A Heuristic Repair Algorithm for the Hospitals/Residents Problem with Ties.

The Hospitals/Residents problem with Ties is a many-to-one stable matching problem and it has several practical applications. In this paper, we present a heuristic repair algorithm to find a stable matching with maximal size for this problem. Our approach is to apply a random-restart algorithm used commonly to deal with constraint satisfaction problems. At each iteration, our algorithm finds and removes the conflicted pairs in terms of preference ranks between hospitals and residents to improve rapidly the stability of the matching. Experimental results show that our approach is efficient in terms of execution time and solution quality for the problem of large sizes.