A Fast Dominance Move Calculation Using Mixed-Integer Programming for Many-objective Optimization

Abstract

The Dominance Move (DoM) is a binary quality indicator used to compare non-dominated solution sets in multi-and many-objective optimization. Despite its intuitive interpretation, the computational burden of calculating DoM is significant, as the complexity of existing mixed-integer programming (MIP) models scales poorly with the number of solutions. This paper proposes a new, compact MIP formulation that improves computational efficiency. Extensive experiments on 3 to 30-objective problems show that the proposed model reduces runtime by up to two orders of magnitude, thereby enhancing the practicality and applicability of the DoM indicator for real-world optimization problems.