Finding Maximum Weakly Stable Matchings for Hospitals/Residents with Ties Problem via Heuristic Search

The Hospitals/Residents with Ties Problem is a many-one stable matching problem, in which residents need to be assigned to hospitals to meet their constraints. In this paper, we propose a simple heuristic algorithm but solve this problem efficiently. Our algorithm starts from an empty matching and gradually builds up a maximum stable matching of residents to hospitals. At each iteration, we propose a heuristic function to choose the best hospital for an active resident to form a resident-hospital pair for the matching. If the chosen hospital overcomes its offered capacity, we propose another heuristic function to remove the worst resident among residents assigned to the hospital in the matching. Our algorithm returns a stable matching if it finds no active resident. Experimental results show that our algorithm is efficient in execution time and solution quality for solving the problem.