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.

我们提出了一种融合了约束编程和深度学习的方法来解决灵活作业车间调度问题，该方法通过使用约束编程生成的最优解来训练深度学习模型，以消除深度强化学习中广泛搜索的需求，并在解决过程中共同应用深度学习和约束编程来提高性能。

在深度学习方法中利用约束编程动态解决柔性车间调度问题

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

The Flexible Job-shop Scheduling Problem (FJSP) is an important combinatorial
optimization problem that arises in manufacturing and service settings. FJSP is
composed of two subproblems, an assignment problem that assigns tasks to
machines, and a scheduling problem that determines the starting times of tasks
on their chosen machines. Solving FJSP instances of realistic size and
composition is an ongoing challenge even under simplified, deterministic
assumptions. Motivated by the inevitable randomness and uncertainties in supply
chains, manufacturing, and service operations, this paper investigates the
potential of using a deep learning framework to generate fast and accurate
approximations for FJSP. In particular, this paper proposes a two-stage
learning framework 2SLFJSP that explicitly models the hierarchical nature of
FJSP decisions, uses a confidence-aware branching scheme to generate
appropriate instances for the scheduling stage from the assignment predictions
and leverages a novel symmetry-breaking formulation to improve learnability.
2SL-FJSP is evaluated on instances from the FJSP benchmark library. Results
show that 2SL-FJSP can generate high-quality solutions in milliseconds,
outperforming a state-of-the-art reinforcement learning approach recently
proposed in the literature, and other heuristics commonly used in practice.

本文提出了一个基于深度学习的两阶段学习框架 2SLFJSP 来解决制造和服务领域中非常重要的组合优化问题 —— 柔性作业车间调度问题（FJSP），该框架能够在毫秒级时间内生成高质量的解决方案，优于文献中最新的强化学习方法和其他常用的启发式方法。