Solving train scheduling with vehicle flexibility using an ensembled Q-learning multi-objective optimization algorithm

doi:10.1016/j.swevo.2026.102459

Solving train scheduling with vehicle flexibility using an ensembled Q-learning multi-objective optimization algorithm

2026-07-01

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DOI：10.1016/j.swevo.2026.102459

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With the development of virtual coupling technologies, train platoon flexibility and passenger satisfaction can be further improved. In this study, we investigated train scheduling for urban rail networks under vehicle flexibility constraints. First, the problem was modeled as a special job shop scheduling problem with blocking constraints, where three objectives were considered, including the minimization of tardiness penalties, passenger dissatisfaction, and the total number of vehicles. A mixed-integer linear programming (MILP) model was proposed to optimize the number of vehicles for each train, the arrival/departure times at each station, and the scheduling sequence of trains. Second, a Q-learning-driven multi-objective evolutionary optimization method was designed with the following features: (1) to improve the global and local search abilities, a hybrid framework combining Q-learning and variable neighborhood search (VNS) heuristics was embedded; (2) to handle the blocking constraints, a problem-specific lemma was proposed and then used to design an efficient multi-block left-insertion decoding heuristic; and (3) ten types of critical-path search operators were designed to fully explore the search space. Third, to evaluate the efficiency and effectiveness of the proposed algorithm, three types of instances were tested, including small-scale instances for validating the mathematical model and realistic data from the Shenzhen metro system for evaluating the performance on large-scale instances. Comprehensive computational comparisons and statistical analyses show that the proposed algorithm achieved an average improvement of about 1.68%-3.03% compared with six state-of-the-art multi-objective algorithms.

Keywords:

Train scheduling

Vehicle flexibility

Passenger dissatisfaction

Ensemble Q-learning

Multi-objective optimization algorithm

Solving train scheduling with vehicle flexibility using an ensembled Q-learning multi-objective optimization algorithm

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