Train Scheduling Optimization for an Urban Rail Transit Line: A Simulated-Annealing Algorithm Using a Large Neighborhood Search Metaheuristic

Abstract

This paper describes an optimization model for an irregular train schedule. The aim is to optimize both the maximum train loading rate and the average deviation of departure intervals under time-varying passenger transport demand for an urban rail transit line in consideration of practical train operation constraints, i.e., headway, running time between stations, dwell time, and capacity. A heuristic simulated-annealing algorithm is designed to solve the optimization model, and a case study of an urban rail transit line is performed to assess its efficacy. The results show that, compared with the current regular train schedule, the total train dwell time under the optimized irregular schedule is reduced from 900 s to 848 s, and the reduction ratio for the maximum train loading rate is from 1.2% to 3.6% for different stations. When the average train departure interval is allowed to vary from 120 to 170 s, the optimized irregular schedule decreases the maximum train loading rate of the collinear and noncollinear sections by 3.21%–4.82% and 2.52%–3.64%, respectively. Sensitivity analysis is performed for a nonnegative weight coefficient, average train departure interval, and proportion of full-length and short-turn routings. The proposed approach can be used to support capacity improvement and schedule optimization for urban rail transit lines.

Bus Rescheduling for Long-Term Benefits: An Integrated Model Focusing on Service Capability and Regularity

“…Moreover, Long [25] took the maximum train-loading rate into account. Researchers [26][27][28][29] have also added deviations from departure intervals to models to satisfy service requirements. Service regularity has gradually become increasingly crucial during rescheduling, which can be represented by departure intervals.…”

“…Thus, researchers have designed many heuristic-based algorithms to reduce the solution space. For example, the greedy heuristic algorithm [11], insertion heuristic algorithm [4], variable neighborhood search heuristic algorithm [33], tabu search algorithm [34], neighborhood search algorithm [35], simulated-annealing algorithm [28], and genetic algorithm [36] have been applied to gradually modify initial solutions by performing local adjustments. Heuristic algorithms are highly effective for solving combinatorial optimization problems and obtaining approximate optimal solutions.…”

An Integrated Optimization Method of High-Speed Railway Rescheduling Problem at the Network Level

“…From the perspective of the algorithm, many algorithms are widely applied to solve the rescheduling problem, such as [20] branch and price algorithm, [25] ant colony algorithm, [26] heuristic simulated-annealing algorithm, etc. [1,5].…”

“…Meng [37] took minimizing the generalized punishment of train operation delay and the stability of train operation as the optimization objective functions and defined the satisfaction of the two objective functions for the two-objective programming problem to obtain a feasible solution. Zhang et al [26] aimed at optimizing both the average deviation of departure intervals and the maximum train loading rate under time-varying passenger transport demand, proposed an optimization model for an irregular train schedule, and designed a heuristic simulated-annealing algorithm to solve the model. Nielsen et al [38] developed a mixed-integer linear programming model with three objective functions: The penalty value of canceling the train, the penalty value of the scheduling plan, and the penalty value of the deviation between the actual end station and the planned end station.…”

“…Constraint (26) ensures that the train sets and standby train sets must execute all subsequent trains when executing the affected circulation.…”