Finding Robust Solutions to Stable Marriage

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 any a pairs break up it is possible to find another stable matching by changing the partners of those a pairs and the partners of 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 first 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 shows that local search outperforms the other approaches.