Optimization of the speed curve for heavy-haul trains considering cyclic air braking: an MILP approach

Abstract

The most difficult problem for the control of heavy-haul trains is the cyclic air braking on long steep downward slopes. Unsuitable positions of the application of air braking will cause large longitudinal impulses, overspeeding and even accidents. This article proposes a mixed-integer linear programming (MILP) approach to the optimization of the speed curve of heavy-haul trains. First, with the objectives of maximizing the operation distance and minimizing the air braking time within a given period, an optimization model of a heavy-haul train is formulated considering multiple practical constraints, such as the speed limit, release time and releasing speed. Second, the optimization problem is transformed into an MILP problem by linearizing the nonlinear conditions, and is solved with existing CPLEX${}^{\circledR }$ solvers. Finally, some case studies are conducted with actual data from the Shuohuang railway in China to illustrate the effectiveness of the proposed method.

Keywords:

• Heavy-haul trains
• cyclic air braking
• long steep downward slopes
• mixed-integer linear programming

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The authors confirm that the data supporting the findings of this study are available within the article and its online supplemental data.

Additional information

Funding

This work was supported by the Fundamental Research Funds for the Central Universities [Grant No. 2020JBZD002].