计算机科学 ›› 2015, Vol. 42 ›› Issue (9): 246-248.doi: 10.11896/j.issn.1002-137X.2015.09.047

• 人工智能 • 上一篇    下一篇

人工蜂群算法的几乎必然强收敛性:鞅方法

孔翔宇,刘三阳,王 贞   

  1. 西安电子科技大学数学与统计学院 西安710071;北方民族大学数学与信息科学学院 银川750021,西安电子科技大学数学与统计学院 西安710071,北方民族大学数学与信息科学学院 银川750021
  • 出版日期:2018-11-14 发布日期:2018-11-14
  • 基金资助:
    本文受国家自然科学基金(61373174),宁夏自然科学基金(NZ13096),宁夏高等学校科研项目(NGY2013086),北方民族大学校级项目(2014XBZ01)资助

Almost Sure Convergence of Artificial Bee Colony Algorithm:A Martingale Method

KONG Xiang-yu, LIU San-yang and WANG Zhen   

  • Online:2018-11-14 Published:2018-11-14

摘要: 已有的人工蜂群算法的收敛性分析是基于算法的遍历性分析,在概率收敛意义下考虑的,这种收敛性分析不能确保算法在有限步内收敛到问题的全局最优解。首次尝试运用鞅论研究人工蜂群算法的几乎必然强收敛性,证明了人工蜂群算法确保能以概率1在有限步内达到全局最优解。这一结论为拓宽人工蜂群算法的应用范围奠定了理论基础,并为人工蜂群算法的改进及收敛性研究提供了新的理论工具。

关键词: 人工蜂群算法,马尔可夫链,鞅,全局收敛,局部收敛

Abstract: The most convergence analysis on artificial bee colony(ABC) algorithm is based on ergodicity analysis and conducted in the sense of probabilistic convergence.Such analysis cannot infer in general that the ABC algorithm will be convergent to a global optimum in a finite number of evolution steps.In this paper,a martingale analysis method was proposed to study the almost sure convergence of ABC algorithm.It is shown that ABC algorithm can surely converge to a global optimum with probability 1 in a finite number of evolution steps.The obtained results underlie application of the ABC algorithm,and the suggested martingale analysis method provides a new technique for convergence analysis of ABC algorithm.

Key words: Artificial bee colony algorithm,Markov chain,Martingale,Global convergence,Local convergence

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