求解多峰全局优化问题的智能辅助函数法

doi:10.3969/j.issn.1001-2400.2013.05.024

J4 ›› 2013, Vol. 40 ›› Issue (5): 148-156.doi: 10.3969/j.issn.1001-2400.2013.05.024

求解多峰全局优化问题的智能辅助函数法

范磊¹;王宇平²;刘西洋¹

(1. 西安电子科技大学软件工程研究所，陕西西安 710071;
2. 西安电子科技大学计算机学院，陕西西安 710071)

收稿日期:2012-05-21 出版日期:2013-10-20 发布日期:2013-11-27
通讯作者: 范磊
作者简介:范磊(1983-)，男，讲师，E-mail：lfan@mail.xidian.edu.cn．
基金资助:
国家自然科学基金资助项目(61272119, 61203372)；中央高校基本科研业务费专项资金资助项目(K5051303009)

Intelligent auxiliary function method for multimodal global optimization problems

FAN Lei¹;WANG Yuping²;LIU Xiyang¹

(1. Research Inst. of Software Engineering, Xidian Univ., Xi'an 710071， China;
2. School of Computer Science and Technology, Xidian Univ., Xi'an 710071， China)

Received:2012-05-21 Online:2013-10-20 Published:2013-11-27
Contact: FAN Lei

摘要/Abstract

摘要：

辅助函数法在求解多峰全局优化问题时通常存在参数敏感和难以求解高维问题的缺陷，针对这两类缺陷提出了一种智能辅助函数法．首先，利用平滑函数来消除比当前找到的最好解差的解，在此基础上设计了一种新的辅助函数，该辅助函数仅包含一个易于设置的参数，而且可以有效地避免由于参数设置不当导致的“Mexican hat”效应; 然后，分析了提出的辅助函数的性质，将辅助函数与智能优化技术相结合来提高算法的搜索能力，从而保证了算法在求解高维问题时能够成功找到全局最优解;最后，在数值实验中，利用13个标准测试函数来测试算法中参数的影响以及算法的搜索性能．

关键词: 多峰优化, 全局优化, 极小化, 智能辅助函数法

Abstract:

When solving multimodal global optimization problems, many auxiliary function methods are sensitive to their parameters and of great difficulty in dealing with high dimensional problems. Aiming to overcome these two disadvantages, a new intelligent auxiliary function method is proposed in this paper. Firstly, the smoothing function is employed to eliminate the solutions worse than the best one found so far. Based on the smoothing function, a novel auxiliary function is constructed, in which there is only one easily-adjusted parameter. This auxiliary function can avoid the unwilling “Mexican hat” effect caused by improper parameter settings. Then, properties of the auxiliary function are analyzed. In order to improve the searching ability, the proposed auxiliary function and intelligent optimization techniques are assembled in the designed method, which can help the method deal with high dimensional problems. Finally, 13 different benchmarks are used to test the influence of the parameter and the performance of the searching method. Experimental results indicate the effectiveness of the proposed method.

Key words: multimodal optimizatioin, global optimization, minimization, intelligent auxiliary function method

范磊;王宇平;刘西洋. 求解多峰全局优化问题的智能辅助函数法[J]. J4, 2013, 40(5): 148-156.

FAN Lei;WANG Yuping;LIU Xiyang. Intelligent auxiliary function method for multimodal global optimization problems[J]. J4, 2013, 40(5): 148-156.

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求解多峰全局优化问题的智能辅助函数法

Intelligent auxiliary function method for multimodal global optimization problems

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