Fuzzy Programming Approach for the Electric Multiple Unit Circulation Planning Problem Using Simulated Annealing

Abstract

Circulation planning for electric multiple units (EMUs) is regarded as one of the key operation issues for a high-speed railway transportation system. The EMU circulation plan consists of determining the connections of trains while accomplishing the passengers’ demands. EMUs need regular maintenance at a certain interval of kilometers or minutes for safety reasons. Consequently, the circulation plan must ensure that EMU trains can reach the maintenance depots in time for their required maintenance. This paper proposes a 0-1 integer programming model for the EMU circulation plan with the aim of minimizing the total costs of the mileage losses of the EMUs, which is incurred when they undergo a maintenance check before the corresponding travel mileage reaches the limit of the cycle. Given that the accumulated travel mileage of EMUs is allowed to be 10% above the standard mileage cycle in practice, an ingenious fuzzy maintenance constraint is presented to tackle the mileage cycle constraint with a certain elasticity. The exterior penalty function is employed to deal with the fuzzy constraint and a simulated annealing (SA) heuristic is employed to solve the model. The modeling and solving approach are applied to a practical instance in the context of China’s high-speed railway system. Compared with the average travel mileage of EMU trains using the manual solution, with the SA solution an increase of 293 km was observed. It can be then concluded that the optimization method presented in this paper can effectively improve the quality of the EMU circulation plan.