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A Mixed Integer Linear Programming Formulation for Subway Timetable Optimization Problems with Passenger Waiting and Energy Saving Objectives
  • Anbang Liu ,
  • Xi Chen
Anbang Liu
Tsinghua University

Corresponding Author:[email protected]

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Subway timetabling problems are important but difficult discrete optimization problems that are usually solved with strict computational time requirements in order to minimize passenger waiting time while maximizing energy-saving profits. To obtain high-quality solutions, a promising direction is to formulate the problems as Mixed Integer Linear Programming (MILP) problems, thereby taking advantage of widely available MILP methods such as Branch-and-Cut (B&C). However, based on existing MILP formulations, the computational efforts required by MILP methods are high because of the large numbers of decision variables and constraints. In this paper, we develop a novel MILP formulation for optimizing subway timetables. In the formulation, train arrival times are innovatively formulated by using decision variables of two types: continuous variables for formulating energy-saving profits and binary variables for formulating passenger waiting time. Compared to existing formulations, the proposed formulation has far fewer decision variables and constraints. Numerical testing results show that high-quality solutions are efficiently obtained using B&C based on the proposed formulation in reasonable time. Thus, the proposed formulation paves the way for efficiently solving subway problems using MILP methods.