J4 ›› 2011, Vol. 38 ›› Issue (1): 47-53.doi: 10.3969/j.issn.1001-2400.2011.01.008

• 研究论文 • 上一篇    下一篇

一种新的差分进化约束优化算法

刘若辰;焦李成;雷七峰;方玲芬   

  1. (西安电子科技大学 智能感知与图像理解教育部重点实验室,陕西 西安   710071)
  • 收稿日期:2010-01-07 出版日期:2011-02-20 发布日期:2011-04-08
  • 通讯作者: 刘若辰
  • 作者简介:刘若辰(1974-),女,副教授,博士,E-mail: ruochenenliu@yahoo.com.cn.
  • 基金资助:

    国家自然科学基金资助项目(60803098, 60703108);国家教育部博士点基金资助项目(20070701022);中国博士后科学基金资助项目(20080431228, 20090451369);陕西省自然科学基金资助项目(2009JQ8015)

New differential evolution constrained optimization algorithm

LIU Ruochen;JIAO Licheng;LEI Qifeng;FANG Lingfen   

  1. (Ministry of Education Key Lab. of Intelligent Perception and Image Understanding, Xidian Univ., Xi'an  710071, China)
  • Received:2010-01-07 Online:2011-02-20 Published:2011-04-08
  • Contact: LIU Ruochen

摘要:

对于约束优化问题,目前提出的差分进化算法大多采用罚函数法,但此方法对罚参数有很强的依赖性.基于此,把约束优化问题中的约束条件当作一个目标函数,从而把约束优化问题转化为有两个目标函数的多目标优化问题.借鉴多目标优化中的Pareto的概念,对种群中的个体规定等级,便于在优胜劣汰过程中确定选择概率.同时,在算法陷入局部最优时,采用一种不可行解替换机制来提高算法搜索能力.对13个标准测试问题的测试结果表明,与动态惩罚函数的进化算法、可行性规则的差分进化算法、采用随机排序的进化策略以及人工免疫响应约束进化策略相比,新算法在求解精度上均具有一定的优势.

关键词: 差分进化算法, 约束优化, 多目标优化

Abstract:

Most existing differential evolution algorithms for the Constrained Optimization Problem(COP) use the penalty function method to handle constrains, which depends strongly on the penalty parameter. So, this paper transforms the COP into two-objective multi-objective optimization by taking constraints as an objective function. Based on the concept of Pareto, the grades of individuals in population are prescribed so as to determine their selection probability in the process of “survival of the fittest”. In addition, when the algorithm gets into a local optimum, an infeasible solution replacing mechanism is also given to improve the search capability. The results of the 13 Standard tests show that compared to the Evolutionary Algorithm based on Homomorphous Maps (EAHM), Constraint Handling Differential Evolution (CHDE), Evolutionary Strategies based on Stochastic Ranking (ESSR) and Artificial Immune Response Constrained Evolutionary Strategy (AIRCES), the proposed algorithm has certain advantages in convergence speed and solution accuracy.

Key words: differential evolution algorithm, constrained optimization, multi-objective optimization