An Almost Everywhere Strong Convergence Proof for a Class of Ant Colony Algorithms

SU Zhao-pin; JIANG Jian-guo; LIANG Chang-yong; ZHANG Guo-fu; XIA Na

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An Almost Everywhere Strong Convergence Proof for a Class of Ant Colony Algorithms

更新时间：2025-07-16

- An Almost Everywhere Strong Convergence Proof for a Class of Ant Colony Algorithms
- Acta Electronica Sinica Vol. 37, Issue 8, Pages: 1646-1650(2009)
- 作者机构：
  
  1. 合肥工业大学计算机与信息学院,安徽,合肥,230009
  2. 合肥工业大学管理科学与工程博士后科研流动站,安徽,合肥,230009
  3. 安全关键工业测控技术教育部工程研究中心,安徽,合肥,230009
  4. 特种显示技术教育部重点实验室,安徽,合肥,230009
  5. 合肥工业大学计算机与信息学院安徽合肥,230009
  6. 合肥工业大学管理科学与工程博士后科研流动站安徽合肥,230009
  7. 安全关键工业测控技术教育部工程研究中心安徽合肥,230009
  8. 特种显示技术教育部重点实验室安徽合肥,230009
- 作者简介：
- 基金信息：
- DOI：
  CLC： TP301
- Published：2009
- 稿件说明：
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SU Zhao-pin, JIANG Jian-guo, LIANG Chang-yong, et al. An Almost Everywhere Strong Convergence Proof for a Class of Ant Colony Algorithms[J]. Acta Electronica Sinica, 2009, 37(8): 1646-1650.
DOI：

SU Zhao-pin, JIANG Jian-guo, LIANG Chang-yong, et al. An Almost Everywhere Strong Convergence Proof for a Class of Ant Colony Algorithms[J]. Acta Electronica Sinica, 2009, 37(8): 1646-1650. DOI：

摘要

蚁群算法是一种新型的模拟进化算法

已在很多组合优化问题中得到成功应用

但其收敛性分析还比较缺乏.以TSP问题来描述一类蚁群算法的数学模型

并通过对状态空间的分解和反射壁的构筑

从鞅理论角度论证了该类蚁群算法的几乎处处强收敛性以及能在有限步内收敛到全局最优解集

试图为蚁群算法的研究探索一条新的思路.

Abstract

Ant Colony Optimization is a novel simulated evolutionary algorithm which has been used successfully to solve many complicated combinatorial optimization problems

but its convergence analysis is seldom researched.The mathematical model of a class of ant colony algorithms is described by TSP problem.On the basis of the decomposition of state space and the construction of reflecting barrier

an almost everywhere strong convergence of the algorithms and the quality that the algorithms can guaranteedly converge to a global optimum set in a finite number of steps are demonstrated by using the martingale theory

and the obtained results may provide a new methodology for convergence analysis of the algorithms.

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