Study on passenger train stopping scheme based on improved Particle Swarm Optimization algorithm

This paper develops a multi-objective optimization model for the passenger train stopping scheme on high-speed railway lines. Minimizing the stopping times for all passenger trains, minimizing travel distance of empty trains and minimizing the number of transfer passengers are the three planning objectives of the model. For a given travel demand and specified capacity of stops, the model is solved by heuristic algorithm. An improved discrete particle swarm optimization (PSO) algorithm is presented to determine the best-compromise train stopping scheme with high effectiveness and stability. In the algorithm, a stop based representation is designed, and a new method is used to update the position and velocity of particles. In order to keep the particle swarm algorithm from premature stagnation, the simulated annealing algorithm, which has local search ability, is combined with the PSO algorithm to make elaborate search near the optimal solution, then the quality of solutions is improved effectively. An empirical study on a given small railway network is conducted to demonstrate the effectiveness of the model and the performance of the algorithm. The experimental results show that the hybrid algorithm has great advantages in both success rate and convergence speed compared with other discrete PSO algorithm and genetic algorithm, and an optimal set of stopping schemes can always be generated for a given demand. To achieve the best planning outcome, the stopping schemes should be flexibly planned, and not constrained by specific ones as often set by the planner.