Panoptic migrating birds optimization with GCN-guided population iteration: a feature-guided intelligent optimizer (FGIO) for flexible job shop scheduling

The Flexible job shop scheduling problem (FJSP) is a well-known challenge in operations research, involving the allocation of jobs to machines while minimizing makespan. Traditional priority-based scheduling rules (PDRs) often suffer from limitations like deadlock, especially in dynamic environments. Deep reinforcement learning (DRL) has shown promise in overcoming some of these challenges, but it requires complex large-scale graph structures that lead to slow convergence and limited exploration of the solution space. To address these issues, this paper proposes a novel approach that integrates multi-graph learning with iterative optimization, called the Feature-Guided intelligent optimizer (FGIO) for FJSP. In our approach, we propose a Multi-Graph feature aggregation-oriented (MG-FAO) structure that reduces node density and enhances the sensitivity of the disjunctive graph to critical paths, efficiently capturing both explicit constraints and implicit topological relationships. To accelerate the optimization rate, we integrate the node information extracted from the MG-FAO structure into the intelligent optimization strategy of the Panoptic migrating birds optimization (PMBO) algorithm through an encoding-decoding operation, ensuring dynamic adaptation to evolving scheduling constraints and providing intelligent guidance for decision-making within the PMBO algorithm. This unprecedented bidirectional cybernetic coupling mechanism allows for better exploration and exploitation of the solution space. Extensive experiments demonstrate that the FGIO significantly outperforms existing heuristic, meta-heuristic, and DRL-based methods, even when applied to new, unseen datasets. Moreover, we introduce the concept of the ideal makespan as a theoretical upper bound, providing a more rigorous evaluation benchmark for FJSP instances. Our results highlight the power of integrating multi-graph learning with swarm intelligence, offering a promising solution to one of the most challenging optimization problems in modern manufacturing and operations management.