A deep Q-network enhanced variable neighborhood search algorithm based on NSGA-II for the multi-AGV flexible job shop scheduling problem with battery constraint

This paper studies the multi-AGV flexible job shop scheduling problem with battery constraints (MAFJSP-BC) and proposes a DQN-enhanced variable neighborhood search algorithm based on NSGA-II (DVNS-NSGA-II) to jointly minimize makespan and total energy consumption. To capture transportation resource limits and AGV battery restrictions often ignored in conventional approaches, we develop a three-layer encoding scheme with a matched decoding procedure, and design six dedicated neighborhood operators acting on the corresponding layers. Instead of selecting operators by predefined rules or randomness as in standard variable neighborhood search (VNS), our method uses a deep Q-network with six key state features to learn an adaptive operator-selection policy. The DQN ranks operators according to their historical effectiveness and the current solution characteristics, guiding systematic neighborhood exploration and improving search efficiency. Experimental results show that DVNS-NSGA-II achieves substantial improvements on MAFJSP-BC instances, delivering better solution quality and faster convergence while maintaining a strong balance between global exploration and local exploitation.