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Variational Approach for Job Shop Scheduling

Seung Heon Oh, Jiwon Baek, Ki Young Cho, Hee Chang Yoon, Jong Hun Woo

TL;DR

The paper tackles the Job Shop Scheduling Problem (JSSP) and the generalization limits of end-to-end DRL by introducing VG2S, a variational graph-based framework that decouples representation learning from policy optimization via an ELBO-based objective with maximum entropy RL to minimize $C_{\max}$. The VG2S architecture combines a variational graph encoder (representation network, latent space model, generative network) with a graph-to-sequence policy decoder, trained in two phases to boost stability and generalization. Empirical results show superior zero-shot generalization and scalability on challenging benchmarks such as DMU and SWV, with latent-space visualizations (UMAP) confirming structured instance clustering. These findings highlight robust, distribution-aware scheduling capabilities and lay groundwork for extending VG2S to dynamic and multi-objective JSSP scenarios in real-world manufacturing.

Abstract

This paper proposes a novel Variational Graph-to-Scheduler (VG2S) framework for solving the Job Shop Scheduling Problem (JSSP), a critical task in manufacturing that directly impacts operational efficiency and resource utilization. Conventional Deep Reinforcement Learning (DRL) approaches often face challenges such as non-stationarity during training and limited generalization to unseen problem instances because they optimize representation learning and policy execution simultaneously. To address these issues, we introduce variational inference to the JSSP domain for the first time and derive a probabilistic objective based on the Evidence of Lower Bound (ELBO) with maximum entropy reinforcement learning. By mathematically decoupling representation learning from policy optimization, the VG2S framework enables the agent to learn robust structural representations of scheduling instances through a variational graph encoder. This approach significantly enhances training stability and robustness against hyperparameter variations. Extensive experiments demonstrate that the proposed method exhibits superior zero-shot generalization compared with state-of-the-art DRL baselines and traditional dispatching rules, particularly on large-scale and challenging benchmark instances such as DMU and SWV.

Variational Approach for Job Shop Scheduling

TL;DR

The paper tackles the Job Shop Scheduling Problem (JSSP) and the generalization limits of end-to-end DRL by introducing VG2S, a variational graph-based framework that decouples representation learning from policy optimization via an ELBO-based objective with maximum entropy RL to minimize . The VG2S architecture combines a variational graph encoder (representation network, latent space model, generative network) with a graph-to-sequence policy decoder, trained in two phases to boost stability and generalization. Empirical results show superior zero-shot generalization and scalability on challenging benchmarks such as DMU and SWV, with latent-space visualizations (UMAP) confirming structured instance clustering. These findings highlight robust, distribution-aware scheduling capabilities and lay groundwork for extending VG2S to dynamic and multi-objective JSSP scenarios in real-world manufacturing.

Abstract

This paper proposes a novel Variational Graph-to-Scheduler (VG2S) framework for solving the Job Shop Scheduling Problem (JSSP), a critical task in manufacturing that directly impacts operational efficiency and resource utilization. Conventional Deep Reinforcement Learning (DRL) approaches often face challenges such as non-stationarity during training and limited generalization to unseen problem instances because they optimize representation learning and policy execution simultaneously. To address these issues, we introduce variational inference to the JSSP domain for the first time and derive a probabilistic objective based on the Evidence of Lower Bound (ELBO) with maximum entropy reinforcement learning. By mathematically decoupling representation learning from policy optimization, the VG2S framework enables the agent to learn robust structural representations of scheduling instances through a variational graph encoder. This approach significantly enhances training stability and robustness against hyperparameter variations. Extensive experiments demonstrate that the proposed method exhibits superior zero-shot generalization compared with state-of-the-art DRL baselines and traditional dispatching rules, particularly on large-scale and challenging benchmark instances such as DMU and SWV.
Paper Structure (24 sections, 39 equations, 6 figures, 2 tables, 1 algorithm)

This paper contains 24 sections, 39 equations, 6 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem definition
  3. Representing JSSP instance
  4. Static information: instance-specific features
  5. Dynamic information: state features
  6. Evidence of lower bound with maximum entropy RL for JSSP
  7. Variational graph-to-scheduler framework for JSSP
  8. Variational graph encoder
  9. Representation network
  10. Latent space model
  11. Generative network
  12. Policy decoder
  13. Practical implementation
  14. Experiment
  15. Test
  16. ...and 9 more sections

Figures (6)

  • Figure 1: Overview of the proposed VG2S framework
  • Figure 2: Architecture of variational graph encoder
  • Figure 3: Learning curves showing validation performance of average makespan on benchmark datasets
  • Figure 4: Trends in Improvement Rate and Performance Variance with respect to Problem Size
  • Figure 5: Latent space visualization using UMAP: Analysis of the learned manifold with points colored by makespan and scaled flowshop index
  • ...and 1 more figures