ABSTRACT Vertical alignment design for heavy‐haul railways not only profoundly affects construction investment but also directly influences train energy consumption. Under complex and interdependent constraints, designers must reconcile the conflict between these two objectives; however, most existing methods require the number of vertical points of intersection (VPIs) to be predetermined and suffer severe efficiency losses as constraints become more intricate. To address these challenges, this study, for the first time, employs an NSGA‐II framework enhanced with struct‐based encoding to achieve bi‐objective optimization of construction cost and energy consumption. The model requires no preset VPIs and naturally satisfies most constraints. Under the given constraints, it can produce schemes that outperform manually designed routes in both construction cost and train energy consumption, achieving reductions of 4.09%–6.41% and 2.37%–5.92%, respectively, under different heavy‐to‐light ratio conditions. while also offering guidance for selecting technically optimal ratios in future heavy‐haul railway design.
Zhuo et al. (Thu,) studied this question.