A note on the ϵ-indicator subset selection

The -indicator subset selection selects a subset of a nondominated point set that is as close as possible to a reference point set with respect to the -indicator. This selection procedure is used by population-based heuristic approaches for multiobjective optimization problems. Given that this procedure is called very often during the run of the heuristic approach, efficient ways of computing the optimal subset are strongly required. In this note, we give a correctness proof of the -indicator subset selection algorithm proposed by Ponte et al. [1] for the bidimensional case as well as several algorithmic improvements in terms of time complexity. Extensions to larger dimension are also discussed.