## 1 Introduction  
As the scale of global industrial activities increases, energy consumption continues to increase. Accordingly, demands for the efficient use of the Earth's limited resources as well as environmental protection of the Earth are increasing. Energy consumption is continuously increasing not only in industrial processes but also in large buildings and transportation systems, requiring their efficient operation. The electric railway system is one of the fields that demand excessive energy. Several studies have attempted to improve the energy efficiency of railways. More than 80% of the total operating-energy consumption of railways is utilized by the train system, while more than 60% of the energy is consumed by the trains' power systems [1]. Therefore, this study focuses on improving the driving energy efficiency of electric trains specifically; whenever a train is mentioned, this means an electric train. Several methods for optimizing train-running energy have been presented in recent years. In an early train-operation optimization study, [PERSON] discussed, in 1980, how to operate trains under minimum-energy control according to timetables and operational constraints [2]. Few studies have applied the evolutionary algorithm (EA) [3; 4; 5]; in 2011, [PERSON] et al. searched various solutions in a continuous search space based on an evolutionary algorithm to address a multipurpose problem involving three criteria: reduced travel time, reduced delay, and minimized energy consumption [3]. In 2015, [PERSON] et al. proposed an energy-efficient approach to reduce traction energy, by optimizing train operation for multiple interstations using a multi-population genetic algorithm (MPGA) [4]. In 2020, [PERSON] presented a simulation-based optimization algorithm to solve the eco-driving problem subject with multiple target-time constraints, by applying the differential evolution algorithm [5]. In 2013, [PERSON] et al. proposed a distance-based train-trajectory search model that applies three optimization algorithms (ants colony optimization (ACO), dynamic programming (DP), and genetic algorithm (GA)) to find the optimal train speed trajectory [6]. In 2016, [PERSON] et al. proposed a fast and effective optimization algorithm based on a two-step method for finding an optimal curve using a maximum-minimum colony optimization system with an approximation of a discrete combinatorial optimization model [7]. In 2011, [PERSON] et al. proposed an optimization method that minimizes energy consumption by considering track alignment, speed limit, and schedule compliance based on the simulated annealing (SA) algorithm [8]. In 2013, [PERSON] et al. developed a simulation annealing algorithm to find the optimal coasting point and proposed an optimization method that minimizes energy consumption by comprehensively considering the speed limit, track alignment, and travel time [9]. A recent study [10] compared the pros and cons of the three primarily used methods for optimizing driving energy--DP, gradient method (GM), and sequential quadratic programming (SQP). According to the analysis results of this study, DP is suitable for design considering speed limit and disturbances such as running resistance and gradient resistance, but it is not advantageous for optimizing calculation speed and multiple inputs. Here, operational constraints such as speed limits and disturbances are used for train models and DP based on train running position using running-track data tables. GM is not suitable for design considering disturbance or speed limit, but it has a fast calculation speed and is suitable for optimizing multiple inputs. In addition, SQP is slow in calculation speed and unfavorable considering disturbance or speed limit, but it has significant multi-input processing and practical applicability. In 2014, [PERSON] et al.