西安电子科技大学学报

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极小极大问题的生物地理学优化邻近点算法

杨国平1;刘三阳1;张建科2   

  1. (1. 西安电子科技大学 数学与统计学院,陕西 西安  710071;
    2. 西安邮电大学 理学院,陕西 西安  710121)
  • 收稿日期:2015-07-28 出版日期:2016-10-20 发布日期:2016-12-02
  • 通讯作者: 杨国平
  • 作者简介:杨国平(1975-),男,副教授,硕士,E-mail: guoping02@126.com.
  • 基金资助:

    国家自然科学基金资助项目(61373174,71271165);陕西省教育厅自然科学专项基金资助项目(2013JK1130,11JK1051);中央高校基本科研业务费专项资金资助项目(JB140705,2014GXNSFBA118023)

Biogeography based optimization-proximal point algorithm for nonlinear minimax problems

YANG Guoping1;LIU Sanyang1;ZHANG Jianke2   

  1. (1. School of Mathematics and Statistics, Xidian Univ., Xi'an  710071, China;
    2. School of Sciences, Xi'an Univ. of Posts and Telecommunications, Xi'an  710121, China)
  • Received:2015-07-28 Online:2016-10-20 Published:2016-12-02
  • Contact: YANG Guoping

摘要:

离散型非线性极小极大问题本质上为一个传统的梯度类算法难以求解的不可微优化问题.针对每个分量函数都是凸函数的此类问题,利用熵函数法将其转化为一个光滑的无约束凸优化问题,并将具有并行搜索机制的生物地理学优化算法和具有全局收敛性的邻近点算法相混合,设计了一种具有全局收敛性的混合算法.为了充分发挥生物地理学优化算法的并行搜索机制和无需使用初始点的优点,该混合算法采用生物地理学优化为内层算法邻近点算法为外层算法.数值仿真结果表明,所提算法是求解此类非线性极小极大问题的一种有效算法.

关键词: 生物地理学优化, 进化算法, 极小极大问题, 邻近点算法

Abstract:

Concerning the discrete nonlinear minimax problems with the convex function as each of its components, a new method, called the biogeography based optimization-proximal point algorithm, is presented. By using maximum-entropy methods, the minimax problem is transformed into the unconstrained optimization problem of the smooth function. The algorithm employs the proximal point algorithm as the outer algorithm, and the biogeography based optimization as the internal algorithm. The proposed algorithm which resolves several minimax problems is global convergent. Preliminary numerical experiments show that the proposed algorithm is an effective algorithm for nonlinear minimax problems.

Key words: biogeography based optimization, evolutionary computation, minimax problems, proximal point algorithm