Optimization of metro vertical alignment for minimized construction costs and traction energy: a dynamic programming approach

Vertical alignment significantly affects the construction costs and train traction energy use of a metro system. Existing studies on this subject mostly optimized the vertical alignment while considering train traction energy consumption or construction costs only. There is still a lack of efficient approach for the vertical alignment optimization problem which considers both construction costs and traction energy consumption. To this end, this paper proposes a two-stage optimization program involving both the design of metro vertical alignment and train speed profile, with the objective of minimizing the total costs of construction and train traction energy. An iterative approach is proposed for solving the two-stage program, in which a dynamic programming (DP) algorithm with a backward search method is designed to seek an optimal vertical alignment given an energy-efficient train speed profile. The model and algorithm approach are tested on real-world case studies on the Line 14 of Guangzhou Metro in China. The results show that compared with the existing heuristic algorithms, the DP approach performs better in computation time and solution quality. Moreover, the optimized vertical alignments outperform that designed by experienced designers in terms of total costs of construction and traction energy consumption, with an average savings rate of 6.0%.