A Heuristic Repair Algorithm for the Maximum Stable Marriage Problem with Ties and Incomplete Lists

This paper proposes a heuristic repair algorithm to find a maximum weakly stable matching for the stable marriage problem with ties and incomplete lists. Our algorithm is designed including a well-known Gale-Shapley algorithm to find a stable matching for the stable marriage problem with ties and incomplete lists and a heuristic repair function to improve the found stable matching in terms of maximum size. Experimental results for large randomly generated instances of the problem showed that our algorithm is efficient in terms of both execution time and solution quality for solving the problem.