New Ant Colony Optimization Algorithms for Variants of Multidimensional Assignments in d-Partite Graphs

This article presents ant algorithms for single- and multi-criteria industrial optimization problems. A common factor in these algorithms is the determination of the set with the maximum number of cliques, which represent the solution to multidimensional assignment problems in d-partite graphs. In the case of weighted incomplete graphs, the goal is to determine the set with the maximum number of cliques and the maximum sum of the weights of their edges. In the case of unweighted incomplete graphs, the goal is to determine the set with the maximum number of maximum cliques. In the case of complete weighted graphs, the goal is to determine all maximum cliques with the minimal sum of their edge weights. These optimization problems are solved using the various ant algorithms proposed in this paper. The proposed algorithms differ not only in terms of the objective function, but also in terms of desirability functions, as previously established, and they achieved a smaller sum of weights for cliques in the case of weighted complete graphs than previous ant algorithms presented in the literature. The same applies to unweighted incomplete graphs. The presented algorithms resulted in a greater number of maximal cliques than previous ant algorithms presented in the literature. This study is the first to propose the presented ant algorithms in the case of weighted incomplete graphs.