The analysis of the convergence of ant colony optimization algorithm

Abstract

The ant colony optimization algorithm has been widely studied and many important results have been obtained. Though this algorithm has been applied to many fields, the analysis about its convergence is much less, which will influence the improvement of this algorithm. Therefore, the convergence of this algorithm applied to the traveling salesman problem (TSP) was analyzed in detail. The conclusion that this algorithm will definitely converge to the optimal solution under the condition of 0⟨q₀⟨1 was proved true. In addition, the influence on its convergence caused by the properties of the closed path, heuristic functions, the pheromone and q₀ was analyzed. Based on the above-mentioned, some conclusions about how to improve the speed of its convergence are obtained.