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Leveraging Constraint Programming in a Deep Learning Approach for Dynamically Solving the Flexible Job-Shop Scheduling Problem

Imanol Echeverria, Maialen Murua, Roberto Santana

TL;DR

The paper addresses real-time solution of the flexible job-shop scheduling problem by bridging constraint programming (CP) with deep learning (DL). It proposes BCxCP, a hybrid framework that learns from CP-optimal trajectories via a heterogeneous graph attention network and uses a CP capability predictor to decide when CP should solve a subproblem, enabling dynamic transitioning between DL and CP. Empirical results on three public FJSSP benchmarks show BCxCP outperforms five state-of-the-art DRL methods and a widely used CP solver (OR-Tools), with performance competitive to meta-heuristics, while MAE of the CP predictor remains low (~0.019). Preliminary TSP experiments suggest the approach generalizes to other combinatorial problems, highlighting potential for broader applicability in hybrid optimization.

Abstract

Recent advancements in the flexible job-shop scheduling problem (FJSSP) are primarily based on deep reinforcement learning (DRL) due to its ability to generate high-quality, real-time solutions. However, DRL approaches often fail to fully harness the strengths of existing techniques such as exact methods or constraint programming (CP), which can excel at finding optimal or near-optimal solutions for smaller instances. This paper aims to integrate CP within a deep learning (DL) based methodology, leveraging the benefits of both. In this paper, we introduce a method that involves training a DL model using optimal solutions generated by CP, ensuring the model learns from high-quality data, thereby eliminating the need for the extensive exploration typical in DRL and enhancing overall performance. Further, we integrate CP into our DL framework to jointly construct solutions, utilizing DL for the initial complex stages and transitioning to CP for optimal resolution as the problem is simplified. Our hybrid approach has been extensively tested on three public FJSSP benchmarks, demonstrating superior performance over five state-of-the-art DRL approaches and a widely-used CP solver. Additionally, with the objective of exploring the application to other combinatorial optimization problems, promising preliminary results are presented on applying our hybrid approach to the traveling salesman problem, combining an exact method with a well-known DRL method.

Leveraging Constraint Programming in a Deep Learning Approach for Dynamically Solving the Flexible Job-Shop Scheduling Problem

TL;DR

The paper addresses real-time solution of the flexible job-shop scheduling problem by bridging constraint programming (CP) with deep learning (DL). It proposes BCxCP, a hybrid framework that learns from CP-optimal trajectories via a heterogeneous graph attention network and uses a CP capability predictor to decide when CP should solve a subproblem, enabling dynamic transitioning between DL and CP. Empirical results on three public FJSSP benchmarks show BCxCP outperforms five state-of-the-art DRL methods and a widely used CP solver (OR-Tools), with performance competitive to meta-heuristics, while MAE of the CP predictor remains low (~0.019). Preliminary TSP experiments suggest the approach generalizes to other combinatorial problems, highlighting potential for broader applicability in hybrid optimization.

Abstract

Recent advancements in the flexible job-shop scheduling problem (FJSSP) are primarily based on deep reinforcement learning (DRL) due to its ability to generate high-quality, real-time solutions. However, DRL approaches often fail to fully harness the strengths of existing techniques such as exact methods or constraint programming (CP), which can excel at finding optimal or near-optimal solutions for smaller instances. This paper aims to integrate CP within a deep learning (DL) based methodology, leveraging the benefits of both. In this paper, we introduce a method that involves training a DL model using optimal solutions generated by CP, ensuring the model learns from high-quality data, thereby eliminating the need for the extensive exploration typical in DRL and enhancing overall performance. Further, we integrate CP into our DL framework to jointly construct solutions, utilizing DL for the initial complex stages and transitioning to CP for optimal resolution as the problem is simplified. Our hybrid approach has been extensively tested on three public FJSSP benchmarks, demonstrating superior performance over five state-of-the-art DRL approaches and a widely-used CP solver. Additionally, with the objective of exploring the application to other combinatorial optimization problems, promising preliminary results are presented on applying our hybrid approach to the traveling salesman problem, combining an exact method with a well-known DRL method.
Paper Structure (21 sections, 9 equations, 9 figures, 10 tables, 2 algorithms)

This paper contains 21 sections, 9 equations, 9 figures, 10 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related work
  3. FJSSP formulation
  4. Proposed method: BCxCP
  5. The FJSSP as a Markov Process
  6. Graph Neural Network Architecture
  7. Training procedure with BC
  8. CP Capability Predictor
  9. Jointly constructing solutions
  10. Experiments
  11. Experimental setup
  12. Configuration
  13. Instance generation and benchmark dataset
  14. Evaluation metric and baselines
  15. Experimental results
  16. ...and 6 more sections

Figures (9)

  • Figure 1: A solution to the FJSSP instance with a makespan of 16.
  • Figure 2: An optimal solution with a makespan of 12.
  • Figure 3: Diagram depicting the components of the methodology and their interaction during the training and inference phases.
  • Figure 4: The evolution of solution quality over time is depicted for two instances
  • Figure 5: Boxplots of the distribution of the mean gap for the different methods considered in this investigation on five public datasets.
  • ...and 4 more figures