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This paper proposes a new multi-objective bi-level programming model for the ring road bus lines and fare design problems. The proposed model consists of two layers: the traffic management operator and travelers. In the upper level, we propose a multi-objective bus lines and fares optimization model in which the operator’s profit and travelers’ utility are set as objective functions. In the lower level, evolutionary multi agent model of travelers’ bounded rational reinforcement learning with social interaction is introduced. A solution algorithm for the multi-objective bi-level programming is developed on the basis of the equalization algorithm of OD matrix. A numerical example based on a real case was conducted to verify the proposed models and solution algorithm. The computational results indicated that travel choice models with different degrees of rationality significantly changed the optimization results of bus lines and the differentiated fares; furthermore, the multi-objective bi-level programming in this paper can generate the solution to reduce the maximum section flow, increase the profit, and reduce travelers’ generalized travel cost.

Multi-Objective Optimization of Differentiated Urban Ring Road Bus Lines and Fares Based on Travelers’ Interactive Reinforcement Learning