Robust optimization of the formation plan of a direct train originating at a technical station under uncertain wagon flow conditions

The technical station direct train formation plan (TSDTFP) plays a vital role in transporting bulk raw materials. However, today’s complex economic environment causes frequent changes in demand for freight wagons. This article studies the TSDTFP under uncertain origin-to-destination wagon flow to minimize total wagon-hours consumption. Furthermore, a robust optimization model of TSDTFP is developed, with symmetrical bounded uncertainty set based on the max–min criterion. This model cannot be solved directly. Therefore, a metaheuristic solution strategy based on robust particle swarm for uncertain wagon flow is designed. Finally, some main tracks in China are selected to build the test railway network, which is used to test the proposed model and metaheuristic algorithm. The stability of the proposed model and the expected value model are evaluated. The results demonstrate that the feasibility measure of the robust optimization model has more advantages than that of the expected value model.