Analyzing Dominance Move (MIP-DoM) Indicator for Multiobjective and Many-Objective Optimization

Dominance move (DoM) is a binary quality indicator that can be used in multiobjective and many-objective optimization to compare two solution sets obtained from different simulations. The DoM differentiate the for certain important features, such as convergence , xmlns:xlink="http://www.w3.org/1999/xlink">spread xmlns:xlink="http://www.w3.org/1999/xlink">uniformity xmlns:xlink="http://www.w3.org/1999/xlink">cardinality . does not require any reference point or representative Pareto set, it has an intuitive physical meaning, similar $\epsilon $ -indicator. It calculates minimum total of members one set so all elements another are dominated identical at least member first set. Despite aforementioned desired properties, hard calculate, particularly higher dimensions. There efficient exact method calculate biobjective problems. This work proposes novel approach using mixed-integer programming (MIP) approach, which handle with more objectives shown overcome issue information loss associated Experiments space done verify model’s correctness. Furthermore, other experiments, 3-, 5-, 10-, 15-, 20-, 25-, 30-objective problems, performed show how model behaves dimensional cases. Algorithms, IBEA, MOEA/D, NSGA-III, NSGA-II, SPEA2, generate sets; however, algorithm also proposed MIP-DoM indicator. Further extensions discussed idiosyncrasies some improve its use scenarios.