Carducci Abstract

Stable Matching Problems with Couples Olivia M. Carducci Department of Mathematics Lafayette College Easton, PA 18042-1781 carducci@lafayette.edu

There several versions of the stable matching problem. The best known is the stable marriage problem. The goal in the stable marriage problem is to pair up men and women in such a way that no man and woman who are not paired with each other prefer each other to their mates. If there were a man and woman who preferred each other to their mates, they would be inclined to drop their mates for each other, creating an unstable situation. The stable marriage problem provides a model for a centralized procedure that is used to assign graduating medical students to hospital residency positions. In this talk we will review the stable marriage problem and an extension where couples graduating from medical school are permitted to express their preferences over pairs of residency positions. We will present a genetic algorithm for enumerating stable matchings in the stable marriage problem with a discussion of how the algorithm can be extended to the problem with couples.