基于分布鲁棒优化的城市轨道交通网络末班车衔接研究

Abstract

With the rapid development and expansion of the urban rail transit network in China, the coordination between different lines brings great challenges to the operation due to its high complexity. In order to minimize the unsuccessful transfer-passenger flows of last-train under the worse case with the given level of tolerance, a distributionally robust chance-constrained programming model is proposed for the last-train connection planning problem in urban rail transit networks under uncertain transfer-passenger demand. In particular, the probability distribution of uncertain parameters is only partially known. By analyzing the relationship between the distributionally robust optimization model and the corresponding robust optimization model, it is proved that the former is an extension of the latter. Furthermore, the original model can be reformulated into a second-order mixed-integer conic programming form under the Gaussian perturbations ambiguity set based on the limited information of expectation and variance, which can be solved by CPLEX. The results of numerical examples indicate that the proposed model can be solved to optimality quickly by CPLEX on a small network, and can effectively avoid over-conservative solutions compared to the robust optimization model and reduce unsuccessful transfer-passenger flows in the extreme situation compared with the stochastic programming model, which exhibits more robust performance.