Two-Sided Matching with Indifferences: Using Heuristics to Improve Properties of Stable Matchings

Abstract

Two-Sided Matching is a widely used approach to allocate resources based on preferences. In Two-Sided Matching problems where indifferences are allowed in the preference lists, finding stable matchings with certain properties is known to be NP-hard and, in some instances, even NP-hard to approximate. This article, therefore, considers the use of heuristics in Two-Sided Matching scenarios with indifferences to find and explore potential solutions and their properties. Two heuristics, a Genetic Algorithm and Threshold Accepting, are compared to existing approaches with respect to their ability to generate alternative stable solutions based on initially stable matchings for scenarios with either complete or incomplete preferences. The evaluation shows that using these types of heuristics is a valid approach to obtain matchings with improved properties such as fairness or average matched rank, compared to existing algorithms. Overall, this approach allows for the exploration of alternative stable matchings and subsequent selection of a best solution given selected evaluation criteria.