Search Results (104)

Aiming at the inherent limitations of the basic White Shark Optimizer (WSO), such as insufficient population diversity, unbalanced global and local search mechanisms, and weak convergence in the later stage, this paper proposes an Improved White Shark Optimizer (IWSO). The algorithm is improved from the following three aspects: Firstly, the Tent chaotic map is introduced to replace the traditional random initialization in the population initialization stage. Secondly, an adaptive nonlinear convergence factor and a dynamic inertia weight adjustment strategy are designed to focus on the fine search in the neighborhood of the optimal solution. Thirdly, the Levy flight perturbation mechanism and the elite opposition-based learning strategy are integrated to expand the search range and further accelerate the convergence speed. To verify the effectiveness and superiority of the IWSO algorithm, the CEC2017 test suite is selected for simulation experiments, and the IWSO is systematically compared with seven other representative swarm intelligence algorithms. The experimental results show that the IWSO is significantly superior to all comparison algorithms in multiple evaluation indicators, including minimum makespan, average convergence value, standard deviation, and successful convergence rate, on scheduling instances of different scales and difficulties. The convergence curve remains leading throughout the iteration process and shows a smoother convergence trend. The multi-strategy enhanced white shark optimizer proposed in this paper effectively overcomes the inherent defects of the basic algorithm, significantly improves the solution accuracy and convergence efficiency of the job shop scheduling problem, and has high theoretical research value and practical engineering application prospects. In the future, the multi-strategy improved White Shark Optimizer will be extended to multi-objective job shop scheduling, dynamic disturbance job shop scheduling, and large-scale production scheduling scenarios with numerous workpieces and machines. 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

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

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

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

The Multi-Objective Flexible Job Shop Scheduling Problem (MOFJSSP) represents a core challenge in modern manufacturing: achieving synergistic optimization of multiple conflicting objectives while pursuing production efficiency and energy sustainability. To address this, this study proposes an enhanced hybrid heuristic algorithm—KNN–Tabu Search NSGA-II (KTNSGA-II)—for simultaneously optimizing completion time, machine load, and total energy consumption. First, a three-objective mathematical model is established. Subsequently, four key strategies are integrated: (1) workload balancing initialization rapidly generates high-quality initial solutions; (2) an adaptive job-level crossover mechanism dynamically adjusts subset sizes during iterations to balance global exploration and local exploitation; (3) K-nearest neighbor-based congestion distance calculation maintains population diversity; (4) tabu search applied to non-dominated solutions on the Pareto front for local refinement. Extensive experiments on standard benchmark instances demonstrate that KTNSGA-II significantly outperforms representative algorithms in terms of convergence and diversity. For large-scale Behnke benchmark instances, KTNSGA-II achieves an average hypervolume (HV) improvement of 32.32% compared to other comparison algorithms. Furthermore, this method substantially enhances solution diversity: the Spacing Performance (SP) metric improved by 39.72%, indicating more uniform distribution of Pareto optimal solutions; the Diversity Metric (DM) increased by 57.54%, reflecting broader coverage and more even distribution along the Pareto frontier boundary. These results confirm that KTNSGA-II generates higher-quality, better-distributed Pareto fronts, achieving a more optimal trade-off between completion time, machine load, and energy consumption. Full article

Distributed manufacturing introduces new challenges to traditional production shop scheduling, and the combination of machine learning and metaheuristic algorithms offers new approaches to solve these problems. To address the distributed hybrid flow shop scheduling problem with missing operations (MDHFSP), a shuffled frog leaping algorithm with Q-learning (QSFLA) is proposed to minimize the maximum completion time. A dual-string encoding method is proposed to represent factory assignment and job sequencing, with heuristic methods utilized during decoding to determine machine assignments. The state set is constructed based on changes in the minimum and average objective values of solutions in the population, while the action set is built from different optimized solutions and learned solutions during the memeplex search process. Symmetry-driven Q-learning is employed to dynamically adjust the optimization objects based on the state of the population. Testing on 140 benchmarks and a real-life example shows that symmetry-driven Q-learning plays a positive role within QSFLA, and QSFLA effectively solves the MDHFSP. Full article

To achieve “carbon peak and carbon neutrality” in manufacturing, this paper tackles high energy consumption in flexible job shop production by developing a low-carbon scheduling optimization model with time-of-use electricity pricing, incorporating a photovoltaic microgrid. The model minimizes makespan, carbon emissions, and costs, considering photovoltaic power uncertainty, energy storage dynamics, and time-of-use pricing. To address coupled scheduling and energy management challenges, a three-stage bilevel collaborative optimization framework is proposed, enhancing the Multi-Objective Particle Swarm Optimization (MOPSO) algorithm to develop a Collaborative MOPSO (CMOPSO). The improved algorithm features a four-layer encoding mechanism with energy factors, chaotic mapping for better global search, and adaptive mutation for population diversity. Validation using the Brandimarte benchmark demonstrates the algorithm’s robustness. Specifically, comparative experiments reveal that the proposed strategy significantly outperforms the traditional scheduling mode. While maintaining a similar makespan, the proposed method reduces production costs by 44.3% and carbon emissions by 29%. Simulations confirm that the method effectively shifts tasks to low-price periods and leverages photovoltaic energy during peak hours, supporting the manufacturing industry’s green transition. Full article

This paper addresses the limitations of genetic algorithms in solving the Flexible Job-Shop Scheduling Problem (FJSP) including slow convergence, susceptibility to local optima, and sensitivity to parameter settings. The paper proposes an Improved Genetic Algorithm based on Reinforcement Learning (IGARL). First, a hybrid population selection mechanism that combines the Queen Bee Mating Flight (QBMF) strategy with the Tournament Selection (TS) method is introduced. This mechanism significantly accelerates convergence by optimizing the population structure. Second, a dynamic population update strategy based on tunnel vision, termed the Solution Space Diversity Awakening (SSDA) strategy, is developed. When the population becomes trapped in local optima, this strategy intelligently triggers random perturbations and introduces high-potential individuals to enhance the algorithm’s ability to escape local optima and promote population diversity. Third, a novel multi-Q-table reinforcement learning framework is embedded within the iterative process to dynamically adjust key genetic algorithm parameters (such as selection, mutation, and crossover rates) and enable multi-dimensional performance evaluation, thereby effectively guiding the search toward better solutions. Experimental results demonstrate that the IGARL algorithm achieves a 10% to 60% improvement in convergence speed on Brandimarte benchmark instances, with solution quality significantly surpassing that of the basic genetic algorithm. Moreover, the fluctuation of the average optimal solution remains within 20%, indicating strong stability and robustness. Full article

With the development of manufacturing industry, traditional fixed process processing methods cannot adapt to the changes in workshop operations and the demand for small batches and multiple orders. Therefore, it is necessary to introduce multiple robots to provide a more flexible production mode. Currently, some Job Shop Scheduling Problems with Transportation (JSP-T) only consider job scheduling and vehicle task allocation, and does not focus on the problem of collision free paths between vehicles. This article proposes a novel solution framework that integrates workshop scheduling, material handling robot task allocation, and conflict free path planning between robots. With the goal of minimizing the maximum completion time (Makespan) that includes handling, this paper first establishes an extended JSP-T problem model that integrates handling time and robot paths, and provides the corresponding workshop layout map. Secondly, in the scheduling layer, an improved Deep Q-Network (DQN) method is used for dynamic scheduling to generate a feasible and optimal machining scheduling scheme. Subsequently, considering the robot’s position information, the task sequence is assigned to the robot path execution layer. Finally, at the path execution layer, the Priority Based Search (PBS) algorithm is applied to solve conflict free paths for the handling robot. The optimized solution for obtaining the maximum completion time of all jobs under the condition of conflict free path handling. The experimental results show that compared with algorithms such as PPO, the scheduling algorithm proposed in this paper has improved performance by 9.7% in Makespan, and the PBS algorithm can obtain optimized paths for multiple handling robots under conflict free conditions. The framework can handle scheduling, task allocation, and conflict-free path planning in a unified optimization process, which can adapt well to job changes and then flexible manufacturing. Full article

The opto-mechanical automated manufacturing process, characterized by stringent process constraints, dynamic disturbances, and conflicting optimization objectives, presents significant control challenges for traditional scheduling and control approaches. We formulate the scheduling problem within a closed-loop control paradigm and propose a novel bi-level intelligent control framework integrating Deep Reinforcement Learning (DRL) and Bayesian Optimization (BO). The core of our approach is a bi-level intelligent control framework. An inner DRL agent acts as an adaptive controller, generating control actions (scheduling decisions) by perceiving the system state and learning a near-optimal policy through a carefully designed reward function, while an outer BO loop automatically tunes the DRL’s hyperparameters and reward weights for superior performance. This synergistic BO-DRL mechanism facilitates intelligent and adaptive decision-making. The proposed method is extensively evaluated against standard meta-heuristics, including Genetic Algorithm (GA) and Particle Swarm Optimization (PSO), on a complex 20-jobs × 20-machines flexible job shop scheduling benchmark specific to opto-mechanical automated manufacturing. The experimental results demonstrate that our BO-DRL algorithm significantly outperforms these benchmarks, achieving reductions in makespan of 13.37% and 25.51% compared to GA and PSO, respectively, alongside higher machine utilization and better on-time delivery. Furthermore, the algorithm exhibits enhanced convergence speed, superior robustness under dynamic disruptions (e.g., machine failures, urgent orders), and excellent scalability to larger problem instances. This study confirms that integrating DRL’s perceptual decision-making capability with BO’s efficient parameter optimization yields a powerful and effective solution for intelligent scheduling in high-precision manufacturing environments. Full article