An Assignment Problem Formulation for Dominance Move Indicator

Dominance move (DoM) is a binary quality indicator to compare solution sets in multiobjective optimization. The indicator allows a more natural and intuitive relation when comparing solution sets. Like the \epsilon-indicators, it is Pareto compliant and does not demand any parameters or reference sets. In spite of its advantages, the combinatorial calculation nature is a limitation. The original formulation presents an efficient method to calculate it in a bi-objective case only. This work presents an assignment formulation to calculate DoM in problems with three objectives or more. Some initial experiments, in the bi-objective space, were done to show that DoM has a similar interpretation as \epsilon-indicators, and to show that our model formulation is correct. Next, other experiments, using three dimensions, were also done to show how DoM could be compared with other indicators: inverted generational distance (IGD) and hypervolume (HV). The assignment formulation for DoM is valid not only for three objectives but for more. Finally, there are some strengths and weaknesses, which are discussed and detailed.