和控制、信息安全、语音信号处理;
骆炎民: 男，1975年生，副教授，博士，研究方向为机器学习、图像处理、智能计算、模式识别

通讯作者: 唐加能,2812280164@qq.com

基金项目: 国家自然科学基金(61605048, 61231002, 51075068)，福建省教育厅项目(JA15035)，泉州市科技局项目(2014Z103, 2015Z114)，华侨大学研究生科研创新能力培养计划资助项目(1611422002)

摘要: 种群多样性与交叉算子在差分进化(DE)算法求解全局优化问题中具有重要作用，该文提出一种多种群协方差学习差分进化(MCDE)算法。首先，采用多种群机制的种群结构，利用每一子种群结合相应的变异策略保证进化过程个体多样性。然后，通过种群间的协方差学习，为交叉操作建立一个适当旋转的坐标系统；同时，使用自适应控制参数来平衡种群的勘测与收敛能力。最后，在单峰函数、多峰函数、偏移函数和高维函数的25个基准测试函数上进行测试，并同其他先进的进化算法对比，实验结果表明该文算法相较于其他算法在求解全局优化问题上达到最优效果。

关键词:

English

Multi-populations Covariance Learning Differential Evolution Algorithm

1.
College of Engineering, Huaqiao University, Quanzhou 362021, China
2.
College of Mechanical Engineering and Automation, Huaqiao University, Xiamen 361021, China
3.
College of Computer Science and Technology, Huaqiao University, Xiamen 361021, China

Corresponding author: Jianeng TANG,2812280164@qq.com

Received Date: 2018-07-06
Accepted Date: 2019-01-28
Available Online: 2019-06-01
Fund Project: The National Natural Science Foundation of China(61605048, 61231002, 51075068), The Fujian Provincial Department of Education Project(JA15035), The Quanzhou Science and Technology Bureau Project(2014Z103, 2015Z114), Huaqiao University Graduate Research Innovation Capacity Development Program Funding Project(1611422002)

Abstract: The diversity of the population and the crossover operator algorithm play an important role in solving global optimization problems in Differential Evolution (DE). The Multi-poplutions Covariance learning Differential Evolution (MCDE) algorithm is proposed. Firstly, the population structure is a multi-poplutions mechanism, and each subpopulation combines the corresponding mutation strategy to ensure the individual diversity in the evolutionary process. Then, the covariance learning establishes a proper rotation coordinate system for the crossover operation in the population. At the same time, the adaptive control parameters are used to balance the ability of population survey and convergence. Finally, the proposed algorithm is conducted on 25 benchmark functions including unimodal, multimodal, shifted and high-dimensional test functions and compared with the state-of-the-art evolutionary algorithms. The experimental results show that the proposed algorithm compared with other algorithms has the best effect on solving the global optimization problem.

Key words:

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图 1 种群进化过程坐标系

下载: 全尺寸图片幻灯片

图 2 4种演化算法在8个测试函数上的平均函数误差

下载: 全尺寸图片幻灯片

表 1 在D=30下3种算法与MCDE的Wilcoxon’s检测结果比较

比较算法	R⁺	R^–	P值	$\alpha $=0.05	$\alpha $=0.10
JADE	240.5	59.5	0.007012	是	是
CoDE	264.5	60.5	0.005181	是	是
CoBiDE	251.0	74.0	0.016633	是	是

下载: 导出CSV

表 2 在D=30下各算法的Friedman平均排名

算法	显著值	最终排名
JADE	3.78	3
CoDE	3.80	4
CoBiDE	3.34	2
MCDE	2.74	1

下载: 导出CSV

表 3 30次独立运行在4种算法的最优解平均值及标准差

函数	JADE	CoDE	CoBiDE	MCDE
F₁	0.00E+00±0.00E+00≈	0.00E+00±0.00E+00≈	0.00E+00±0.00E+00≈	0.00E+00±0.00E+00
F₂	1.26E–28±1.22E–28+	6.77E–15±3.44E–15–	1.60E–12±2.90E–12–	8.49E–28±3.75E–28
F₃	8.42E+03±6.58E+03–	5.65E+05±5.66E+04–	7.26E+04±5.64E+04–	2.74E–12±2.82E–11
F₄	4.13E–16±3.45E–16–	6.21E–03±4.67E–02–	1.16E–03±2.74E–03–	7.57E–22±4.26E–21
F₅	7.59E–08±5.65E–07–	3.16E+02±3.62E+02–	8.03E+02±1.51E+01–	5.38E–10±7.12E–10
F₆	1.16E+01±3.16E+01–	3.32E–01±6.57E–01–	4.13E–02±9.21E–02+	3.19E–01±1.09E–01
F₇	8.27E–03±8.22E–03–	7.39E–03±6.45E–03–	1.77E–03±3.73E–03–	1.52E–03±4.11E–03
F₈	2.09E+01±1.68E–01≈	2.01E+01±1.25E–01+	2.07E+01±3.75E–01+	2.09E+01±4.21E–02
F₉	0.00E+00±0.00E+00+	0.00E+00±0.00E+00+	0.00E+00±0.00E+00+	2.64E–07±5.87E–07
F₁₀	2.42E+01±5.44E+00–	4.21E+01±2.84E+01–	4.41E+01±1.29E+01–	2.28E+01±4.27E+00
F₁₁	2.57E+01±2.21E+00–	1.24E+01±3.55E+00+	5.62E+00±2.19E+00+	1.51E+01±6.81e+00
F₁₂	6.45E+03±2.89E+03–	3.21E+03±4.48E+03–	2.94E+03±3.93E+03–	2.12E+03±1.34E+03
F₁₃	1.47E+00±1.15E–01+	1.66E+00±3.25E–01+	2.64E+00±1.13E+00–	1.74E+00±2.04E–01
F₁₄	1.23E+01±3.21E–01≈	1.23E+01±3.56E–01≈	1.23E+01±4.90E–01≈	1.23E+01±2.66E–01
F₁₅	3.61E+02±2.24E+02+	4.00E+02±5.24E+01≈	4.04E+02±5.03E+01–	4.00E+02±1.09E+02
F₁₆	9.33E+01±1.31E+02–	7.25E+01±6.22E+01+	7.38E+01±3.66E+01–	5.37E+01±3.01E+01
F₁₇	1.21E+02±1.08E+02–	7.16E+01±2.35E+01–	7.25E+01±2.02e+01–	6.36E+01±6.41E+01
F₁₈	9.04E+02±1.24E–01≈	9.04E+02±1.34E+00≈	9.03E+02±1.05E+01≈	9.03E+02±6.01E–01
F₁₉	9.04E+02±8.32E+00≈	9.04E+02±3.22E–01≈	9.03E+02±1.04E+01≈	9.03E+02±2.31E–01
F₂₀	9.04E+02±7.65E–01≈	9.04E+02±7.11E–01≈	9.04E+02±5.95E–01≈	9.03E+02±2.45E–01
F₂₁	5.00E+02±4.67E–13≈	5.00E+02±4.68E–13≈	5.00E+02±4.62E–13≈	5.00E+02±4.51E–14
F₂₂	8.68E+02±2.24E+01≈	8.78E+02±3.54E+01≈	8.69E+02±2.80E+01≈	8.69E+02±1.89E+01
F₂₃	5.48E+02±8.62E+01–	5.34E+02±4.45E–04≈	5.34E+02±1.30E–04≈	5.34E+02±2.49E–13
F₂₄	2.00E+02±2.12E–14≈	2.00E+02±2.62E–14≈	2.00E+02±2.90E–14≈	2.00E+02±2.90E–14
F₂₅	2.11E+02±7.35E–01–	2.11E+02±6.82E–01–	2.10E+02±7.73E–01–	2.09E+02±2.78E–01
+/–/≈	3/13/9	5/10/10	4/13/8

下载: 导出CSV

表 4 30次独立运行在CLPSO, CMA-ES, GL-25, MCDE最优解平均值及标准差

Function	CLPSO	CMA-ES	GL-25	MCDE
F₁	0.00E+00±0.00e+00≈	1.58E–25±3.35E–26–	5.60E–27±1.76E–26–	0.00E+00±0.00E+00
F₂	8.40E+02±1.90E+02–	1.12E–24±2.93E–25–	4.04E+01±6.28E+01–	8.49E–28±3.75E–28
F₃	1.42E+07±4.19E+06–	5.54E–21±1.69E–21+	2.19E+06±1.08E+06–	2.74E–12±2.82E–11
F₄	6.99E+03±1.73E+03–	9.15E+05±2.16E+06–	9.07E+02±4.25E+02–	7.57E–22±4.26E–21
F₅	3.86E+03±4.35E+02–	2.77E–10±5.04E–11+	2.51E+03±1.96E+02–	5.38E–10±7.12E–10
F₆	4.16E+00±3.48E+00–	4.78E–01±1.32E+00–	2.15E+01±1.17E+00–	3.19E–01±1.09E–01
F₇	4.51E–01±8.47E–02–	1.82E–03±4.33E–03–	2.78E–02±3.62E–02–	1.52E–03±4.11E–03
F₈	2.09E+01±4.41E–02–	2.03E+01±5.72E–01+	2.09E+01±5.94E–02–	2.09E+01±4.21E–02
F₉	0.00e+00±0.00e+00+	4.45E+02±7.12E+01–	2.45E+01±7.35E+00–	2.64E–07±5.87E–07
F₁₀	1.04E+02±1.53E+01–	4.63E+01±1.16E+01–	1.42E+02±6.45E+01–	2.28E+01±4.27E+00
F₁₁	2.60E+01±1.63E+00–	7.11E+00±2.14E+00+	3.27E+01±7.79E+00–	1.51E+01±6.81e+00
F₁₂	1.79E+04±5.24E+03–	1.26E+04±1.74E+04–	6.53E+04±4.69E+04–	2.12E+03±1.34E+03
F₁₃	2.06E+00±2.15E–01–	3.43E+00±7.60E–01–	6.23E+00±4.88E+00–	1.74E+00±2.04E–01
F₁₄	1.28E+01±2.48E–01–	1.47E+01±3.31E–01–	1.31E+01±1.84E–01–	1.23E+01±2.66E–01
F₁₅	5.77E+01±2.76E+01–	5.55E+02±3.32E+02–	3.04E+02±1.99E+01+	4.00E+02±1.09E+02
F₁₆	1.74E+02±2.82E+01–	2.98E+02±2.08E+02–	1.32E+02±7.60E+01–	5.37E+01±3.01E+01
F₁₇	2.46E+02±4.81E+01–	4.43E+02±3.34E+02–	1.61E+02±6.80E+01–	6.36E+01±6.41E+01
F₁₈	9.13E+02±1.42E+00–	9.04E+02±3.01E–01≈	9.07E+02±1.48E+00–	9.03E+02±6.01E–01
F₁₉	9.14E+02±1.45E+00–	9.16E+02±6.03E+01–	9.06E+02±1.24E+00–	9.03E+02±2.31E–01
F₂₀	9.14E+02±3.62E+00–	9.04E+02±2.71E–01≈	9.07E+02±1.35E+00–	9.03E+02±2.45E–01
F₂₁	5.00E+02±3.39E–13≈	5.00E+02±2.68E–12≈	5.00E+02±4.83E–13≈	5.00E+02±4.51E–14
F₂₂	9.72E+02±1.20E+01–	8.26E+02±1.46E+01+	9.28E+02±7.04E+01–	8.69E+02±1.89E+01
F₂₃	5.34E+02±2.19E–04≈	5.36E+02±5.44E+00≈	5.34E+02±4.66E–04≈	5.34E+02±2.49E–13
F₂₄	2.00E+02±1.49E–12≈	2.12E+02±6.00E+01–	2.00E+02±5.52E–11≈	2.00E+02±2.90E–14
F₂₅	2.00E+02±1.96E+00+	2.07E+02±6.07E+00≈	2.17E+02±1.36E–01–	2.09E+02±2.78E–01
+/–/≈	2/19/4	5/15/5	1/21/3

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