吉林大学学报(理学版) ›› 2019, Vol. 57 ›› Issue (5): 1075-10880.

• 数学 • 上一篇    下一篇

基于单纯形法进行局部优化的人群搜索算法求解绝对值方程

封京梅1,2, 刘三阳1   

  1. 1. 西安电子科技大学 数学与统计学院, 西安 710126; 
    2. 陕西广播电视大学 工程与建筑学院, 西安 710119
  • 收稿日期:2018-12-10 出版日期:2019-09-26 发布日期:2019-09-19
  • 通讯作者: 刘三阳 E-mail:liusanyang@126.com

Seeker Algorithm Based on Simplex Method for LocalOptimization to Solve Absolute Value Equations

FENG Jingmei1,2, LIU Sanyang1   

  1. 1. School of Mathematics and Statistics, Xidian University, Xi’an 710126, China;
    2. School of Engineering and Architecture, Shaanxi Radio and TV University, Xi’an 710119, China
  • Received:2018-12-10 Online:2019-09-26 Published:2019-09-19
  • Contact: LIU Sanyang E-mail:liusanyang@126.com

摘要: 设计一种利用单纯形法进行局部优化的人群搜索算法求解一类形如Ax-|x|=b的不可微绝对值方程的新算法. 该算法通过引进单纯形算法, 提高基本人群搜索算法的局部搜索能力, 增加跳出局部最优解的概率, 从而有效改进人群搜索算法在计算后期易陷入局部最优的缺点. 实验结果表明, 该算法在求解绝对值方程时, 计算精度高、 鲁棒性能好.

关键词: 人群搜索算法, 单纯形算法, 绝对值方程

Abstract: We designed a seeker algorithm using the simplex method for local optimization to solve a class of nondifferentiable absolute value equations, such as Ax-|x|=b. The algorithm improved the local search ability of the basic seeker algorithm by introducing the simplex algorithm, and increased the probability of jumping out of the local optimal solution. Thus, it effectively improved the disadvantages that the seeker algorithm was easy to fall into local optimum in the late  stage of calculation. The experimental results show that the algorithm has high computational accuracy and good robustness in solving absolute value equations.

Key words: seeker algorithm, simplex method , absolute value equation

中图分类号: 

  • O221