In this paper, we propose a heuristic search algorithm based on maximum conflicts to find a weakly stable matching of maximum size for the stable marriage problem with ties and incomplete lists. The key idea of our approach is to define a heuristic function based on the information extracted from undominated blocking pairs from the men’s point of view. By choosing a man corresponding to the maximum value of the heuristic function, we aim to not only remove all the blocking pairs formed by the man but also reject as many blocking pairs as possible for an unstable matching from the women’s point of view to obtain a solution of the problem as quickly as possible. Experiments show that our algorithm is efficient in terms of both execution time and solution quality for solving the problem.

在本文中，我们提出了一种基于最大冲突的启发式搜索算法，以找到具有联系和不完整列表的稳定婚姻问题的最大大小的弱稳定匹配。我们的方法的关键思想是基于从男性的角度出发，从未支配的对中提取的信息来定义启发式函数。通过选择与启发式函数的最大值对应的男人，我们的目标不仅是要删除该男人形成的所有障碍物对，而且要从女人的角度出发，尽可能多地为不稳定的匹配而拒绝尽可能多的障碍物对，以获得一个尽快解决问题。实验表明，我们的算法在解决问题的执行时间和解决方案质量上都是有效的。