计算机工程

• 人工智能及识别技术 • 上一篇    下一篇

基于熵和隶属度函数的高维多目标优化问题求解

刘超,贺利军,朱光宇   

  1. (福州大学 机械工程及自动化学院,福州 350116)
  • 收稿日期:2015-04-07 出版日期:2016-06-15 发布日期:2016-06-15
  • 作者简介:刘超(1990-),男,硕士研究生,主研方向为智能制造;贺利军,硕士研究生;朱光宇,教授、博士。
  • 基金项目:
    福建省自然科学基金资助项目(2014J01183);福建省教育厅科技基金资助项目(JK2013006)。

Solution of High Dimension Multi-objective Optimization Problem Based on Entropy and Membership Function

LIU Chao,HE Lijun,ZHU Guangyu   

  1. (College of Mechanical Engineering and Automation,Fuzhou University,Fuzhou 350116,China)
  • Received:2015-04-07 Online:2016-06-15 Published:2016-06-15

摘要: 为求解高维多目标优化问题,提出一种新的适应度分配策略,即模糊关联熵方法(FREM)。结合模糊信息熵理论和隶属度函数给出FREM,采用隶属度函数将Pareto解和理想解映射为模糊集,运用模糊信息熵理论处理Pareto解模糊集与理想解模糊集之间的内在关系,并进行适应度分配。以模糊关联熵系数引导群体智能算法进化。在DTLZ测试函数集上的实验结果表明,FREM能够解决高维多目标优化问题,避免子目标数量增加对算法的影响,并得到比随机权重法和NSGA-II更好的优化效果。

关键词: 高维多目标优化, 模糊关联熵方法, 适应度分配策略, 隶属度函数, 信息熵理论

Abstract: A new fitness assignment strategy is proposed for solving the high dmension multi-objective optimization problem,which is the Fuzzy Relevance Entropy Method(FREM).The FREM is built by integrating the fuzzy information entropy theory and the membership function.The membership function is used for transforming the ideal solution and the Pareto solution into fuzzy set.The fuzzy information entropy theory is used for calculating the internal relations between the ideal solution fuzzy set and the Pareto solution fuzzy set,meanwhile the fuzzy relevance entropy coefficient is used as the fitness value to guide the evolution of the swarm intelligence algorithm.Experimental test is conducted on DTLZ test function set.The results show that FREM can solve the high dmension multi-objective optimization problem,avoid the influence of the increasing number of the sub-objectives on the algorithm,and the solutions are better than those of random weighting method and NSGA-II.

Key words: high dmension multi-objective optimization, Fuzzy Relevance Entropy Method(FREM), fitness assignment strategy, membership function, information entropy theory

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