A Q-Learning Improved Particle Swarm Optimization for Aircraft Pulsating Assembly Line Scheduling Problem Considering Skilled Operator Allocation

Aircraft assembly is characterized by stringent precedence constraints, limited resource availability, spatial restrictions, and a high degree of manual intervention. These factors lead to considerable variability in operator workloads and significantly increase the complexity of scheduling. To address this challenge, this study investigates the Aircraft Pulsating Assembly Line Scheduling Problem (APALSP) under skilled operator allocation, with the objective of minimizing assembly completion time. A mathematical model considering skilled operator allocation is developed, and a Q-Learning improved Particle Swarm Optimization algorithm (QLPSO) is proposed. In the algorithm design, a reverse scheduling strategy is adopted to effectively manage large-scale precedence constraints. Moreover, a reverse sequence encoding method is introduced to generate operation sequences, while a time decoding mechanism is employed to determine completion times. The problem is further reformulated as a Markov Decision Process (MDP) with explicitly defined state and action spaces. Within QLPSO, the Q-learning mechanism adaptively adjusts inertia weights and learning factors, thereby achieving a balance between exploration capability and convergence performance. To validate the effectiveness of the proposed approach, extensive computational experiments are conducted on benchmark instances of different scales, including small, medium, large, and ultra-large cases. The results demonstrate that QLPSO consistently delivers stable and high-quality solutions across all scenarios. In ultra-large-scale instances, it improves the best solution by 25.2% compared with the Genetic Algorithm (GA) and enhances the average solution by 16.9% over the Q-learning algorithm, showing clear advantages over the comparative methods. These findings not only confirm the effectiveness of the proposed algorithm but also provide valuable theoretical references and practical guidance for the intelligent scheduling optimization of aircraft pulsating assembly lines.