Multi-agent assisted co-evolutionary memetic algorithm for lot-streaming flexible job shop energy-efficient scheduling problem with asynchronous assembly

Mass customization increasingly requires flexible manufacturing systems in which component processing, material transfer, and multi-station assembly must be coordinated simultaneously. This study investigates a lot-streaming flexible job shop energy-efficient scheduling problem with asynchronous assembly (LS-FJSEP-AA). It integrates lot streaming and flexible processing with inter-stage transportation and an unpaced assembly line subject to precedence and blocking constraints. A bi-objective mixed-integer linear programming model is formulated to minimize makespan and total energy consumption, with energy accounting for processing, setup, machine idle/on–off, transportation, assembly, and assembly-station idle states. Based on the cross-stage timing relationships, two structural properties are identified to guide critical-operation adjustment and assembly prioritization. To efficiently solve the resulting strongly coupled problem, a multi-agent assisted co-evolutionary memetic algorithm (MA-CoEA) is developed. MA-CoEA integrates offline GEP-assisted initialization, objective-oriented cooperative evolution, problem-specific neighborhood search, and DQN-based adaptive control. Computational experiments show that MA-CoEA achieves competitive solution quality and convergence performance against state-of-the-art algorithms, while exhibiting stable performance across independent runs on representative benchmark instances. An industrially inspired case further demonstrates the effectiveness of lot streaming and cross-stage schedule adjustment in improving the trade-off between makespan and energy consumption.