In recent years, when solving MOPs, especially discrete path optimization problems, MOACOs concerning other meta-heuristic algorithms have been used and improved often, and they have become a hot research topic. This article will start from the basic process of ant colony algorithms for solving MOPs to illustrate the differences between each step. Secondly, we provide a relatively complete classification of algorithms from different aspects, in order to more clearly reflect the characteristics of different algorithms. After that, considering the classification result, we have carried out a comparison of some typical algorithms which are from different categories on different sizes TSP (traveling salesman problem) instances and analyzed the results from the perspective of solution quality and convergence rate. Finally, we give some guidance about the selection of these MOACOs to solve problem and some research works for the future.
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