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应用科学学报 ›› 2004, Vol. 22 ›› Issue (3): 407-410.

• 论文 • 上一篇    下一篇

基于特殊选择的抽象进化算法的收敛性

薛明志1,3, 朱秀阁2, 焦李成1   

  1. 1 西安电子科技大学雷达信号处理国家重点实验室 陕西西安 710071;
    2 河南大学计算中心 河南开封 475001;
    3 商丘师范学院数学系 河南商丘 476000
  • 收稿日期:2003-04-01 修回日期:2003-07-14 出版日期:2004-09-30 发布日期:2004-09-30
  • 作者简介:薛明志(1967-),男,河南商丘人,副教授,博士生;焦李成(1959-),男,陕西白水人,教授,博导.
  • 基金资助:
    国家自然科学基金(60133010);河南省教育厅自然科学基金(2000110019)资助课题

The Convergence of the Abstract Evolutionary Algorithm Based on a Special Selection Mechanism

XUE Ming-zhi1,3, ZHU Xiu-ge2, JIAO Li-cheng1   

  1. 1. National Key Lab for Radar Signal Processing, Xidian University, Xi'an 710071, China;
    2. Computer Center, Henan University, Kaifeng 475001, China;
    3. Department of Mathematics, Shangqiu Normal College, Shangqiu 476000, China
  • Received:2003-04-01 Revised:2003-07-14 Online:2004-09-30 Published:2004-09-30

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摘要： 首先定义了抽象选择算子和抽象进化算子,基于这两种算子给出了一般抽象进化算法的定义.特别讨论了一种基于特殊选择的抽象进化算法,根据状态空间的分类,分析了这种特殊选择进化算法种群的一步转移概率矩阵的性质,最后证明了这种算法的Markov链存在极限概率分布.

关键词: 抽象进化算法, 转移矩阵, 收敛性

Abstract: evolutionary algorithm. In this paper, the definition of the abstract selection and evolution operators is given. The abstract evolutionary algorithm, which describes the evolution as an abstract stochastic process composed of these two fundamental abstract operators is defined. In particular, a kind of abstract evolutionary algorithms based on a special selection mechanism is discussed. According to the sorting of the state space, the properties of the single step transition matrix for the algorithm are analyzed. Finally, we prove the existence of the limit probability distribution of the Markov chains.

Key words: abstract evolutionary algorithm, transition matrix, convergence

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