Multi-agent cooperative multi-network group framework for energy-efficient distributed fuzzy flexible job shop scheduling problem

The increasing integration of industrial intelligence and the Industrial Internet of Things (IIoT) has promoted distributed flexible manufacturing (DFM) as a fundamental component of smart manufacturing systems. However, the rising complexity in dynamic demands, production uncertainties, and the urgent need for energy efficiency pose significant challenges. To address these challenges, this study investigates the energy-efficient distributed fuzzy flexible job shop scheduling problem (EE-DFFJSP), which aims to minimize both makespan and total energy consumption (TEC) in DFM environments. To tackle fuzzy uncertainties and complex coupling characteristics inherent in EE-DFFJSP, a multi-agent cooperative multi-network group (MACMNG) framework is proposed. First, a mixed-integer linear programming (MILP) model for EE-DFFJSP is formulated, followed by an analysis of the problem’s properties. A triple Markov decision process formulation adapted to the problem's characteristics is designed, enabling problem decoupling and multi-agent decision-making through specific state representations and reward functions. Next, an innovative multi-network group framework is devised, and coupled decisions are effectively handled via interaction and collaboration among independent subnets. Based on problem decomposition method, EE-DFFJSP is decomposed into a set of subproblems represented by subnets within the network group. These subnets cooperate by sharing experience and knowledge through a domain parameter transfer strategy (DPTS) to enable efficient training. Finally, MACMNG employs a multi-objective DQN (MO-DQN) integrated with a dynamic weighting mechanism, enabling subnets to effectively balance between makespan and TEC during cooperative decision-making and network parameter updating. Experimental results show that MACMNG achieves superior performance compared with three priority dispatch rules (PDRs) across various scenarios. The MACMNG outperforms seven state-of-the-art multi-objective algorithms in terms of different metrics across 69 benchmark instances. This study contributes an efficient learning-driven and multi-agent collaborative promising paradigm for the energy-efficient scheduling in DFM, providing practical insights for advancing smart manufacturing in IIoT architectures.