Integrating Energy-Efficient Train Control in railway Vertical Alignment Optimization: A novel Mixed-Integer Linear Programming approach

Abstract

Incorporating train control into the railway design process enables a practical and comprehensive evaluation of the lifecycle utility of a track profile. This paper proposes a novel integrated approach, termed EETC-VAO, which combines railway track Vertical Alignment Optimization (VAO) and Energy-Efficient Train Control (EETC). Initially formulated as a Mixed-Integer Nonlinear Programming (MINLP) problem, EETC-VAO aims to meet various geometric constraints and simultaneously minimize construction costs, traction energy consumption, and section running times in both directions. The model is subsequently reformulated into an equivalent Mixed-Integer Linear Programming (MILP) model using linearization methods and is further enhanced with valid inequalities, logic cuts, and a warm start algorithm with random velocity generation. The model has been extensively tested across a variety of case studies and train types, from synthetic small-scale scenarios to challenging real-world cases spanning from 3 to 71.2 km. Our findings demonstrate that operational costs can be significantly reduced with only marginal increases in construction costs. The integrated approach achieves reductions in total lifecycle costs of up to 40%, revealing a critical trade-off between construction and operational expenses. Notably, our results also indicate that lower construction costs do not inherently conflict with reduced operational costs, emphasizing the critical importance of integrating the train control scheme into the VAO problem.