Abstract: In order to enhance the perception satisfaction of two-sided agents towards matching scheme, aiming to address a one-to-many two-sided matching problem between postgraduates and supervisors, prospect theory is introduced to address this issue by considering their psychological factors from the perspective of behavior science. Firstly, selection process between postgraduates and supervisors is defined asa one-to-many two-sided matching problem, and then is further transformed into a one-to-onematching problem. Next, prospect theory is used to characterize the psychological perception of agents under different preference ordinals, thus developing corresponding perception satisfaction function with stable matching condition. After that, a two-sided matching decision model to maximize overall perception satisfaction of postgraduates and supervisors is proposed. Finally, genetic algorithm is designed to solve the multi-objective model. Besides, a numerical example is also presented to illustrate proposed model and method. Computational results demonstrate their significant potential advantages in the matching problem between postgraduates and supervisors.

Key words: one-to-many two-sided matching, preference ordinal, prospect theory, perception satisfaction, genetic algorithm

摘要： 为提高研究生新生(以下简称“研究生”)与导师对匹配方案的整体感知满意度,针对导师和研究生形成的一对多双边匹配问题,从行为科学视角,梳理师生双方对匹配方案感知的心理因素,结合前景理论解决此类问题。首先,将师生双向互选过程描述为一对多双边匹配问题,并将其转化为一对一双边匹配问题;接着,基于前景理论刻画双边主体在不同偏好序下的心理感知,构建师生双方基于偏好序的感知满意度函数;然后,建立稳定匹配条件下最大化师生整体感知满意度的双边匹配决策模型。最后,结合遗传算法对问题进行求解,并通过数值算例验证了算法及模型的有效性和可行性。

关键词: 一对多双边匹配, 偏好序, 前景理论, 感知满意度, 遗传算法