Search Results (188)

Market competition is increasingly intense and sustainable development has attracted widespread attention. The flexible job shop scheduling problem requires the collaborative optimization of production efficiency and machine energy consumption. This scheduling problem has high solution complexity. It is difficult to balance multiple conflicting objectives and obtain stable scheduling results with traditional optimization methods. A Dual-Layer Proximal Policy Optimization algorithm (DL-PPO) based on a hierarchical decision-making mechanism is proposed to achieve the collaborative optimization of production efficiency and energy consumption in solving the Energy-Aware Flexible Job Shop Scheduling Problem (EA-FJSP). First, a hierarchical scheduling framework based on DL-PPO is designed to solve the EA-FJSP. In this framework, the high-level controller selects sub-objectives from a global optimization perspective, while the low-level controller executes feasible dispatching rules according to the selected sub-objectives. Twelve key state features extracted from four dimensions, time, energy consumption, job, and machine, are used to construct a multi-dimensional state space. These features enable a comprehensive state representation of the scheduling environment and provide accurate input for the DL-PPO. The global optimization objective is decomposed into four sub-objectives employing a goal decoupling policy. Four dedicated reward functions are designed for the sub-objectives to guide the low-level controller to make optimal decisions in terms of time and energy consumption, thereby achieving multi-objective collaborative optimization. Considering the two decisions of job selection and machine assignment in solving the EA-FJSP, twenty dual-decision-point dispatching rules are designed as the action space for the low-level controller to achieve the global optimization objective. Finally, the effectiveness, applicability, and superiority of the DL-PPO in EA-FJSP are demonstrated through comparisons with dispatching rules and other deep reinforcement learning methods. Full article

Against the backdrop of mass customization, research interest in hybrid flow shop scheduling for standard and customized part production has been on the rise. However, most extant studies focus on single-shop scheduling optimization, and the inter-shop coordination mechanism for heterogeneous multi-shop systems remains underexplored. This paper investigates a heterogeneous hybrid flow shop scheduling problem featuring a distributed flow shop for standardized parts and a flexible job shop for customized parts, with the dual objectives of minimizing makespan and total cost. For this problem with the core complexity of heterogeneous cross-shop production reliance and conflicting dual-objective optimization, we propose a multi-objective grey wolf optimizer (MOGWO) combined with problem-specific local search strategies. Computational experiments on a set of test instances are carried out to evaluate the MOGWO’s performance, which is further compared with four classic multi-objective evolutionary algorithms of analogous algorithmic frameworks. Experimental results confirm that the proposed algorithm achieves superior solution quality and convergence efficiency for the multi-objective heterogeneous hybrid flow shop scheduling problem under study. Full article

The flexible job shop scheduling problem (FJSP) is a typical combinatorial optimization problem in smart manufacturing. Although existing methods have considered machine competition relationships, they lack explicit structured modeling of machine competition relationships induced by candidate operations and are not systematically integrated across state representation, representation learning, and decision-making processes. To address this, this paper proposes a competition-aware dual-attention deep reinforcement learning method. We construct a dynamic heterogeneous graph representation, where machine competition is modeled as state-dependent edges instantiated via a 3D competition tensor, transforming machine competition relationships into structured information, thereby enhancing the model’s ability to characterize complex resource competition patterns. On this basis, we have designed the Competition-Aware Dual-Attention Network (CADAN), which injects competition information into both the attention computation and representation learning processes via a dual-path mechanism, enabling more expressive modeling of machine competition relationships, and which introduces a head-wise competition bias to capture heterogeneous competition patterns. Furthermore, we have developed an adaptive decision head to refine the scores of candidate actions. Our experimental results demonstrate that the proposed method outperforms classical dispatching rules and achieves competitive or superior performance compared with representative evolutionary and learning-based methods on synthetic datasets, public benchmark datasets, and a real-world industrial machining scenario involving mechanical transmission components. Full article

To achieve an optimal trade-off between production efficiency and energy benefits in complex manufacturing environments, this paper addresses the Green Flexible Job Shop Scheduling Problem (GFJSP) by establishing a multi-objective mathematical model that minimizes both makespan and total energy consumption. An Improved Non-dominated Sorting Genetic Algorithm II (INSGA-II) is proposed to solve this model. In the population initialization phase, chaotic mapping is integrated with multiple heuristic rules to generate a high-quality and uniformly distributed initial population. Furthermore, an enhanced elite selection mechanism is employed to effectively prevent premature convergence. Subsequently, adaptive crossover and mutation operators are designed to enable differentiated evolution across sub-populations, effectively coordinating global exploration and local exploitation. Finally, experimental results on the Brandimarte and Hurink benchmark datasets demonstrate the superiority of the proposed algorithm in terms of convergence and diversity, providing a robust solution for optimizing green industrial production scheduling. Full article

This paper addresses the flexible job-shop scheduling problem (FJSP) as a constrained combinatorial optimization task with a large discrete action space. Although action-masked reinforcement learning has shown promise for such problems, the effect of structured vector-state encoding in scheduling has received less attention. The main contribution of this work is a structured block-wise state representation and a multi-branch feature extraction module for action-masked Proximal Policy Optimization (PPO). The proposed representation decomposes the scheduling state into three heterogeneous components capturing resource availability, operation readiness, and temporal attributes of operation–machine alternatives. Instead of flattening these signals into a single vector, the proposed encoder processes each block separately before aggregation, with the aim of preserving semantic structure during policy learning. To isolate the effect of representation design, we compare the proposed multi-branch encoder with a baseline single-branch multilayer perceptron under identical PPO hyperparameters and training conditions. Experiments on the Brandimarte MK benchmark suite show that the proposed architecture yields a lower best-achieved makespan on nine of ten instances and improves the best baseline result by up to 27.84%. Additional validation on selected Behnke and Geiger instances indicates that the BR encoder’s advantage extends to larger FJSP cases while preserving sub-second inference. Full article

Robot swarm manufacturing is a promising direction in smart manufacturing that aggregates multiple robots to collaboratively complete production jobs; however, achieving conflict-free scheduling remains a significant challenge. Traditional methods struggle to address this issue since robot swarms are inherently prone to conflicts. This article puts forward a non-sorted metaheuristic method to solve it. First, the conflict-free robot swarm manufacturing problem—integrating a multi-objective optimization problem (MOP), a flexible job-shop scheduling problem (FJSP) for job processing, and a flow-shop scheduling problem (FSP) for robot travel—is formulated as a multi-objective job-flow-shop scheduling problem (MJFSP). The robot swarm must accomplish all manufacturing jobs while achieving high manufacturing performance, energy efficiency, and conflict-free operations. Second, a non-sorted metaheuristic algorithm based on an artificial plant community (APC) is proposed. It employs a sequential-pairwise single-elimination tournament system (SSTS) to select elites with a time complexity of $O\left(n\right)$, which scales linearly with the population size $\left(n\right)$. This surpasses the sorting-based elite selection with polynomial time complexity employed in most metaheuristic methods, such as the $O(n^2)$ of the non-dominated sorting genetic algorithm-III (NSGA-III). Third, an MJFSP benchmark dataset is built, and the experimental results uncover the complex dependencies between the FJSP for job processing and the FSP for robot traveling. The proposed method improves the makespan by up to 13.10% and reduces non-loaded energy consumption by up to 13.49%, achieving zero collision time and an average solution time 11.18% faster than NSGA-III. Full article

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

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