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Learning Memory-Enhanced Improvement Heuristics for Flexible Job Shop Scheduling

Jiaqi Wang, Zhiguang Cao, Peng Zhao, Rui Cao, Yubin Xiao, Yuan Jiang, You Zhou

TL;DR

A Memory-enhanced Improvement Search framework with heterogeneous graph representation with heterogeneous graph representation--MIStar is proposed, which significantly outperforms both traditional handcrafted improvement heuristics and state-of-the-art DRL-based constructive methods.

Abstract

The rise of smart manufacturing under Industry 4.0 introduces mass customization and dynamic production, demanding more advanced and flexible scheduling techniques. The flexible job-shop scheduling problem (FJSP) has attracted significant attention due to its complex constraints and strong alignment with real-world production scenarios. Current deep reinforcement learning (DRL)-based approaches to FJSP predominantly employ constructive methods. While effective, they often fall short of reaching (near-)optimal solutions. In contrast, improvement-based methods iteratively explore the neighborhood of initial solutions and are more effective in approaching optimality. However, the flexible machine allocation in FJSP poses significant challenges to the application of this framework, including accurate state representation, effective policy learning, and efficient search strategies. To address these challenges, this paper proposes a Memory-enhanced Improvement Search framework with heterogeneous graph representation--MIStar. It employs a novel heterogeneous disjunctive graph that explicitly models the operation sequences on machines to accurately represent scheduling solutions. Moreover, a memoryenhanced heterogeneous graph neural network (MHGNN) is designed for feature extraction, leveraging historical trajectories to enhance the decision-making capability of the policy network. Finally, a parallel greedy search strategy is adopted to explore the solution space, enabling superior solutions with fewer iterations. Extensive experiments on synthetic data and public benchmarks demonstrate that MIStar significantly outperforms both traditional handcrafted improvement heuristics and state-of-the-art DRL-based constructive methods.

Learning Memory-Enhanced Improvement Heuristics for Flexible Job Shop Scheduling

TL;DR

A Memory-enhanced Improvement Search framework with heterogeneous graph representation with heterogeneous graph representation--MIStar is proposed, which significantly outperforms both traditional handcrafted improvement heuristics and state-of-the-art DRL-based constructive methods.

Abstract

The rise of smart manufacturing under Industry 4.0 introduces mass customization and dynamic production, demanding more advanced and flexible scheduling techniques. The flexible job-shop scheduling problem (FJSP) has attracted significant attention due to its complex constraints and strong alignment with real-world production scenarios. Current deep reinforcement learning (DRL)-based approaches to FJSP predominantly employ constructive methods. While effective, they often fall short of reaching (near-)optimal solutions. In contrast, improvement-based methods iteratively explore the neighborhood of initial solutions and are more effective in approaching optimality. However, the flexible machine allocation in FJSP poses significant challenges to the application of this framework, including accurate state representation, effective policy learning, and efficient search strategies. To address these challenges, this paper proposes a Memory-enhanced Improvement Search framework with heterogeneous graph representation--MIStar. It employs a novel heterogeneous disjunctive graph that explicitly models the operation sequences on machines to accurately represent scheduling solutions. Moreover, a memoryenhanced heterogeneous graph neural network (MHGNN) is designed for feature extraction, leveraging historical trajectories to enhance the decision-making capability of the policy network. Finally, a parallel greedy search strategy is adopted to explore the solution space, enabling superior solutions with fewer iterations. Extensive experiments on synthetic data and public benchmarks demonstrate that MIStar significantly outperforms both traditional handcrafted improvement heuristics and state-of-the-art DRL-based constructive methods.
Paper Structure (38 sections, 2 theorems, 11 equations, 8 figures, 7 tables, 1 algorithm)

This paper contains 38 sections, 2 theorems, 11 equations, 8 figures, 7 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related work
  3. Preliminaries
  4. Flexible job shop scheduling problem.
  5. Disjunctive graph.
  6. The Nopt2 neighbourhood Structure.
  7. Methodology
  8. MDP Formulation
  9. Directed Heterogeneous Graph
  10. Memory-enhanced Heterogeneous Graph Neural Network
  11. Operation Node Embedding
  12. Machine Node Embedding
  13. Historical Action Embedding
  14. Decision Making
  15. Training Algorithm
  16. ...and 23 more sections

Key Result

Theorem 1

The Rearrangement Inequality states that, for two sequences $a_1 \leq a_2 \leq \cdots \leq a_n$ and $b_1 \leq b_2 \leq \cdots \leq b_n$, the inequalities hold, where $\pi(1), \pi(2), \ldots, \pi(n)$ is any permutation of $1, 2, \ldots, n$.

Figures (8)

  • Figure 1: Graph representations of FJSP. (a) FJSP instance in a disjunctive graph; (b) feasible solution in a disjunctive graph; (c) feasible solution in our graph.
  • Figure 2: Nopt2 neighborhood structure.
  • Figure 3: The architecture of MIStar.
  • Figure 4: The network architecture of the memory-enhanced heterogeneou GNN.
  • Figure 5: Infeasible exchange caused by the N5 neighborhood in FJSP. Dotted lines of different colors are critical blocks.
  • ...and 3 more figures

Theorems & Definitions (3)

  • Theorem 1
  • Theorem 2
  • proof