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The energy-efficient driving of automatic train operation (ATO) system in high-speed railway systems has attracted more and more attention. Different from the energy-efficient automatic train control problem for metro trains, the traction/braking forces given by high-speed ATO systems are currently not continuous but discrete values corresponding to traction/braking notches due to the limited communication interface between ATO systems and rolling stocks. In addition, since high-speed trains are powered by single-phase alternating current, there is no power supply for train traction in neutral sections, which is introduced to separate two catenaries powered by currents with different phases. In this paper, we propose a discrete-space based mathematical formulation for the energy-efficient automatic train control problem for high-speed trains, where binary variables are introduced to indicate the traction/braking notch selections and to indicate whether a discrete space interval is a neutral section or not. The mathematical formulation is then transformed into a mixed integer linear programming (MILP) model, which can be solved by existing solvers. However, due to the discretization of the space the discrete traction/braking notches, the resulting MILP problem could be infeasible and the optimal driving strategy cannot be obtained. Hence, we present a novel relaxation method, i.e., the final braking notch relaxation method, to relax a few constraints in the final braking phase and to generate a feasible speed profile. Comprehensive experiments are investigated based on Beijing–Harbin high-speed railway line, where the energy consumption of the speed profiles with discrete (i.e., notch-based) traction/braking forces is slightly higher than that with continuous traction/braking forces. Moreover, the impacts of the neutral section locations and the effects of different numbers of traction/braking notches are deeply analyzed. • Energy-efficient automatic train operation for high speed railway lines. • A new optimal train control model with discrete notches and neutral sections. • Practically inspired final braking notch relaxation method to eliminate infeasibility. • The relaxation of discrete notches enhances computational efficiency. • Our model and method were tested based on data of Chinese high-speed railways. [ABSTRACT FROM AUTHOR]