Dueto uncertainties in real-world production, dynamic factors have become increasingly critical in the research of distributed flexible job shop scheduling problems. Effectively responding to dynamic events can significantly enhance the adaptability and quality of scheduling solutions, thereby improving the resilience of manufacturing systems. This study addresses the dynamic distributed flexible job shop scheduling problem, which involves random job arrivals and machine breakdowns, and proposes an effective discrete improved gray wolf optimization (DIGWO) algorithm-based predictive–reactive method. The first contribution of our work lies in its dynamic scheduling strategy: a periodic- and event-driven approach is used to capture the dynamic nature of the problem, and a static scheduling window is constructed based on updated factory and workshop statuses to convert dynamic scheduling into static scheduling at each rescheduling point. Second, a mathematical model of multi-objective distributed flexible job shop scheduling (MODDFJSP) is established, optimizing makespan, tardiness, maximal factory load, and stability. The novelty of the model is that it is capable of optimizing both production efficiency and operational stability in the workshop. Third, by designing an efficacious initialization mechanism, prey search, and an external archive, the DIGWO algorithm is developed to solve conflicting objectives and search for a set of trade-off solutions. Experimental results in a simulated dynamic distributed flexible job shop demonstrate that DIGWO outperforms three well-known algorithms (NSGA-II, SPEA2, and MOEA/D). The proposed method also surpasses completely reactive scheduling approaches based on rule combinations. This study provides a reference for distributed manufacturing systems facing random job arrivals and machine breakdowns.

A novel multiobjective memetic algorithm based on decomposition (MOMAD) is proposed to solve multiobjective flexible job shop scheduling problem (MOFJSP), which simultaneously minimizes makespan, total workload, and critical workload. Firstly, a population is initialized by employing an integration of different machine assignment and operation sequencing strategies. Secondly, multiobjective memetic algorithm based on decomposition is presented by introducing a local search to MOEA/D. The Tchebycheff approach of MOEA/D converts the three‐objective optimization problem to several single‐objective optimization subproblems, and the weight vectors are grouped by K‐means clustering. Some good individuals corresponding to different weight vectors are selected by the tournament mechanism of a local search. In the experiments, the influence of three different aggregation functions is first studied. Moreover, the effect of the proposed local search is investigated. Finally, MOMAD is compared with eight state‐of‐the‐art algorithms on a series of well‐known benchmark instances and the experimental results show that the proposed algorithm outperforms or at least has comparative performance to the other algorithms.

Dynamic flexible job shop scheduling (DFJSS) is an important and complex combinatorial optimization problem. Heuristic methods have been extensively studied and proven to be effective in solving the job shop scheduling problems, but they still suffer from difficulties in real-time scheduling when dealing with dynamic environments. In comparison to heuristic methods, genetic programming hyper-heuristic (GPHH) is more suitable for tackling dynamic events since it can make real-time decisions by dispatching rules (DRs) automatically generated based on the current job shop state. However, most existing DR-based studies focus on time-related optimization objectives (e.g., makespan, tardiness, etc.), ignoring energy consumption, which is crucial for meeting the urgent needs of green manufacturing in current society. Therefore, this paper systematically designs the energy-efficient terminals for GPHH, following an in-depth analysis of energy flow in the job shop. Besides, the paper proposes the energy-efficient manually designed DRs based on the DR construction method. Experimental results demonstrate that the DRs containing the proposed energy-efficient terminals can effectively optimize energy-related objectives.

Uncertainty in processing times is a key issue in distributed production; it severely affects scheduling accuracy. In this study, we investigate a dynamic distributed flexible job shop scheduling problem with variable processing times (DDFJSP-VPT), in which the processing time follows a normal distribution. First, the mathematical model is established by simultaneously considering the makespan, tardiness, and total factory load. Second, a chance-constrained approach is employed to predict uncertain processing times to generate a robust initial schedule. Then, a heuristic scheduling method which involves a left-shift strategy, an insertion-based local adjustment strategy, and a DMOGWO-based global rescheduling strategy is developed to dynamically adjust the scheduling plan in response to the context of uncertainty. Moreover, a hybrid initialization scheme, discrete crossover, and mutation operations are designed to generate a high-quality initial population and update the wolf pack, enabling GWO to effectively solve the distributed flexible job shop scheduling problem. Based on the parameter sensitivity study and a comparison with four algorithms, the algorithm’s stability and effectiveness in both static and dynamic environments are demonstrated. Finally, the experimental results show that our method can achieve much better performance than other rules-based reactive scheduling methods and the hybrid-shift strategy. The utility of the prediction strategy is also validated.

Attention mechanism takes a crucial role among the key technologies in transformer-based visual tracking. However, the current methods for attention computing neglect the correlation between the query and the key, which results in erroneous correlations. To address this issue, a CWCTrack framework is proposed in this study for transformer visual tracking. To balance the weights of the attention module and enhance the feature extraction of the search region and template region, a consistent weighted correlation (CWC) module is introduced into the cross-attention block. The CWC module computes the correlation score between each query and all keys. Then, the correlation multiplies the consistent weights of the other query–key pairs to acquire the final attention weights. The weights of consistency are computed by the relevance of the query–key pairs. The correlation is enhanced for the relevant query–key pair and suppressed for the irrelevant query–key pair. Experimental results conducted on four prevalent benchmarks demonstrate that the proposed CWCTrack yields preferable performances.