The classical Job Shop Scheduling Problem (JSSP) focuses on optimizing makespan under deterministic constraints. Real-world production environments introduce additional complexities that cause traditional scheduling approaches to be less effective. Reinforcement learning (RL) holds potential in addressing these challenges, as it allows agents to learn adaptive scheduling strategies. However, there is a lack of a comprehensive, general-purpose frameworks for effectively training and evaluating RL agents under real-world constraints. To address this gap, we propose a modular framework that extends classical JSSP formulations by incorporating key real-world constraints inherent to the shopfloor, including transport logistics, buffer management, machine breakdowns, setup times, and stochastic processing conditions, while also supporting multi-objective optimization. The framework is a customizable solution that offers flexibility in defining problem instances and configuring simulation parameters, enabling adaptation to diverse production scenarios. A standardized interface ensures compatibility with various RL approaches, providing a robust environment for training RL agents and facilitating the standardized comparison of different scheduling methods under dynamic and uncertain conditions. We release JobShopLab as an open-source tool for both research and industrial applications, accessible at: https://github.com/proto-lab-ro/jobshoplab
The job shop scheduling problem is an NP-hard combinatorial optimization problem relevant to manufacturing and timetabling. Traditional approaches use priority dispatching rules based on simple heuristics. Recent work has attempted to replace these with deep learning models, particularly graph neural networks (GNNs), that learn to assign priorities from data. However, training such models requires customizing numerous factors: graph representation, node features, action space, and reward functions. The lack of modular libraries for experimentation makes this research time-consuming. This work introduces JobShopLib, a modular library that allows customizing these factors and creating new components with its reinforcement learning environment. We trained several dispatchers through imitation learning to demonstrate the environment's utility. One model outperformed various graph-based dispatchers using only individual operation features, highlighting the importance of feature customization. Our GNN model achieved near state-of-the-art results on large-scale problems. These results suggest significant room for improvement in developing such models. JobShopLib provides the necessary tools for future experimentation.
Multi-objective optimization is fundamental in complex decision-making tasks. Traditional algorithms, while effective, often demand extensive problem-specific modeling and struggle to adapt to nonlinear structures. Recent advances in Large Language Models (LLMs) offer enhanced explainability, adaptability, and reasoning. This work proposes Reflective Evolution of Multi-objective Heuristics (REMoH), a novel framework integrating NSGA-II with LLM-based heuristic generation. A key innovation is a reflection mechanism that uses clustering and search-space reflection to guide the creation of diverse, high-quality heuristics, improving convergence and maintaining solution diversity. The approach is evaluated on the Flexible Job Shop Scheduling Problem (FJSSP) in-depth benchmarking against state-of-the-art methods using three instance datasets: Dauzere, Barnes, and Brandimarte. Results demonstrate that REMoH achieves competitive results compared to state-of-the-art approaches with reduced modeling effort and enhanced adaptability. These findings underscore the potential of LLMs to augment traditional optimization, offering greater flexibility, interpretability, and robustness in multi-objective scenarios.
Large language models (LLMs) excel at rapid generation of text and multimodal content, yet they falter on transaction-style planning that demands ACID-like guarantees and real-time disruption recovery. We present Adaptive LLM Agent System (ALAS), a framework that tackles four fundamental LLM deficits: (i) absence of self-verification, (ii) context erosion, (iii) next-token myopia, and (iv) lack of persistent state. ALAS decomposes each plan into role-specialized agents, equips them with automatic state tracking, and coordinates them through a lightweight protocol. When disruptions arise, agents apply history-aware local compensation, avoiding costly global replanning and containing cascade effects. On real-world, large-scale job-shop scheduling benchmarks, ALAS sets new best results for static sequential planning and excels in dynamic reactive scenarios with unexpected disruptions. These gains show that principled modularization plus targeted compensation can unlock scalable and resilient planning with LLMs.
The Flexible Job-Shop Scheduling Problem (FJSSP) is an NP-hard combinatorial optimization problem, with several application domains, especially for manufacturing purposes. The objective is to efficiently schedule multiple operations on dissimilar machines. These operations are gathered into jobs, and operations pertaining to the same job need to be scheduled sequentially. Different methods have been previously tested to solve this problem, such as Constraint Solving, Tabu Search, Genetic Algorithms, or Monte Carlo Tree Search (MCTS). We propose a novel algorithm derived from the Generalized Nested Rollout Policy Adaptation, developed to solve the FJSSP. We report encouraging experimental results, as our algorithm performs better than other MCTS-based approaches, even if makespans obtained on large instances are still far from known upper bounds.
Recently, deep reinforcement learning has emerged as a promising approach for solving complex combinatorial optimization problems. Broadly, deep reinforcement learning methods fall into two categories: policy-based and value-based. While value-based approaches have achieved notable success in domains such as the Arcade Learning Environment, the combinatorial optimization community has predominantly favored policy-based methods, often overlooking the potential of value-based algorithms. In this work, we conduct a comprehensive empirical evaluation of value-based algorithms, including the deep q-network and several of its advanced extensions, within the context of two complex combinatorial problems: the job-shop and the flexible job-shop scheduling problems, two fundamental challenges with multiple industrial applications. Our results challenge the assumption that policy-based methods are inherently superior for combinatorial optimization. We show that several value-based approaches can match or even outperform the widely adopted proximal policy optimization algorithm, suggesting that value-based strategies deserve greater attention from the combinatorial optimization community. Our code is openly available at: https://github.com/AJ-Correa/Unraveling-the-Rainbow.
As the continuous deepening of low-carbon emission reduction policies, the manufacturing industries urgently need sensible energy-saving scheduling schemes to achieve the balance between improving production efficiency and reducing energy consumption. In energy-saving scheduling, reasonable machine states-switching is a key point to achieve expected goals, i.e., whether the machines need to switch speed between different operations, and whether the machines need to add extra setup time between different jobs. Regarding this matter, this work proposes a novel machine multi states-based energy saving flexible job scheduling problem (EFJSP-M), which simultaneously takes into account machine multi speeds and setup time. To address the proposed EFJSP-M, a kind of discrete differential evolution particle swarm optimization algorithm (D-DEPSO) is designed. In specific, D-DEPSO includes a hybrid initialization strategy to improve the initial population performance, an updating mechanism embedded with differential evolution operators to enhance population diversity, and a critical path variable neighborhood search strategy to expand the solution space. At last, based on datasets DPs and MKs, the experiment results compared with five state-of-the-art algorithms demonstrate the feasible of EFJSP-M and the superior of D-DEPSO.
Neural Combinatorial Optimization (NCO) has emerged as a promising approach for NP-hard problems. However, prevailing RL-based methods suffer from low sample efficiency due to sparse rewards and underused solutions. We propose Preference Optimization for Combinatorial Optimization (POCO), a training paradigm that leverages solution preferences via objective values. It introduces: (1) an efficient preference pair construction for better explore and exploit solutions, and (2) a novel loss function that adaptively scales gradients via objective differences, removing reliance on reward models or reference policies. Experiments on Job-Shop Scheduling (JSP), Traveling Salesman (TSP), and Flexible Job-Shop Scheduling (FJSP) show POCO outperforms state-of-the-art neural methods, reducing optimality gaps impressively with efficient inference. POCO is architecture-agnostic, enabling seamless integration with existing NCO models, and establishes preference optimization as a principled framework for combinatorial optimization.
Large Language Models (LLMs) have shown remarkable capabilities across various domains, but their potential for solving combinatorial optimization problems remains largely unexplored. In this paper, we investigate the applicability of LLMs to the Job Shop Scheduling Problem (JSSP), a classic challenge in combinatorial optimization that requires efficient job allocation to machines to minimize makespan. To this end, we introduce Starjob, the first supervised dataset for JSSP, comprising 130k instances specifically designed for training LLMs. Leveraging this dataset, we fine-tune the LLaMA 8B 4-bit quantized model with the LoRA method to develop an end-to-end scheduling approach. Our evaluation on standard benchmarks demonstrates that the proposed LLM-based method not only surpasses traditional Priority Dispatching Rules (PDRs) but also achieves notable improvements over state-of-the-art neural approaches like L2D, with an average improvement of 15.36% on DMU and 7.85% on Taillard benchmarks. These results highlight the untapped potential of LLMs in tackling combinatorial optimization problems, paving the way for future advancements in this area.
Long-horizon combinatorial optimization problems (COPs), such as the Flexible Job-Shop Scheduling Problem (FJSP), often involve complex, interdependent decisions over extended time frames, posing significant challenges for existing solvers. While Rolling Horizon Optimization (RHO) addresses this by decomposing problems into overlapping shorter-horizon subproblems, such overlap often involves redundant computations. In this paper, we present L-RHO, the first learning-guided RHO framework for COPs. L-RHO employs a neural network to intelligently fix variables that in hindsight did not need to be re-optimized, resulting in smaller and thus easier-to-solve subproblems. For FJSP, this means identifying operations with unchanged machine assignments between consecutive subproblems. Applied to FJSP, L-RHO accelerates RHO by up to 54% while significantly improving solution quality, outperforming other heuristic and learning-based baselines. We also provide in-depth discussions and verify the desirable adaptability and generalization of L-RHO across numerous FJSP variates, distributions, online scenarios and benchmark instances. Moreover, we provide a theoretical analysis to elucidate the conditions under which learning is beneficial.
Combinatorial optimization problems, such as scheduling and route planning, are crucial in various industries but are computationally intractable due to their NP-hard nature. Neural Combinatorial Optimization methods leverage machine learning to address these challenges but often depend on sequential decision-making, which is prone to error accumulation as small mistakes propagate throughout the process. Inspired by self-evaluation techniques in Large Language Models, we propose a novel framework that generates and evaluates subsets of assignments, moving beyond traditional stepwise approaches. Applied to the Job-Shop Scheduling Problem, our method integrates a heterogeneous graph neural network with a Transformer to build a policy model and a self-evaluation function. Experimental validation on challenging, well-known benchmarks demonstrates the effectiveness of our approach, surpassing state-of-the-art methods.
The Job Shop Scheduling Problem (JSSP) is a well-known optimization problem in manufacturing, where the goal is to determine the optimal sequence of jobs across different machines to minimize a given objective. In this work, we focus on minimising the weighted sum of job completion times. We explore the potential of Monte Carlo Tree Search (MCTS), a heuristic-based reinforcement learning technique, to solve large-scale JSSPs, especially those with recirculation. We propose several Markov Decision Process (MDP) formulations to model the JSSP for the MCTS algorithm. In addition, we introduce a new synthetic benchmark derived from real manufacturing data, which captures the complexity of large, non-rectangular instances often encountered in practice. Our experimental results show that MCTS effectively produces good-quality solutions for large-scale JSSP instances, outperforming our constraint programming approach.
In Production Scheduling, the Flexible Job Shop Scheduling Problem (FJSSP) aims to optimize a sequence of operations and assign each to an eligible machine with varying processing times. For integration of the workforce, each machine also requires a worker to be present to process an operation which additionally affects the processing times. The resulting problem is called Flexible Job Shop Scheduling Problem with Worker Flexibility (FJSSP-W). The FJSSP has been approached with various problem representations, including Mixed Integer Linear Programming (MILP), Constrained Programming (CP), and Simulation-based Optimization (SBO). In the latter area in particular, there exists a large number of specialized Evolutionary Algorithms (EA) like Particle Swarm Optimization (PSO) or Genetic Algorithms (GA). Yet, the solvers are often developed for single use cases only, and validated on a few selected test instances, let alone compared with results from solvers using other problem representations. While suitable approaches do also exist, the design of the FJSSP-W instances is not standardized and the algorithms are hardly comparable. This calls for a systematic benchmarking environment that provides a comprehensive set of FJSSP(-W) instances and supports targeted algorithm development. It will facilitate the comparison of algorithmic performance in the face of different problem characteristics. The present paper presents a collection of 402 commonly accepted FJSSP instances and proposes an approach to extend these with worker flexibility. In addition, we present a detailed procedure for the evaluation of scheduling algorithms on these problem sets and provide suitable model representations for this purpose. We provide complexity characteristics for all presented instances as well as baseline results of common commercial solvers to facilitate the validation of new algorithmic developments.
Neural combinatorial optimization (NCO) has gained significant attention due to the potential of deep learning to efficiently solve combinatorial optimization problems. NCO has been widely applied to job shop scheduling problems (JSPs) with the current focus predominantly on deterministic problems. In this paper, we propose a novel attention-based scenario processing module (SPM) to extend NCO methods for solving stochastic JSPs. Our approach explicitly incorporates stochastic information by an attention mechanism that captures the embedding of sampled scenarios (i.e., an approximation of stochasticity). Fed with the embedding, the base neural network is intervened by the attended scenarios, which accordingly learns an effective policy under stochasticity. We also propose a training paradigm that works harmoniously with either the expected makespan or Value-at-Risk objective. Results demonstrate that our approach outperforms existing learning and non-learning methods for the flexible JSP problem with stochastic processing times on a variety of instances. In addition, our approach holds significant generalizability to varied numbers of scenarios and disparate distributions.
The rise of Industry 5.0 has introduced new demands for manufacturing companies, requiring a shift in how production schedules are managed to address human centered, environmental, and economic goals comprehensively. The flexible job shop scheduling problem (FJSSP), which involves processing operations on various capable machines, accurately reflects the complexities of modern manufacturing settings. This paper investigates the FJSSP involving reconfigurable machine tools with configuration dependent setup times, while integrating human aspects like worker assignments, moving time, and rest periods, as well as minimizing total energy consumption. A mixed-integer programming (MIP) model is developed to simultaneously optimize these objectives. The model determines the assignment of operations to machines, workers, and configurations while sequencing operations, scheduling worker movements, and respecting rest periods, and minimizing overall energy consumption. Given the NPhard nature of the FJSSP with worker assignments and reconfigurable tools, a memetic algorithm (MA) is proposed. This metaheuristic evolutionary algorithm features a three layer chromosome encoding method, specialized crossover and mutation strategies, and neighborhood search mechanisms to enhance solution quality and diversity. Comparisons of MA with MIP and genetic algorithms (GA) on benchmark instances demonstrate the MA efficiency and effectiveness, particularly for larger problem instances where MIP becomes impractical. This research paves the way for sustainable and resilient production schedules tailored for the factory of the future under the Industry 5.0 paradigm. The work bridges a crucial gap in current literature by integrating worker and environmental impact into the FJSSP with reconfigurable machine models.
Heuristic dispatching rules (HDRs) are widely regarded as effective methods for solving dynamic job shop scheduling problems (DJSSP) in real-world production environments. However, their performance is highly scenario-dependent, often requiring expert customization. To address this, genetic programming (GP) and gene expression programming (GEP) have been extensively used for automatic algorithm design. Nevertheless, these approaches often face challenges due to high randomness in the search process and limited generalization ability, hindering the application of trained dispatching rules to new scenarios or dynamic environments. Recently, the integration of large language models (LLMs) with evolutionary algorithms has opened new avenues for prompt engineering and automatic algorithm design. To enhance the capabilities of LLMs in automatic HDRs design, this paper proposes a novel population self-evolutionary (SeEvo) method, a general search framework inspired by the self-reflective design strategies of human experts. The SeEvo method accelerates the search process and enhances exploration capabilities. Experimental results show that the proposed SeEvo method outperforms GP, GEP, end-to-end deep reinforcement learning methods, and more than 10 common HDRs from the literature, particularly in unseen and dynamic scenarios.
Recent advances in deep learning have shown significant potential for solving combinatorial optimization problems in real-time. Unlike traditional methods, deep learning can generate high-quality solutions efficiently, which is crucial for applications like routing and scheduling. However, existing approaches like deep reinforcement learning (RL) and behavioral cloning have notable limitations, with deep RL suffering from slow learning and behavioral cloning relying solely on expert actions, which can lead to generalization issues and neglect of the optimization objective. This paper introduces a novel offline RL method designed for combinatorial optimization problems with complex constraints, where the state is represented as a heterogeneous graph and the action space is variable. Our approach encodes actions in edge attributes and balances expected rewards with the imitation of expert solutions. We demonstrate the effectiveness of this method on job-shop scheduling and flexible job-shop scheduling benchmarks, achieving superior performance compared to state-of-the-art techniques.
In a flexible job shop environment, using Automated Guided Vehicles (AGVs) to transport jobs and process materials is an important way to promote the intelligence of the workshop. Compared with single-load AGVs, multi-load AGVs can improve AGV utilization, reduce path conflicts, etc. Therefore, this study proposes a history-guided regional partitioning algorithm (HRPEO) for the flexible job shop scheduling problem with limited multi-load AGVs (FJSPMA). First, the encoding and decoding rules are designed according to the characteristics of multi-load AGVs, and then the initialization rule based on the branch and bound method is used to generate the initial population. Second, to prevent the algorithm from falling into a local optimum, the algorithm adopts a regional partitioning strategy. This strategy divides the solution space into multiple regions and measures the potential of the regions. After that, cluster the regions into multiple clusters in each iteration, and selects individuals for evolutionary search based on the set of clusters. Third, a local search strategy is designed to improve the exploitation ability of the algorithm, which uses a greedy approach to optimize machines selection and transportation sequence according to the characteristics of FJSPMA. Finally, a large number of experiments are carried out on the benchmarks to test the performance of the algorithm. Compared with multiple advanced algorithms, the results show that the HRPEO has a better advantage in solving FJSPMA.
This paper explores the potential application of Deep Reinforcement Learning in the furniture industry. To offer a broad product portfolio, most furniture manufacturers are organized as a job shop, which ultimately results in the Job Shop Scheduling Problem (JSSP). The JSSP is addressed with a focus on extending traditional models to better represent the complexities of real-world production environments. Existing approaches frequently fail to consider critical factors such as machine setup times or varying batch sizes. A concept for a model is proposed that provides a higher level of information detail to enhance scheduling accuracy and efficiency. The concept introduces the integration of DRL for production planning, particularly suited to batch production industries such as the furniture industry. The model extends traditional approaches to JSSPs by including job volumes, buffer management, transportation times, and machine setup times. This enables more precise forecasting and analysis of production flows and processes, accommodating the variability and complexity inherent in real-world manufacturing processes. The RL agent learns to optimize scheduling decisions. It operates within a discrete action space, making decisions based on detailed observations. A reward function guides the agent's decision-making process, thereby promoting efficient scheduling and meeting production deadlines. Two integration strategies for implementing the RL agent are discussed: episodic planning, which is suitable for low-automation environments, and continuous planning, which is ideal for highly automated plants. While episodic planning can be employed as a standalone solution, the continuous planning approach necessitates the integration of the agent with ERP and Manufacturing Execution Systems. This integration enables real-time adjustments to production schedules based on dynamic changes.
The Job Shop Scheduling Problem (JSSP) is a complex combinatorial optimization problem. While online Reinforcement Learning (RL) has shown promise by quickly finding acceptable solutions for JSSP, it faces key limitations: it requires extensive training interactions from scratch leading to sample inefficiency, cannot leverage existing high-quality solutions, and often yields suboptimal results compared to traditional methods like Constraint Programming (CP). We introduce Offline Reinforcement Learning for Learning to Dispatch (Offline-LD), which addresses these limitations by learning from previously generated solutions. Our approach is motivated by scenarios where historical scheduling data and expert solutions are available, although our current evaluation focuses on benchmark problems. Offline-LD adapts two CQL-based Q-learning methods (mQRDQN and discrete mSAC) for maskable action spaces, introduces a novel entropy bonus modification for discrete SAC, and exploits reward normalization through preprocessing. Our experiments demonstrate that Offline-LD outperforms online RL on both generated and benchmark instances. Notably, by introducing noise into the expert dataset, we achieve similar or better results than those obtained from the expert dataset, suggesting that a more diverse training set is preferable because it contains counterfactual information.