Bus Bridging for Rail Disruptions: A Distributionally Robust Fuzzy Optimization Approach

Dealing with uncertain rail disruptions effectively raises a significant challenge for computational intelligence research. This article studies the bus bridging problem under demand uncertainty, where the passenger demand is represented as parametric interval-valued fuzzy variables and their associated uncertainty distribution sets. A distributionally robust fuzzy optimization model is proposed to minimize the maximum travel time and to search for the optimal scheme for vehicle allocation, route selection, and frequency determination. To solve the proposed robust model, we discuss the computational issues concerning credibilistic constraints, turning the robust counterpart model into computationally tractable equivalent formulations. The proposed approach is verified, and the resulting method is validated with a report on uncertain parameters in a real-world disrupted event of Shanghai Rail Line 1. Experimental results show that the distributionally robust fuzzy optimization approach can provide a better uncertainty-immunized solution.