Priority dispatching rule (PDR) is widely used for solving real-world Job-shop scheduling problem (JSSP). However, the design of effective PDRs is a tedious task, requiring a myriad of specialized knowledge and often delivering limited performance. In this paper, we propose to automatically learn PDRs via an end-to-end deep reinforcement learning agent. We exploit the disjunctive graph representation of JSSP, and propose a Graph Neural Network based scheme to embed the states encountered during solving. The resulting policy network is size-agnostic, effectively enabling generalization on large-scale instances. Experiments show that the agent can learn high-quality PDRs from scratch with elementary raw features, and demonstrates strong performance against the best existing PDRs. The learned policies also perform well on much larger instances that are unseen in training.

In the paper, we adopt the Proximal Policy Optimization (PPO) algorithm [36] to train our agent. Here we provide details of our algorithm in terms of pseudo code, as shown in Algorithm 1. Similar In this section, we show how the baseline PDRs compute the priority index for the operations. Here we present the complete results on Taillard's benchmark. In Table S.1, we report the results of In Table S.2, we report the generalization performance of our polices trained on The "UB" column is the best solution from The "UB" column is the best solution from Similar conclusion can be drawn from results on DMU benchmark. In Table S.3, we report results In Table S.4 which focuses on The "UB" column is the best solution from The "UB" column is the best solution from We show training curves for all problems in Figure.1.

Dynamic job shop scheduling, a fundamental combinatorial optimisation problem in various industrial sectors, poses substantial challenges for effective scheduling due to frequent disruptions caused by the arrival of new jobs. State-of-the-art methods employ machine learning to learn scheduling policies offline, enabling rapid responses to dynamic events. However, these offline policies are often imperfect, necessitating the use of planning techniques such as Monte Carlo Tree Search (MCTS) to improve performance at online decision time. The unpredictability of new job arrivals complicates online planning, as decisions based on incomplete problem information are vulnerable to disturbances. To address this issue, we propose the Dynamic Robust MCTS (DyRo-MCTS) approach, which integrates action robustness estimation into MCTS. DyRo-MCTS guides the production environment toward states that not only yield good scheduling outcomes but are also easily adaptable to future job arrivals. Extensive experiments show that DyRo-MCTS significantly improves the performance of offline-learned policies with negligible additional online planning time. Moreover, DyRo-MCTS consistently outperforms vanilla MCTS across various scheduling scenarios. Further analysis reveals that its ability to make robust scheduling decisions leads to long-term, sustainable performance gains under disturbances.

The Job Shop Scheduling (JSS) problem can be viewed as an integer optimization program with linear objective function and linear, disjunctive constraints. The Lagrangian-based deep learning model does not necessarily produce feasible schedules directly. The model presented below is used to construct solutions that are integral, and feasible to the original problem constraints. The experimental setting, as defined by the training and test data, simulates a situation in which some component of a manufacturing system'slows down', causing processing times to extend on The model training follows the selection of parameters presented in Table 3.Parameter V alue Parameter V alue Epochs 500 Batch Size 16 Learning rate [1 . Finally, Constraints (23) capture Kirchho ff's Current Law and Constraints (24) capture Ohm's Law.

Additional Feedback: Global comments: I think the authors did not use the proper NeurIPS LaTex template. Line numbers are missing, as well as footnotes. The global look and number of pages seem ok though. Figures 1, 2 and 3 are of poor quality, as they appear visually pixelated. I strongly suggest the authors to use images in vector graphics.

The reviewers all agree that the paper is above the acceptance threshold. There is novelty in how the paper applies learning to JSSP, and the results are promising. But as Reviewer 4 points out, the paper hasn't shown how the proposed approach trades off solution quality and running time, without which it is difficult to judge whether it is a significant advance over existing techniques. Adding such results will strengthen the paper considerably.

Priority dispatching rule (PDR) is widely used for solving real-world Job-shop scheduling problem (JSSP). However, the design of effective PDRs is a tedious task, requiring a myriad of specialized knowledge and often delivering limited performance. In this paper, we propose to automatically learn PDRs via an end-to-end deep reinforcement learning agent. We exploit the disjunctive graph representation of JSSP, and propose a Graph Neural Network based scheme to embed the states encountered during solving. The resulting policy network is size-agnostic, effectively enabling generalization on large-scale instances.

Learned construction heuristics for scheduling problems have become increasingly competitive with established solvers and heuristics in recent years. In particular, significant improvements have been observed in solution approaches using deep reinforcement learning (DRL). While much attention has been paid to the design of network architectures and training algorithms to achieve state-of-the-art results, little research has investigated the optimal use of trained DRL agents during inference. Our work is based on the hypothesis that, similar to search algorithms, the utilization of trained DRL agents should be dependent on the acceptable computational budget. We propose a simple yet effective parameterization, called $\delta$-sampling that manipulates the trained action vector to bias agent behavior towards exploration or exploitation during solution construction. By following this approach, we can achieve a more comprehensive coverage of the search space while still generating an acceptable number of solutions. In addition, we propose an algorithm for obtaining the optimal parameterization for such a given number of solutions and any given trained agent. Experiments extending existing training protocols for job shop scheduling problems with our inference method validate our hypothesis and result in the expected improvements of the generated solutions.

We introduce an open-source GitHub repository containing comprehensive benchmarks for a wide range of machine scheduling problems, including Job Shop Scheduling (JSP), Flow Shop Scheduling (FSP), Flexible Job Shop Scheduling (FJSP), FJSP with Assembly constraints (FAJSP), FJSP with Sequence-Dependent Setup Times (FJSP-SDST), and the online FJSP (with online job arrivals). Our primary goal is to provide a centralized hub for researchers, practitioners, and enthusiasts interested in tackling machine scheduling challenges.

Job scheduling is a well-known Combinatorial Optimization problem with endless applications. Well planned schedules bring many benefits in the context of automated systems: among others, they limit production costs and waste. Nevertheless, the NP-hardness of this problem makes it essential to use heuristics whose design is difficult, requires specialized knowledge and often produces methods tailored to the specific task. This paper presents an original end-to-end Deep Reinforcement Learning approach to scheduling that automatically learns dispatching rules. Our technique is inspired by natural language encoder-decoder models for sequence processing and has never been used, to the best of our knowledge, for scheduling purposes. We applied and tested our method in particular to some benchmark instances of Job Shop Problem, but this technique is general enough to be potentially used to tackle other different optimal job scheduling tasks with minimal intervention. Results demonstrate that we outperform many classical approaches exploiting priority dispatching rules and show competitive results on state-of-the-art Deep Reinforcement Learning ones.