Targeted Pareto Optimization for Subset Selection With Monotone Objective Function and Cardinality Constraint

Abstract

Subset selection, a fundamental problem in various domains, is to choose a subset of elements from a large candidate set under a given objective or multiple objectives. Pareto optimization for subset selection (POSS) has emerged as a powerful paradigm for addressing subset selection problems. Recently, some POSS variants have been proposed to further improve its performance. In this article, we propose a new POSS variant, named targeted POSS (TPOSS). TPOSS differs from POSS in four aspects: 1) problem formulation; 2) population initialization; 3) mutation; and 4) environmental selection. The main idea of TPOSS is to focus the search on the target region of subset selection with respect to the subset cardinality in order to improve the search efficiency. We conduct comprehensive experiments to compare TPOSS with six state-of-the-art algorithms on three subset selection tasks (i.e., sparse regression, unsupervised feature selection, and hypervolume subset selection) where the size of the candidate sets ranges from 20 to 400. Experimental results show that with respect to the objective value of the best feasible subset, TPOSS outperforms the other algorithms on all the three tasks, which suggests the potential of TPOSS to enhance subset selection in various domains.