Performance analysis of the multi-objective ant colony optimization algorithms for the traveling salesman problem

Most real world combinatorial optimization problems are difficult to solve with multiple objectives which have to be optimized simultaneously. Over the last few years, researches have been proposed several ant colony optimization algorithms to solve multiple objectives. The aim of this paper is to review the recently proposed multi-objective ant colony optimization (MOACO) algorithms and compare their performances on two, three and four objectives with different numbers of ants and numbers of iterations. Moreover, a detailed analysis is performed for these MOACO algorithms by applying them on several multi-objective benchmark instances of the traveling salesman problem. The results of the analysis have shown that most of the considered MOACO algorithms obtained better performances for more than two objectives and their performance depends slightly on the number of objectives, number of iterations and number of ants used.