An empirical local search for the stable marriage problem

Abstract

This paper proposes a local search algorithm to find the egalitarian and the sex-equal stable matchings in the stable marriage problem. Based on the dominance relation of stable matchings from the men’s point of view, our approach discovers the egalitarian and the sex-equal stable matchings from the man-optimal stable matching. By employing a breakmarriage strategy to find stable neighbor matchings of the current stable matching and moving to the best neighbor matching, our local search finds the solutions while moving towards the woman-optimal stable matching. Simulations show that our proposed algorithm is efficient for the stable marriage problem.