Convergence proof for a Monte Carlo method, for combinatorial optimization problems

Abstract

In this paper we prove the convergence of a Monte Carlo (MC) method for Combinatorial Optimization Problems (COPs). The Ant Colony Optimization (AGO) is a MC method, created to solve efficiently COPs. The Ant Colony Optimization (AGO) algorithms are being applied successfully to diverse heavily problems. To show that AGO algorithms could be good alternatives to existing algorithms for hard combinatorial optimization problems, recent research in this area has mainly focused on the development of algorithmic variants which achieve better performance than previous one. In this paper we present AGO algorithm with Additional Reinforcement (ACO-AR) of the pheromone to the unused movements. ACO-AR algorithm differs from AGO algorithms in several important aspects. In this paper we prove the convergence of ACO-AR algorithm. © Springer-Verlag Berlin Heidelberg 2004.