一种简单蚂蚁算法及其收敛性分析

该文首先介绍了一种可用于函数优化的简单蚂蚁算法，该算法具备了传统蚂蚁算法的基本特征，并给出了变异和最优保存两点改进．然后在给定近似精度的基础上通过Markov过程分析，得出了该算法的全局收敛性．同时，通过对衰减度、变异率等参数的定性讨论，得出了参数的取值对算法性能的影响，并从理论上说明，传统蚁群算法通常的选择概率公式是有缺陷的，而具有变异机制的蚂蚁算法要好于传统蚂蚁算法．该文的实例则说明了文中所给算法的有效性和相关理论论述的正确性．

Ant Algorithm and Analysis on its Convergence

This paper introduces a simple Ant Algorithm (SAA) which can be used to function optimization. The simplified model has all the basic characters of traditional Ant Algorithm and is improved by adding mutation mechanism and preserving elitists. Then based on the given approximation its global convergence is concluded by importing status vectors and using Markov Process analysis. At the same time, the qualitatively analysis shows how the value of the degree of attenuation and mutation rate affect the performance of the algorithm, and selection probablity formula of the traditional algorithm has shortcoming, but the algorithm with mutation mechanism will be better than the traditional one. At the last, the experimental results indicate the algorithm in this paper is effective and the theoretically discussion is reasonable.