A New Perspective to Stable Marriage Problem in Profit Maximization of Matrimonial Websites

For many years, matching in a bipartite graph has been widely used in various assignment problems, such as stable marriage problem (SMP). As an application of bipartite matching, the problem of stable marriage is defined over equally sized sets of men and women to identify a stable matching in which each person is assigned a partner of opposite gender according to their preferences. The classical SMP proposed by Gale and Shapley uses preference lists for each individual (men and women) which are infeasible in real world applications for a large populace of men and women such as matrimonial websites. In this paper, we have proposed an enhancement to the SMP by computing a weighted score for the users registered at matrimonial websites. The proposed enhancement has been formulated into profit maximization of matrimonial websites in terms of their ability to provide a suitable match for the users. The proposed formulation to maximize the profits of matrimonial websites leads to a combinatorial optimization problem. We have proposed greedy and genetic algorithm based approaches to solve the proposed optimization problem. We have shown that the proposed genetic algorithm based approaches outperform the existing Gale-Shapley algorithm on the dataset crawled from matrimonial websites.