基于稳定匹配的路径选择行为研究

为了证明是否能用双边匹配理论研究出行者路径选择行为，构建了以出行者和路径为主体的二部图，从图论的角度证明了所构建二部图的稳定匹配是路径选择的最终结果，且稳定匹配存在纳什均衡，可以用来分析出行选择行为. 在综合考虑出行者阻抗和路径影响的基础上，建立了不考虑流量和通行能力影响与考虑流量和通行能力影响的两类多目标优化模型，使用线性加权法转化为指派模型，利用匈牙利算法进行求解. 结合数值算例说明所建模型的正确性和合理性. 算例结果表明，两类模型的路径选择结果均满足用户均衡原理，可以在此方法的基础上建立对应的交通分配模型.

Path Selection Behavior Based on Stable Matching

To better investigate traveler path selection behaviors by the two- sided matching theory, a modified bipartite graph embedded with traveler and path is proposed. By using the proposed method, it is found that there is a Nash equilibrium within the stable matching thus the derived Nash equilibrium can be further used to analyze travel selection behaviors. Moreover, a multi-objective optimization model considering both the traveler's income and route influence is established. The multi- objective optimization model includes two assignment models that one is considering the influence of flow and capacity while the another is not. This established problem is solved by the Hungarian algorithm. The simulation results of the numerical example show that the path selection behaviors are satisfied the user equilibrium principle in both conditions, i.e., with and without considering the flow and capacity. Thus, it is efficient to establish the corresponding traffic assignment model.