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<p>The flexible job-shop scheduling problem (FJSP) is a classical NP-hard combinatorial optimization challenge, where the goal is to assign each operation in a job sequence to the most suitable machine while satisfying precedence and resource constraints. Traditional heuristic and rule-based methods often struggle with the high complexity introduced by multi-relational structures, such as variable operation-machine mappings, which makes accurate state representation and optimal decision-making particularly difficult. To address these limitations, this paper introduces a novel hierarchical graph-based knowledge reinforcement learning framework that explicitly captures the relationships among operations and machines in a graph neural network architecture. The hierarchical graph structure enables comprehensive encoding of FJSP instances, serving as the foundation for learning representations of scheduling states and actions. On top of this structure, a two-part graph-based knowledge reinforcement learning (GKRL) model, comprising an environment module and a decision module, is proposed to guide the agent in selecting optimal actions at each decision point. Additionally, we incorporate graph-based domain knowledge and tailored reward signals to enhance the model’s learning efficiency and exploitation capacity. Numerical experiments demonstrate the effectiveness of the proposed approach in minimizing makespan and improving scheduling quality under complex and uncertain conditions.</p>

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Graph-Based Knowledge Reinforcement Learning for Flexible Job-Shop Scheduling

  • 期刊论文

  • 发表日期：

    2025年11月6日

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  • Guolin Li,
  • Linli Zhang,
  • Debin Yin,
  • Dewei Li

摘要

The flexible job-shop scheduling problem (FJSP) is a classical NP-hard combinatorial optimization challenge, where the goal is to assign each operation in a job sequence to the most suitable machine while satisfying precedence and resource constraints. Traditional heuristic and rule-based methods often struggle with the high complexity introduced by multi-relational structures, such as variable operation-machine mappings, which makes accurate state representation and optimal decision-making particularly difficult. To address these limitations, this paper introduces a novel hierarchical graph-based knowledge reinforcement learning framework that explicitly captures the relationships among operations and machines in a graph neural network architecture. The hierarchical graph structure enables comprehensive encoding of FJSP instances, serving as the foundation for learning representations of scheduling states and actions. On top of this structure, a two-part graph-based knowledge reinforcement learning (GKRL) model, comprising an environment module and a decision module, is proposed to guide the agent in selecting optimal actions at each decision point. Additionally, we incorporate graph-based domain knowledge and tailored reward signals to enhance the model’s learning efficiency and exploitation capacity. Numerical experiments demonstrate the effectiveness of the proposed approach in minimizing makespan and improving scheduling quality under complex and uncertain conditions.