Finding Robust Solutions to Stable Marriage

Finding Robust Solutions to Stable Marriage

Begum Genc, Mohamed Siala, Barry O'Sullivan, Gilles Simonin

Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence
Main track. Pages 631-637. https://doi.org/10.24963/ijcai.2017/88

We study the notion of robustness in stable matching problems. We first define robustness by introducing (a,b)-supermatches. An (a,b)-supermatch is a stable matching in which if a pairs break up it is possible to find another stable matching by changing the partners of those a pairs and at most b other pairs. In this context, we define the most robust stable matching as a (1,b)-supermatch where b is minimum. We show that checking whether a given stable matching is a (1,b)-supermatch can be done in polynomial time. Next, we use this procedure to design a constraint programming model, a local search approach, and a genetic algorithm to find the most robust stable matching. Our empirical evaluation on large instances show that local search outperforms the other approaches.
Keywords:
Constraints and Satisfiability: Modeling/Formulation
Knowledge Representation, Reasoning, and Logic: Preferences
Combinatorial & Heuristic Search: Heuristic Search
Agent-based and Multi-agent Systems: Social Choice Theory