Research on convergence of ACO subset algorithms

Abstract

PurposeThe purpose of this paper is to show that the theoretical proofs of convergence in solution of ant colony optimization (ACO) algorithms have significant values of theory and application.Design/methodology/approachThis paper adapts the basic ACO algorithm framework and proves two important ACO subclass algorithms which are ACObs,τmin and ACObs,τmin (t).FindingsThis paper indicates that when the minimums of pheromone trial decay to 0 with the speed of logarithms, it is ensured that algorithms can, at least, get a certain optimal solution. Even if the randomicity and deflection of random algorithms are disturbed infinitesimally, algorithms can obtain optimal solution.Originality/valueThis paper focuses on the analysis and proof of the convergence theory of ACO subset algorithm to explore internal mechanism of ACO algorithm.