多種群協(xié)方差學(xué)習(xí)差分進化算法

杜永兆; 范宇凌; 柳培忠; 唐加能; 駱炎民

doi:10.11999/JEIT180670

多種群協(xié)方差學(xué)習(xí)差分進化算法

doi: 10.11999/JEIT180670

杜永兆¹,
范宇凌¹,
柳培忠¹,
唐加能^{1, 2, ,},
駱炎民³

1.
華僑大學(xué)工學(xué)院? ?泉州? ?362021
2.
華僑大學(xué)機電及自動化學(xué)院? ?廈門? ?361021
3.
華僑大學(xué)計算機科學(xué)與技術(shù)學(xué)院? ?廈門? ?361021

基金項目: 國家自然科學(xué)基金(61605048, 61231002, 51075068)，福建省教育廳項目(JA15035)，泉州市科技局項目(2014Z103, 2015Z114)，華僑大學(xué)研究生科研創(chuàng)新能力培養(yǎng)計劃(1611422002)

詳細信息

作者簡介:
杜永兆：男，1985年生，副教授，博士，研究方向為智能計算、光學(xué)成像優(yōu)化、醫(yī)學(xué)圖像處理

范宇凌：男，1995年生，碩士生，研究方向為智能計算、圖像處理

柳培忠：男，1976年生，副教授，博士，研究方向為智能計算、視覺媒體檢索、深度學(xué)習(xí)、信息安全

唐加能：男，1983年生，副教授，博士，研究方向為智能計算、混沌同步和控制、網(wǎng)絡(luò)同步和控制、信息安全、語音信號處理

駱炎民：男，1975年生，副教授，博士，研究方向為機器學(xué)習(xí)、圖像處理、智能計算、模式識別

通訊作者:
唐加能　2812280164@qq.com

中圖分類號: TP18
計量
- 文章訪問數(shù): 2272
- HTML全文瀏覽量: 1091
- PDF下載量: 103
- 被引次數(shù): 0
出版歷程
- 收稿日期: 2018-07-06
- 修回日期: 2019-01-28
- 網(wǎng)絡(luò)出版日期: 2019-02-18
- 刊出日期: 2019-06-01

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

Funds: 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)

摘要

摘要: 種群多樣性與交叉算子在差分進化(DE)算法求解全局優(yōu)化問題中具有重要作用，該文提出一種多種群協(xié)方差學(xué)習(xí)差分進化(MCDE)算法。首先，采用多種群機制的種群結(jié)構(gòu)，利用每一子種群結(jié)合相應(yīng)的變異策略保證進化過程個體多樣性。然后，通過種群間的協(xié)方差學(xué)習(xí)，為交叉操作建立一個適當旋轉(zhuǎn)的坐標系統(tǒng)；同時，使用自適應(yīng)控制參數(shù)來平衡種群的勘測與收斂能力。最后，在單峰函數(shù)、多峰函數(shù)、偏移函數(shù)和高維函數(shù)的25個基準測試函數(shù)上進行測試，并同其他先進的進化算法對比，實驗結(jié)果表明該文算法相較于其他算法在求解全局優(yōu)化問題上達到最優(yōu)效果。
- 差分進化 /
- 多種群 /
- 協(xié)方差學(xué)習(xí) /
- 自適應(yīng)參數(shù)
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.
- Differential Evolution (DE) /
- Multi-poplutions /
- Covariance learning /
- Self-adaptive parameter

HTML全文

圖 1 種群進化過程坐標系

下載: 全尺寸圖片幻燈片

圖 2 4種演化算法在8個測試函數(shù)上的平均函數(shù)誤差

下載: 全尺寸圖片幻燈片

表 1 在D=30下3種算法與MCDE的Wilcoxon’s檢測結(jié)果比較

比較算法	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

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表 2 在D=30下各算法的Friedman平均排名

算法	顯著值	最終排名
JADE	3.78	3
CoDE	3.80	4
CoBiDE	3.34	2
MCDE	2.74	1

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表 3 30次獨立運行在4種算法的最優(yōu)解平均值及標準差

函數(shù)	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

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表 4 30次獨立運行在CLPSO, CMA-ES, GL-25, MCDE最優(yōu)解平均值及標準差

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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