A Mixed Integer Linear Programming Formulation for Subway Timetable
Optimization Problems with Passenger Waiting and Energy Saving
Objectives
Abstract
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.