Search Results (347)

Sustainable manufacturing requires schedules that balance environmental responsibility with delivery reliability. This paper studies the Carbon-Aware Flexible Job Shop Scheduling Problem with Tardiness Penalty (CAFJSP-T), where total carbon emissions and total tardiness penalty are the primary objectives. We propose a Policy-based Rough Optimization with a Large Neighborhood Search (Pro-LNS) framework integrating Proximal Policy Optimization (PPO) and adaptive Large Neighborhood Search (LNS). PPO constructs a feasible schedule by selecting operation-machine assignments from job-readiness, machine-availability, earliest-completion, and critical-path features. This policy-generated schedule provides a structurally informed incumbent, enabling LNS to avoid unguided search and focus destroy-and-repair refinement on high-impact operations. Both phases use the same normalized scalarized carbon-tardiness objective, which guides PPO rewards and LNS removal, reinsertion, and acceptance while preserving precedence, eligibility, and capacity constraints. Experiments on small, medium, and large workcenter benchmarks show strong due-date performance and controlled carbon emissions. Under equal objective weighting, Pro-LNS achieves a median optimality gap of 6.12% relative to the exact formulation, with all instances within 14%, while requiring 4.08 s on average and at most 10.51 s. Comparisons with PPO-only, Advantage Actor-Critic (A2C), Soft Actor-Critic (SAC), and Genetic Algorithm (GA) schedulers show that Pro-LNS attains the best weighted scalarized objective across representative instance-weight settings. Friedman and Holm-corrected Wilcoxon tests confirm significant improvements over all competitors, with average weighted-objective gains of 4.90%, 7.25%, 8.81%, and 9.51% over PPO-only, A2C, SAC, and GA, respectively. These results demonstrate that Pro-LNS is an effective and computationally practical hybrid approach for carbon-aware, tardiness-sensitive flexible job shop scheduling. Full article

In recent years, with the advancement of production technology in the manufacturing industry, the scheduling problems that rely on modeling in real-world scenarios have gradually evolved into complex process flows. Aiming at the limited problem modeling capabilities of existing scheduling problems, this study proposes Multi-Stage Flexible Job Shop Scheduling Problem (MS-FJSP). MS-FJSP alters the fixed operation processing sequence of jobs in conventional scheduling problems and introduces staged processing to incorporate flexible constraints on operation selection. Furthermore, MS-FJSP modifies the constraint of unique machine compatibility, enabling arbitrary adjustments to machine combinations according to processing requirements. To address the complex flexibility and large-scale solution space of MS-FJSP, we propose a particle swarm optimization algorithm based on double neighborhood tabu search (TS-PSO). Specifically, the PSO algorithm determines a superior neighborhood structure for this problem, while the TS algorithm improves and optimizes the solution quality within the neighborhood of this solution structure. We verify the algorithm’s performance using a dataset consisting of 12,000 MS-FJSP instances and an MS-FJSP instance modeled from a real-world scheduling scenario. Experimental results demonstrate that TS-PSO can achieve excellent solution quality within a reasonable time, and MS-FJSP possesses efficient modeling capability for real-world scheduling scenarios. Full article

In this study, a special version of the Flexible Job Shop Scheduling Problem with equally and consistently batching constraints (hereafter called ECBFJSP) is considered, which involves multiple aspects of coordination, such as machine selection, process sorting, and batch splitting, which is highly complex and places strict demands on the optimization strategy. To effectively meet this challenge, this study constructs a dual-action deep reinforcement learning algorithm framework based on the Enhanced Heterogeneous Graph Neural Network (EHGNN). First, an enhanced heterogeneous graph and EHGNN model for the ECBFJSP is innovatively proposed. By integrating multi-dimensional node features such as work order priority, machine tool processing capability, and process constraints, dynamic feature aggregation of various types of information is achieved with the help of GATs and GRUs. The model can output context-aware representations containing global resource constraints, greatly improving the joint optimization efficiency of job scheduling and batch partitioning and significantly enhancing the adaptability of the dual-action decision framework to the complexity of the ECBFJSP. At the decision-making mechanism level, this study designed a dual-action decision space of process sequencing–machine selection action and batch partitioning action and used the DAPPO algorithm to collaboratively optimize the dual-action strategy to ensure the stability and efficiency of the decision-making process. The experimental data results show that compared with traditional algorithms, the proposed intelligent decision framework performs better in scheduling quality when solving the ECBFJSP, which fully verifies the significant effectiveness and practicality of the framework in solving the ECBFJSP. Full article

Multi-objective flexible job shop scheduling requires balancing conflicting objectives while supporting real-time decision-making in industrial environments. However, although traditional metaheuristics are effective for global search, their high computational cost limits their applicability in time-sensitive scenarios. To address this issue, this paper proposes dual-pool guided preference-conditioned graph reinforcement learning (DPG-GRL), an encoder–decoder framework for the multi-objective flexible job shop scheduling problem. In DPG-GRL, a graph attention network encoder extracts operation and machine-level representations from a heterogeneous graph, while the decoder is conditioned on a preference vector to generate scheduling solutions with different trade-offs using a single trained policy. To improve sample efficiency and training stability, a dual-pool guidance mechanism is introduced, in which an offline expert pool provides a stable behavioral prior for policy initialization and an online elite pool continuously replays high-quality trajectories to refine the policy. Experimental results show that DPG-GRL outperforms representative multi-objective evolutionary algorithms, including the non-dominated sorting genetic algorithm II (NSGA-II) and the multi-objective evolutionary algorithm based on decomposition (MOEA/D), on synthetic instances, with more pronounced advantages in solution quality and inference efficiency as the problem scale grows. In addition, evaluations on public benchmark instances using a model trained only on the small synthetic setting demonstrate rapid Pareto-front approximation, high-quality solution sets, and promising generalization to unseen instances. These results indicate the potential of DPG-GRL for real-time production scheduling and energy-aware manufacturing. Full article

Industry 4.0 is transforming the way companies manufacture, improve, and distribute products, moving toward fast, intelligent, and flexible manufacturing, which will bring about fundamental changes in enterprises’ production capabilities. The Flexible Job Shop Scheduling Problem (FJSP) allows a single job to be divided into multiple operations, each of which can be processed on multiple machines. Due to its high flexibility and complexity, traditional scheduling methods are difficult to meet the needs of dynamic production. Dispatching rules struggle to effectively perceive the global precedence relationships among jobs and the distribution of machine workloads; metaheuristic approaches suffer from slow iterative convergence; existing deep reinforcement learning methods often employ a single policy network to handle both operation sequencing and machine assignment in a coupled manner, which tends to cause training instability and slow convergence. This paper proposes a deep reinforcement learning model that integrates Multi-Proximal Policy Optimization (MPPO) and Dual Attention Network (DAN) to address the FJSP. The model uses the operation message attention block and machine message attention block of DAN to capture the dependency relationships between operations and the dynamic competitive relationships between machines, respectively, and extract deep features. At the same time, MPPO designs dual actor networks to handle operation sequencing and machine assignment decisions separately, and combines a centralized critic to optimize the policy. This balances exploration and exploitation and improves training stability. Experiments are conducted based on the SD1 and SD2 datasets. In FJSP instances of four scales, the model is compared with PPO-DAN, PPO-HGNN, traditional scheduling rules, and OR-Tools. The results show that the algorithm reduces makespan by up to 4.2% on SD1 and 10.1% on SD2. Moreover, it achieves better performance than traditional scheduling rules. Its comprehensive performance is superior to that of the comparison methods, verifying its effectiveness and practical application potential in solving the FJSP. Full article

Distributed hybrid flow-shop scheduling problems (DHFSPs) are widely encountered in manufacturing systems. Their complexity increases significantly when multiple overhead cranes are used for material handling. This paper investigates a distributed hybrid flow-shop scheduling problem with multiple overhead crane transportation (DHFSP-MCT), aiming to simultaneously minimize makespan and total energy consumption (including machining and transport). A hierarchical reinforcement learning-based bi-population collaborative metaheuristic algorithm (HRL-BCMA) is proposed. In HRL-BCMA, an iterated greedy strategy is first adopted to generate an initial population. Then, a two-level reinforcement learning framework is designed: a high-level agent decides when to release jobs to the shop floor, while a low-level agent based on a graph isomorphism network selects improvement operators. Furthermore, a bi-population co-evolutionary framework and a knowledge-informed strategy are introduced to enhance solution quality and diversity. Experimental evaluations on both randomly generated instances and a real-world-inspired aluminum manufacturing case show that HRL-BCMA reduces makespan by 8.6% and total energy consumption by 12.3% on average compared to the best existing algorithm (CBMA) while achieving superior Pareto front coverage. These results demonstrate the effectiveness of the proposed method for green scheduling problems with crane transport constraints. Full article

The flexible job shop scheduling problem (FJSP), which simultaneously involves machine assignment and operation sequencing under multiple constraints, is a typical NP-hard combinatorial optimization problem, and efficient scheduling is of great importance for improving production efficiency and manufacturing flexibility. To address this problem, the success-history beaver behavior optimizer (SHBBO) is introduced to solve FJSP with the objective of minimizing the makespan. First, considering the discrete characteristics of FJSP, an effective encoding and decoding scheme is designed to represent operation sequences and machine assignments. Then, the adaptive success-history mechanism of SHBBO is employed to dynamically adjust the search parameters during the optimization process, enabling a better balance between global exploration and local exploitation. Meanwhile, the behavioral update strategy of SHBBO is adapted to the scheduling environment so that candidate solutions can be effectively evolved in the discrete solution space. In addition, a population updating strategy and elite-guided search mechanism are incorporated to enhance solution quality and convergence performance. Finally, extensive experiments are conducted on benchmark FJSP instances to verify the effectiveness of the proposed method. Experimental results show that SHBBO achieves the best average results on 11 out of 12 CEC2022 benchmark functions, with particularly notable improvements over the original beaver behavior optimizer (BBO) on functions such as F6 (56.69%), F5 (12.20%), and F10 (9.18%). On the BRdata benchmark instances, SHBBO obtains the best or tied-best makespan on all 10 instances, with an average percentage relative deviation (PRD) of 0, and reduces the makespan by 7.69% on MK10 and 6.25% on MK06 compared with BBO. Full article

The Flexible Job Shop Scheduling Problem (FJSP) is central to smart manufacturing, yet standard algorithms often prioritize productivity (makespan) at the expense of cost and reliability. This paper introduces t-MOHHO, a collaborative optimization framework designed to equilibrate machine load, processing costs, and delivery timeliness alongside throughput. By incorporating an adaptive Student’s t-distribution mutation operator and a non-linear energy escape mechanism, t-MOHHO effectively navigates high-dimensional search spaces. Extensive validation on 10 MK benchmark instances reveals that t-MOHHO demonstrates significant advantages over classic HHO, MOPSO, and MOEA/D across most metrics. Notably, in comparison to the state-of-the-art NSGA-III, t-MOHHO executes a clear trade-off: it trades marginal makespan efficiency for substantial reductions in cost and tardiness. Specifically, on the large-scale MK10 instance, t-MOHHO reduces total tardiness by 56.2% and lowers processing costs by 3.4% compared to NSGA-III. These results demonstrate that t-MOHHO can strategically sacrifice maximum speed to secure superior punctuality and cost-efficiency, making it a robust decision-support tool for Just-in-Time (JIT) production environments. Full article

This paper investigates a tri-objective green flexible job shop rescheduling problem under urgent order insertion and multi-speed machining conditions, where makespan, total energy consumption, and total tool wear are jointly optimized. First, an event-driven freezing mechanism is introduced, in which completed and ongoing operations are fixed, while only the rescheduling window composed of waiting operations and urgent-order operations is re-optimized. On this basis, two rescheduling strategies, namely complete rescheduling and deferred rescheduling, are designed and compared. Second, to improve the solution capability in complex dynamic environments, an improved multi-objective evolutionary algorithm based on decomposition (IMOEA/D) with a three-layer encoding scheme is proposed. The algorithm incorporates hybrid initialization, tabu-guided crossover, simulated annealing mutation, and critical-path-based variable neighborhood search. Experimental results show that the proposed method performs well in energy consumption optimization and tool wear control, while effectively improving the diversity and distribution quality of the Pareto solution set. Further analysis indicates that deferred rescheduling generally outperforms complete rescheduling, while the original-orders-first and urgents-first strategies exhibit different strengths in convergence, solution quality, and objective optimization. The proposed study provides an effective modeling and optimization framework for multi-objective green rescheduling problems and offers theoretical support for production scheduling decisions that need to balance production efficiency, energy saving, and tool-related cost control in practical manufacturing systems. Full article

With the evolution from Industry 4.0 to 5.0, flexible assembly scheduling must simultaneously address production efficiency, environmental sustainability, and human factors, while remaining adaptive to real-time disruptions. This study investigates the dynamic green scheduling problem in dual-resource Flexible Assembly Job Shops with worker learning and forgetting, aiming to minimize makespan and total energy consumption. To tackle this problem, a Hierarchical Dual-Agent Deep Reinforcement Learning algorithm (HAD-DRL) is proposed. The framework integrates a Heterogeneous Graph Neural Network to extract real-time workshop states and employs two collaborative agents, i.e., a high-level preference decision agent and a low-level scheduling execution agent. The upper agent dynamically adjusts the preference weights between economic and environmental objectives, while the lower agent generates corresponding scheduling actions. Unlike existing multi-agent methods that optimize a single objective at each step, HAD-DRL achieves adaptive coordination and balanced trade-offs among conflicting goals. Experimental results demonstrate that the proposed method outperforms heuristic and baseline DRL approaches in both objectives, validating its effectiveness and practical applicability for intelligent and sustainable manufacturing. Full article

Symmetry plays a crucial role in balancing production efficiency and energy consumption within distributed manufacturing systems. This study leverages symmetric decision-making structures in resource allocation and maintenance scheduling to achieve an equilibrium between productivity and sustainability. To address the multi-factory collaboration requirements for large-scale orders, a distributed dual-resource flexible job shop scheduling model considering multiple speeds and preventive maintenance on energy consumption is constructed. It aims to minimize the maximum completion time and total machine energy consumption. An artificial bee colony algorithm with adaptive scout bees is proposed to solve the model. An improved decoding method is designed according to the model characteristics to enhance convergence speed. Neighborhood structures based on preventive maintenance and machine speeds are designed, and a dynamic neighborhood search strategy is proposed to improve the local search capability. Three food source generation methods are defined as actions, and Q-learning is employed to dynamically select actions, ensuring population diversity while improving population quality. Extensive experiments are conducted to validate the effectiveness of the improved strategies, and the superiority of the proposed algorithm is verified through performance comparisons with state-of-the-art algorithms. Full article

In the dynamic flexible job shop scheduling problem (DFJSP) where the environment changes irregularly, priority rules are used to calculate priorities for each job and machine, determining the processing order. To achieve efficient scheduling, it is necessary to select appropriate priority rules that match the problem’s characteristics whenever the environment changes. To address such problems, Genetic Programming (GP) has been proposed to derive mathematically expressed priority rules. Various GP-based methods exist, among which Population-based Fluctuation GP (PF-GP) is an efficient technique that reuses individuals adapted to problem characteristics. However, optimizing the DFJSP using PF-GP requires significant computational cost. Therefore, methods have been developed to adaptively change the population size for more efficient resource utilization. This paper modifies the adaptive population size change into a population growth method designed to balance scheduling performance and computational efficiency in the DFJSP. By applying this proposed method to various scheduling problems, this paper investigates its effectiveness. Furthermore, this paper compares population growth methods and demonstrates that the proposed method addresses conventional issues in existing population adjustment techniques, enabling the more efficient utilization of computational resources. Full article

Operations scheduling of mass customized products is vital in the modern make-to-order (MTO) supply chains. In these systems, order acceptance decisions should be coordinated with available capacity in different sections of the supply chain while considering their potential correlations and interactions. One of the fundamental challenges in optimization of these systems is the computation time of solving models with multiple coupling constraints between supply chain units. This paper addresses this issue by proposing a game-based framework that decomposes the related mixed integer programming mathematical model and it is coordinated and solved using integrated game-based Alternating Direction Method of Multipliers (ADMM). The proposed Stackelberg Leader-Follower game optimizes order acceptance decisions while considering the requirements in supply, production planning, maintenance, inventory, and distribution units. To validate the efficiency of the proposed framework, the model is tested with a simulated four-layer supply chain. The results of experiments proved that decompositions of the model to smaller subsections and solving it in a distributed manner not only optimizes supply chain participating units but also coordinate their movements to achieve the global optimal solution. The proposed framework offers managers a practical decision layer that preserve local autonomy of the supply chain units and reduce their data sharing and computation burdens and concerns. Full article

The Flexible Job-shop Scheduling Problem (FJSP), a pivotal NP-hard challenge in intelligent manufacturing, has been increasingly addressed by Deep Reinforcement Learning (DRL) methods. However, existing approaches face a dilemma: Proximal Policy Optimization (PPO) ensures stability but suffers from conservative exploration, while Soft Actor–Critic (SAC) enhances exploration but lacks stability in discrete scheduling spaces. To resolve this trade-off, this study proposes PPO-Graph Explorer, a novel framework that integrates a Graph Isomorphism Attention Network (GIAN) with an Entropy-Adjusted PPO (EAE-PPO). Unlike generic Graph Transformers, our GIAN employs a structure-aware hybrid design specifically tailored for FJSP’s disjunctive graph topology. EAE-PPO introduces a structured exploration curriculum that enables the agent to mimic aggressive search behaviors early in training without sacrificing on-policy stability. Extensive experiments on standard benchmarks (Brandimarte, Hurink, Dauzère–Pérès) demonstrate our method’s superiority. Compared to state-of-the-art DRL baselines, it achieves an average makespan gap reduction of 5.1 percentage points with zero statistical outliers. Qualitative analysis further reveals an 8.95% reduction in makespan on representative instances, accompanied by a significant increase in average machine utilization from 89.0% to 98.1%. Full article

Conventional research on flexible job shop scheduling (FJSP) often overlooks critical factors such as workpiece handling, machine preventive maintenance, and variable machining speeds, resulting in scheduling schemes with limited practicality and suboptimal performance. To tackle these issues, this study establishes a Flexible Job Shop Scheduling Problem with Workpiece Handling and Machine Preventive Maintenance (WHMPM-FJSP) model, aiming to minimize both makespan and total energy consumption. An Improved Multi-Objective Discrete Grey Wolf Optimization (IMOD-GWO) algorithm is proposed to solve this model. The algorithm incorporates three key innovations: (1) A tri-level encoding structure that integrates machine assignments, operation sequences, and machining speed selection, tailored to the problem’s characteristics. (2) Multiple effective population initialization strategies combined with novel individual update mechanisms. (3) Implementation of distributed computing methods to enhance search efficiency within limited timeframes. To verify the rationality and efficacy of the model and the algorithm, comparative experiments were conducted using benchmark instances of varying scales against existing multi-objective optimization algorithms. The experimental results show that in medium- to large-scale cases, IMOD-GWO outperforms other methods, demonstrating significant advantages and highlighting its enhanced global search capability in solving WHMPM-FJSP problems. The proposed model and algorithm effectively solve the scheduling problem in flexible workshops with integrated processing and maintenance, demonstrating strong performance and practicality. Full article