Transformation of Bi-level Transit Network Design Problem into Single-objective Unconstrained Optimization

초록

The present study provides a methodology to solve the network design problem for a newly projected metro line. The transit network design problem, which takes the form of bi-level programing, is reduced to an unconstrained single objective optimization problem, so that a gradient-descent algorithm can be applied to solving it. The primary objective of the study is to enhance the speed and efficiency of solving the Transit Network Design Problem (TNDP) by transforming it into continuous optimization. The proposed methodology leverages advanced machine learning techniques to outperform traditional methods in computational speed and accuracy. Three schemes are adopted to do so. First, the Gumbel soft-max function continuously approximates the discrete design variable of the upper-level problem. Second, the operational constraints change to a penalty function to ensure that the upper-level problem takes the unconstrained form. And, third, the Jacobian of the lower-level solution with respect to the upper-level variable is derived using the implicit differentiation for the Karush-Kuhn-Tucker conditions of the lower-level transit assignment problem. Solving the reduced problem using the gradient-based algorithm is competitive with 'state-of-the-art' metaheuristics in both accuracy and efficiency.

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