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Learning Topological Representations with Bidirectional Graph Attention Network for Solving Job Shop Scheduling Problem

Cong Zhang, Zhiguang Cao, Yaoxin Wu, Wen Song, Jing Sun

TL;DR

This work tackles the Job Shop Scheduling Problem (JSSP) by introducing TBGAT, a topology-aware bidirectional graph attention network that embeds disjunctive graphs from both forward and backward perspectives. Leveraging forward and backward topological sorts via a novel MPTS-based computation, TBGAT learns discriminative representations that guide a neural local search with entropy-regularized REINFORCE, achieving linear time complexity in $| ext{J}|$ and $| ext{M}|$. Empirical results on five synthetic datasets and seven classic benchmarks demonstrate state-of-the-art performance, strong generalization (even in zero-shot settings), and competitive runtime compared to exact solvers. The approach offers practical impact for large-scale JSSP instances and provides a foundation for further topology-aware learning in scheduling and related DAG-structured problems.

Abstract

Existing learning-based methods for solving job shop scheduling problems (JSSP) usually use off-the-shelf GNN models tailored to undirected graphs and neglect the rich and meaningful topological structures of disjunctive graphs (DGs). This paper proposes the topology-aware bidirectional graph attention network (TBGAT), a novel GNN architecture based on the attention mechanism, to embed the DG for solving JSSP in a local search framework. Specifically, TBGAT embeds the DG from a forward and a backward view, respectively, where the messages are propagated by following the different topologies of the views and aggregated via graph attention. Then, we propose a novel operator based on the message-passing mechanism to calculate the forward and backward topological sorts of the DG, which are the features for characterizing the topological structures and exploited by our model. In addition, we theoretically and experimentally show that TBGAT has linear computational complexity to the number of jobs and machines, respectively, strengthening our method's practical value. Besides, extensive experiments on five synthetic datasets and seven classic benchmarks show that TBGAT achieves new SOTA results by outperforming a wide range of neural methods by a large margin. All the code and data are publicly available online at https://github.com/zcaicaros/TBGAT.

Learning Topological Representations with Bidirectional Graph Attention Network for Solving Job Shop Scheduling Problem

TL;DR

This work tackles the Job Shop Scheduling Problem (JSSP) by introducing TBGAT, a topology-aware bidirectional graph attention network that embeds disjunctive graphs from both forward and backward perspectives. Leveraging forward and backward topological sorts via a novel MPTS-based computation, TBGAT learns discriminative representations that guide a neural local search with entropy-regularized REINFORCE, achieving linear time complexity in and . Empirical results on five synthetic datasets and seven classic benchmarks demonstrate state-of-the-art performance, strong generalization (even in zero-shot settings), and competitive runtime compared to exact solvers. The approach offers practical impact for large-scale JSSP instances and provides a foundation for further topology-aware learning in scheduling and related DAG-structured problems.

Abstract

Existing learning-based methods for solving job shop scheduling problems (JSSP) usually use off-the-shelf GNN models tailored to undirected graphs and neglect the rich and meaningful topological structures of disjunctive graphs (DGs). This paper proposes the topology-aware bidirectional graph attention network (TBGAT), a novel GNN architecture based on the attention mechanism, to embed the DG for solving JSSP in a local search framework. Specifically, TBGAT embeds the DG from a forward and a backward view, respectively, where the messages are propagated by following the different topologies of the views and aggregated via graph attention. Then, we propose a novel operator based on the message-passing mechanism to calculate the forward and backward topological sorts of the DG, which are the features for characterizing the topological structures and exploited by our model. In addition, we theoretically and experimentally show that TBGAT has linear computational complexity to the number of jobs and machines, respectively, strengthening our method's practical value. Besides, extensive experiments on five synthetic datasets and seven classic benchmarks show that TBGAT achieves new SOTA results by outperforming a wide range of neural methods by a large margin. All the code and data are publicly available online at https://github.com/zcaicaros/TBGAT.
Paper Structure (36 sections, 4 theorems, 7 equations, 6 figures, 7 tables, 1 algorithm)

This paper contains 36 sections, 4 theorems, 7 equations, 6 figures, 7 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Literature
  3. Prerequisite
  4. The job shop scheduling problem.
  5. The disjunctive graph representation.
  6. The local search algorithm with proposed TBGAT network
  7. The forward and backward views of DGs
  8. Graph embedding with TBGAT
  9. The forward embedding module
  10. The backward embedding module
  11. Merging the forward and backward embeddings
  12. Action selection
  13. The entropy-regularized REINFORCE algorithm
  14. Experiment
  15. Experimental setup
  16. ...and 21 more sections

Key Result

Lemma 1

For any two operations $O_{ji}, O_{mk} \in \mathcal{O}$, if $O_{ji}$ is a prerequisite operation of $O_{mk}$, then $\overrightarrow{\Phi}(O_{ji}) < \overrightarrow{\Phi}(O_{mk})$ and $EST_{ji} < EST_{mk}$, where $\overrightarrow{\Phi}: \mathcal{O} \rightarrow \mathbb{Z}$ is the topological sort calc

Figures (6)

  • Figure 1: Disjunctive graph representations for JSSP instance and solution.
  • Figure 2: The local search procedure with TBGAT network.
  • Figure 3: The $N_5$ neighborhood structure.
  • Figure 4: The forward and backward view of the DG.
  • Figure 5: The architecture of the policy network.
  • ...and 1 more figures

Theorems & Definitions (5)

  • Definition 1
  • Lemma 1
  • Corollary 1
  • Theorem 1
  • Theorem 2