  Dominance move (DoM) is a binary quality indicator that can be used in
multiobjective optimization. It can compare solution sets while representing
some important features such as convergence, spread, uniformity, and
cardinality. DoM has an intuitive concept and considers the minimum move of one
set needed to weakly Pareto dominate the other set. Despite the aforementioned
properties, DoM is hard to calculate. The original formulation presents an
efficient and exact method to calculate it in a biobjective case only. This
work presents a new approach to calculate and extend DoM to deal with three or
more objectives. The idea is to use a mixed integer programming (MIP) approach
to calculate DoM. Some initial experiments, in the biobjective space, were done
to verify the model correctness. Furthermore, other experiments, using three,
five, and ten objective functions were done to show how the model behaves in
higher dimensional cases. Algorithms such as IBEA, MOEAD, NSGAIII, NSGAII, and
SPEA2 were used to generate the solution sets, however any other algorithms
could be used with DoM indicator. The results have confirmed the effectiveness
of the MIP DoM in problems with more than three objective functions. Final
notes, considerations, and future research are discussed to exploit some
solution sets particularities and improve the model and its use for other
situations.
