Graph-Based Knowledge-Integrated Deep Reinforcement Learning for Dynamic Multi-Objective Reentrant Hybrid Flow-Shop Scheduling Problem With Batch Processing Machines

Abstract The reentrant hybrid flow-shop scheduling problem with batch processing machines (RHFSP-BPMs), characterized by reentrant routing and batch processing, is widely observed in industrial settings such as electronics manufacturing. Its complexity is further increased by dynamic disruptions, i.e., new job arrivals, and multi-objective optimization demands. To achieve fast and high-quality scheduling under dynamic environments with multi-objective optimization, deep reinforcement learning (DRL) has received growing attention. However, DRL tailored to RHFSP-BPM remains scarce, and existing DRLs often rely on handcrafted features while failing to leverage domain knowledge, thus limiting their effectiveness. To supplement these gaps, a graph-based knowledge-integrated deep reinforcement learning (GKI-DRL) method is proposed for RHFSP-BPM. First, a disjunctive graph with reentry arcs and a Markov decision process are constructed to represent reentrancy and batch operations. On this basis, a dual-agent framework is developed to decouple objective selection and scheduling execution, with a weighted batching policy designed to handle batch decisions effectively. Furthermore, a knowledge-integrated message-passing mechanism is embedded into the graph neural network, enabling heuristic-aware decision-making. The effectiveness of the proposed method and its core improvements are validated based on numerous dynamic RHFSP-BPM instances through ablation studies and comparisons with composite dispatching rules and existing DRL approaches.