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Graph Neural Networks for Job Shop Scheduling Problems: A Survey

Igor G. Smit, Jianan Zhou, Robbert Reijnen, Yaoxin Wu, Jian Chen, Cong Zhang, Zaharah Bukhsh, Yingqian Zhang, Wim Nuijten

TL;DR

This survey analyzes graph neural networks for solving Job Shop Scheduling Problems (JSSP) and related Flow-Shop Problems (FSP), emphasizing graph representations, GNN architectures (e.g., GCN, GIN, GAT), and training with deep reinforcement learning (DRL) or non-DRL approaches. It categorizes methods into non-DRL and DRL branches, further dividing DRL work into basic JSSP, flexible JSSP, dynamic JSSP, and distributed JSSP, and extends discussion to FSP variants. Key findings include widespread use of disjunctive graphs and PPO/REINFORCE, notable successes on large instances, and a set of shared challenges such as representation choices, benchmarking, and scalability. The paper advocates future directions such as generic foundation models, unified graph formulations, robustness and explainability, and standardized benchmarks to accelerate practical adoption of GNN-based scheduling.

Abstract

Job shop scheduling problems (JSSPs) represent a critical and challenging class of combinatorial optimization problems. Recent years have witnessed a rapid increase in the application of graph neural networks (GNNs) to solve JSSPs, albeit lacking a systematic survey of the relevant literature. This paper aims to thoroughly review prevailing GNN methods for different types of JSSPs and the closely related flow-shop scheduling problems (FSPs), especially those leveraging deep reinforcement learning (DRL). We begin by presenting the graph representations of various JSSPs, followed by an introduction to the most commonly used GNN architectures. We then review current GNN-based methods for each problem type, highlighting key technical elements such as graph representations, GNN architectures, GNN tasks, and training algorithms. Finally, we summarize and analyze the advantages and limitations of GNNs in solving JSSPs and provide potential future research opportunities. We hope this survey can motivate and inspire innovative approaches for more powerful GNN-based approaches in tackling JSSPs and other scheduling problems.

Graph Neural Networks for Job Shop Scheduling Problems: A Survey

TL;DR

This survey analyzes graph neural networks for solving Job Shop Scheduling Problems (JSSP) and related Flow-Shop Problems (FSP), emphasizing graph representations, GNN architectures (e.g., GCN, GIN, GAT), and training with deep reinforcement learning (DRL) or non-DRL approaches. It categorizes methods into non-DRL and DRL branches, further dividing DRL work into basic JSSP, flexible JSSP, dynamic JSSP, and distributed JSSP, and extends discussion to FSP variants. Key findings include widespread use of disjunctive graphs and PPO/REINFORCE, notable successes on large instances, and a set of shared challenges such as representation choices, benchmarking, and scalability. The paper advocates future directions such as generic foundation models, unified graph formulations, robustness and explainability, and standardized benchmarks to accelerate practical adoption of GNN-based scheduling.

Abstract

Job shop scheduling problems (JSSPs) represent a critical and challenging class of combinatorial optimization problems. Recent years have witnessed a rapid increase in the application of graph neural networks (GNNs) to solve JSSPs, albeit lacking a systematic survey of the relevant literature. This paper aims to thoroughly review prevailing GNN methods for different types of JSSPs and the closely related flow-shop scheduling problems (FSPs), especially those leveraging deep reinforcement learning (DRL). We begin by presenting the graph representations of various JSSPs, followed by an introduction to the most commonly used GNN architectures. We then review current GNN-based methods for each problem type, highlighting key technical elements such as graph representations, GNN architectures, GNN tasks, and training algorithms. Finally, we summarize and analyze the advantages and limitations of GNNs in solving JSSPs and provide potential future research opportunities. We hope this survey can motivate and inspire innovative approaches for more powerful GNN-based approaches in tackling JSSPs and other scheduling problems.
Paper Structure (18 sections, 5 equations, 3 figures, 5 tables)

This paper contains 18 sections, 5 equations, 3 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Problem Description
  3. Graph Neural Networks
  4. GNNs for Job Shop Scheduling Problems
  5. Non-DRL Methods
  6. DRL Methods
  7. Preliminaries on DRL
  8. MDP formulations of JSSPs
  9. Basic JSSPs
  10. Flexible JSSPs
  11. Dynamic JSSPs
  12. Distributed JSSPs
  13. FSPs with the Variants
  14. Discussion
  15. Recurring Challenges:
  16. ...and 3 more sections

Figures (3)

  • Figure 1: Disjunctive graph representation of JSSPs.Left panel represents a 3 (jobs) $\times$ 3 (machines) JSSP instance. The black arrows are conjunctive arcs, representing the precedence among operations within the same job. The dotted lines are disjunctive arcs whose directions are to be assigned. The disjunctive arcs (or the operation nodes) with the same color require the same machine for processing. Right panel represents a feasible solution. Best viewed in color.
  • Figure 2: Disjunctive graph representation of Distributed JSSPs.Left panel represents a 4 (jobs) $\times$ 3 (machines) DiJSSP instance. All jobs should be processed in either $f_1$ or $f_2$. Right panel represents a feasible solution. Best viewed in color.
  • Figure 3: Disjunctive graph representation of Flexible JSSPs.Left panel represents a 3 (jobs) $\times$ 3 (machines) FJSSP instance. Each operation can be processed on any machine from a subset of available machines capable of performing that operation. Right panel represents a feasible solution. Best viewed in color.