Integrated line planning and train timetabling through price-based cross-resolution feedback mechanism

Railway line planning and train timetabling are two key planning steps that determine theoperating cost and passenger service quality of a railway operator under the infrastructurecapacity limitations. Traditionally, the line planning and train timetabling problems are solvedsequentially at the strategic and tactical level, respectively. In this study, by introducing twotypes of binary decision variables, we first propose a unified integer linear programming(ILP) model for the integrated optimization of line planning and train timetabling. The lineplanning problem is modeled using ILP to satisfy passenger demand, whereas the cyclic traintimetabling problem is formulated as a multi-commodity network flow model with a sidetrack capacity constraint. The two types of binary decision variables are coupled by a cross-resolution consistency constraint, which ensures the conformity of the line planning and traintimetabling decisions. Furthermore, a dual decomposition mechanism based on the AlternatingDirection Method of Multipliers (ADMM) is developed to dualize the cross-resolution consistencyand track capacity constraints, such that the original ILP model is decomposed into a lineplanning sub-problem and a set of train-specific sub-problems. After the linearization of thequadratic penalty terms in the ADMM, each sub-problem contains the Lagrangian relaxationprice information based on the cross-resolution consistency constraint. Moreover, the primaland dual solutions are obtained by iteratively and efficiently solving the line planning sub-problem using a commercial solver, and each train-specific sub-problem through a tailoredforward dynamic programming algorithm. Furthermore, a real-life case study is conducted basedon the Beijing-Shanghai high-speed railway corridor to verify the efficiency and effectivenessof the proposed model and algorithm. The results of the numerical experiments demonstratethat the ADMM can achieve significantly smaller optimality gaps than Lagrangian relaxation,and the integrated optimization approach can improve the objective value by 5.78% on averagecompared with the sequential optimization approach.*Corresponding author.E-mail addresses:bk20100249@my.swjtu.edu.cn (Y. Zhang), qiyuan-peng@swjtu.cn (Q. Peng), lugongyuan@swjtu.cn (G. Lu),qingweizhong@my.swjtu.edu.cn (Q. Zhong), yanxu@my.swjtu.edu.cn (X. Yan), xzhou74@asu.edu (X. Zhou).https://doi.org/10.1016/j.trb.2021.11.009Received 16 October 2020; Received in revised form 31 October 2021; Accepted 20 November 2021