# Fusion Swarm-Intelligence-Based Decision Optimization for Energy-Efficient Train-Stopping Schemes
## 1 Introduction  
In recent years, urban rail transportation has seen a golden period of development as the scope of urbanization continues to expand, and the travel demand of tourists increases daily. In order to fully meet the travel demand of tourists, urban rail transit has increased the capacity, equipment, scheduling, and operating hours of the system, leading to problems such as operational management difficulties and huge energy consumption in urban rail systems. Regenerative braking technology, as an important part of the process of energy-efficient train operation, provides a practical and less costly solution for energy saving and emission reduction in urban rail transit systems [1]. In a multitrain, multizonal urban rail system, the planning of stopping schemes oriented to regenerative braking directly affects the efficiency of energy saving during train operation, and is the key to decision making in urban rail transportation systems [2]. The main research of the train stopping time planning problem involves the train schedule problem [3]. In order to reflect the real situation of a train stopping, researchers have extended a variety of decision factors. [PERSON] et al. developed an optimal model of stopping time for provincial, local, and county-level stations for different levels of cities where each station is located [4]. [PERSON] et al. studied train stopping planning under variable train lengths and stopping times, and constructed a train stopping planning model under stochastic demand [5]. However, all of the above studies only considered objective factors, such as the train itself and the stopping cities, and did not take the core of theproblem, i.e., passengers, into account. For this reason, [PERSON] et al. introduced the passenger travel rate into train stopping scheme optimization and constructed a mixed-integer planning model to improve the train's operational efficiency from the passenger's perspective [6]; [PERSON] et al. introduced the ideal departure time interval of passengers from the origin station to the destination station into the train stopping scheme, and built an integer linear planning model to fully consider the passengers' demand in real train operation [7]. In summary, in order to explore real and feasible stopping patterns under the influence of objective conditions, this paper focuses on the combination of static-game and train-stopping-time problems. In the optimization problem of a train stopping scheme, which is essentially an NP-hard problem with high complexity that is difficult to solve, metaheuristic algorithms are mostly used to solve it [8]. Among them, the particle swarm algorithm (PSO) [9] and genetic algorithm (GA) [10] are used to solve the problem. With the increase in problem size and complexity, general metaheuristic algorithms are lacking in convergence accuracy and speed. To further enhance the optimization capability of the algorithm, researchers have introduced hybrid mechanisms based on the metaheuristic algorithm. [PERSON] et al. designed a combined simulated annealing algorithm (CSA), and the experimental simulation results showed its strong solving capability [11]. [PERSON] et al. designed a genetic algorithm based on the ideal-point method on the basis of the genetic algorithm, which effectively solved the problem of the algorithm easily falling into a local optimum. This shows that the use of hybrid metaheuristic algorithms has good benefits for solving large-scale complex optimization problems. On the basis of the above research, this paper focuses on the train stopping time planning problem involving static games. First, force analysis during train movement was carried out, on which basis an optimization model was established to determine the train stopping time at each stage by introducing the benefit function of the train group-passenger group in the game and discretizing the analysis.