The Difficulties and Optimization of Marriage Matching: An Analysis in the Context of Chinas Modern Economy

This study delves into the use of matching theory in addressing the stable marriage problem, examining ways to optimize overall utility for both women and men across all stable matchings. The paper introduce the concept of energy, denoted by the ranking where a lower rank signifies higher priority, as a metric for individual satisfaction in a match. The primary objective is to identify a stable match that reduces the average energy expended by both genders. By emphasizing average energy, this study aims to pinpoint a stable match that optimally minimizes this metric. A variety of optimization algorithms and mathematical models are utilized to navigate the solution space and determine the best match. A comprehensive analysis of stable matchings, alongside their associated energies for men and women, unveils the inherent trade-offs and dilemmas stemming from individual preferences. The essence of stability is also explored, underscoring the imperative of balancing individual contentment with the durability of the match. The paper concludes by accentuating the necessity for continued research to bolster overall utility in stable matchings, encompassing the investigation of supplementary constraints and preferences.