A model induced max-min ant colony optimization for asymmetric traveling salesman problem

A large number of hybrid metaheuristics for asymmetric traveling salesman problem (ATSP) have been proposed in the past decades which produced better solutions by exploiting the complementary characteristics of different optimization strategies. However, most of the hybridizations are criticized due to lacking of sufficient analytical basis. In this paper, a model induced max-min ant colony optimization (MIMM-ACO) is proposed to bridge the gap between hybridizations and theoretical analysis. The proposed method exploits analytical knowledge from both the ATSP model and the dynamics of ACO guiding the behavior of ants which forms the theoretical basis for the hybridization. The contribution of this paper mainly includes three supporting propositions that lead to two improvements in comparison with classical max-min ACO optimization (MM-ACO): (1) Adjusted transition probabilities are developed by replacing the static biased weighting factors with the dynamic ones which are determined by the partial solution that ant has constructed. As a byproduct, nonoptimal arcs will be indentified and excluded from further consideration based on the dual information derived from solving the associated assignment problem (AP). (2) A terminal condition is determined analytically based on the state of pheromone matrix structure rather than intuitively as in most traditional hybrid metaheuristics. Apart from the theoretical analysis, we experimentally show that the proposed algorithm exhibits more powerful searching ability than classical MM-ACO and outperforms state of art hybrid metaheuristics.