求解全局优化问题的正交协方差矩阵自适应进化策略算法

doi:10.3724/SP.J.1087.2012.00981

计算机应用 ›› 2012, Vol. 32 ›› Issue (04): 981-985.DOI: 10.3724/SP.J.1087.2012.00981

求解全局优化问题的正交协方差矩阵自适应进化策略算法

黄亚飞¹,²,梁昔明²,陈义雄²

1. 长沙理工大学电气与信息工程学院, 长沙 410114
2. 中南大学信息科学与工程学院, 长沙 410083

收稿日期:2011-09-23 修回日期:2011-11-20 发布日期:2012-04-20 出版日期:2012-04-01
通讯作者: 黄亚飞
作者简介:黄亚飞(1975-),男,湖南郴州人,讲师,博士研究生,主要研究方向:最优化方法及其应用、进化计算;
梁昔明(1967-),男,湖南汨罗人,教授,博士生导师,主要研究方向:过程控制及系统优化、最优化方法;
陈义雄(1974-),男,湖南湘潭人,讲师,博士研究生,主要研究方向:智能优化算法。
基金资助:
国家自然科学基金资助项目;教育部留学回国人员科研启动基金;湖南省教育厅项目

Hybrid orthogonal CMAES for solving global optimization problems

HUANG Ya-fei¹,²,LIANG Ximing²,CHEN Yi-xiong²

1. School of Electric and Information Engineering, Changsha University of Science and Technology, Changsha Hunan 410114, China
2. School of Information Science and Engineering, Central South University, Changsha Hunan 410083, China

Received:2011-09-23 Revised:2011-11-20 Online:2012-04-20 Published:2012-04-01
Contact: HUANG Ya-fei
Supported by:
;Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry, China (SRF for ROCS, SEM)

摘要/Abstract

摘要： 针对协方差矩阵自适应进化策略(CMAES)求解高维多模态函数时存在早熟收敛及求解精度不高的缺陷, 提出一种融合量化正交设计(OD/Q)思想的正交CMAES算法。首先利用小种群的CMAES进行快速搜索, 当算法陷入局部极值时, 依据当前最好解的位置动态选取基向量, 接着利用OD/Q构造的试验向量探测包括极值附近区域在内的整个搜索空间, 从而引导算法跳出局部最优。通过对6个高维多模态标准函数进行测试并与其他算法相比较, 其结果表明, 正交CMAES算法具有更好的搜索精度、收敛速度和全局寻优性能。

关键词: 协方差矩阵自适应进化策略, 正交设计, 高维多模态, 进化策略, 函数优化

Abstract: In order to overcome the shortcomings of Covariance Matrix Adaptation Evolution Strategy (CMAES), such as premature convergence and low precision, when it is used in high-dimensional multimodal optimization, a hybrid algorithm combined CMAES with Orthogonal Design with Quantization (OD/Q) was proposed. Firstly, the small population CMAES was used to realize a fast searching. When orthogonal CMAES algorithm trapped in local extremum, base vectors for OD/Q were selected dynamically based on the position of current best solution. Then the entire solution space, including the field around extreme value, was explored by trial vectors generated by OD/Q. The proposed algorithm was guided by this process jumping out of the local optimum. The new approach was tested on six high-dimensional multimodal benchmark functions. Compared with other algorithms, the new algorithm has better searching precision, convergence speed and capacity of global search.

Key words: Covariance Matrix Adaptation Evolution Strategy (CMAES), orthogonal design, high-dimensional multimodal, Evolutionary Strategy (ES), function optimization

黄亚飞梁昔明陈义雄. 求解全局优化问题的正交协方差矩阵自适应进化策略算法[J]. 计算机应用, 2012, 32(04): 981-985.

HUANG Ya-fei LIANG Ximing CHEN Yi-xiong. Hybrid orthogonal CMAES for solving global optimization problems[J]. Journal of Computer Applications, 2012, 32(04): 981-985.

参考文献

［1］ HANSEN N, OSTERMEIER A. Adapting arbitrary normal mutation distributions in evolution strategies: The covariance matrix adaptation［C］// Proceedings of the 1996 IEEE Conference on Evolutionary Computation. Piscataway: IEEE, 1996:312-317. ［2］ HANSEN N, OSTERMEIER A. Completely derandomized self-adaptation in evolution strategies［J］. IEEE Transactions on Evolutionary Computation, 2001, 9(2):159-195. ［3］ SUTTORP T, HANSEN N, IGEL C. Efficient covariance matrix update for variable metric evolution strategies［J］. Machine Learning, 2009, 75(2):167-197. ［4］周文杰, 徐勇. 基于CMA-ES算法的支持向量机模型选择［J］. 计算机仿真, 2010,27(4):163-166. ［5］苏国韶, 武振兴, 燕柳斌. 基于自适应协方差矩阵进化策略的结构可靠度计算［J］. 四川建筑科学研究, 2011, 37(2): 13-16. ［6］ LEUNG Y W, WANG Y P. An orthogonal genetic algorithm with quantization for global numerical optimization［J］. IEEE Transactions on Evolutionary Computation, 2001, 5(1): 41-53. ［7］ WANG Y, LIU H, CAI Z, et al. An orthogonal design based constrained evolutionary optimization algorithm［J］. Engineering Optimization, 2007,39(6):715-736. ［8］江中央, 蔡自兴, 王勇. 求解全局优化问题的混合自适应正交遗传算法［J］. 软件学报, 2010, 21(6): 1296-1307. ［9］曾三友,魏巍,康立三,等. 基于正交设计的多目标演化算法［J］. 计算机学报, 2005, 28(7): 1153-1162. ［10］拓守恒, 汪文勇. 求解高维多模优化问题的正交小生境自适应差分演化算法［J］. JOCA, 2011, 31(4): 1094-1098. ［11］ HANSEN N. The CMA evolution strategy: A comparing review［C］// Towards a New Evolutionary Computation: Advances on Estimation of Distribution Algorithms. Berlin: Springer, 2006: 75-102. ［12］ FANG K T, WANG Y. Number-theoretic methods in statistics［M］. New York: Chapman and Hall, 1994. ［13］ WANG Y P, DANG C Y. An evolutionary algorithm for global optimization based on level-set evolution and Latin squares［J］. IEEE Transactions on Evolutionary Computation, 2007,11(5):579-595.

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求解全局优化问题的正交协方差矩阵自适应进化策略算法

Hybrid orthogonal CMAES for solving global optimization problems

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