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Dominance move (DoM) is a binary quality indicator that can be used inmultiobjective optimization. It can compare solution sets while representingsome important features such as convergence, spread, uniformity, andcardinality. DoM has an intuitive concept and considers the minimum move of oneset needed to weakly Pareto dominate the other set. Despite the aforementionedproperties, DoM is hard to calculate. The original formulation presents anefficient and exact method to calculate it in a biobjective case only. Thiswork presents a new approach to calculate and extend DoM to deal with three ormore objectives. The idea is to use a mixed integer programming (MIP) approachto calculate DoM. Some initial experiments, in the biobjective space, were doneto verify the model correctness. Furthermore, other experiments, using three,five, and ten objective functions were done to show how the model behaves inhigher dimensional cases. Algorithms such as IBEA, MOEAD, NSGAIII, NSGAII, andSPEA2 were used to generate the solution sets, however any other algorithmscould be used with DoM indicator. The results have confirmed the effectivenessof the MIP DoM in problems with more than three objective functions. Finalnotes, considerations, and future research are discussed to exploit somesolution sets particularities and improve the model and its use for othersituations.

Dominance Move calculation using a MIP approach for comparison of multi and many-objective optimization solution sets