A computationally fast but approximate MIP-DoM calculation for multi-objective optimization

Quality indicators play an essential role in multi- and many-objective optimization. Dominance move (DoM) is a binary indicator that compares two solution sets. It measures the minimum move in elements of one set P must do in a way that every element of Q is dominated to at least one element of the moved set P'. As an indicator, it presents some outstanding characteristics as Pareto compliant, absence of the use of reference point or set, and robustness in terms of dominance-resistant solutions. However, DoM computation presents a combinatorial nature. A recent paper proposes a mixed-integer programming model, MIP-DoM, which exhibits a polynomial computational complexity to the number of solutions. Considering practical situations, its calculation on some problems may take hours. Using a cluster-based and divide-and-conquer strategy, this paper presents a computationally fast approximate MIP-DoM to deal with the combinatorial nature of the original calculation. Some classical problem sets are tested, showing that our approach is computationally faster and provides accurate estimates for the exact MIP-DoM.