In recent years, industrial chain cooperation has evolved into multiplex network structures where product agents are linked through diverse types of interdependencies. While such architectures enhance coordination flexibility, resource-sharing efficiency, and system-level resilience, they also introduce complex hybrid dynamics. These dynamics emerge from fluctuating task demands, continuous changes in network topology as agents join or leave, and variations in production capacities across agents. Their interactions generate cascading cross-layer effects that disrupt load balance and challenge conventional scheduling and resource management strategies. This work addresses the resulting complexity by proposing the hierarchical grouped task migration (HGTM) algorithm, which migrates tasks in groups rather than individually. Leveraging its hierarchical design, HGTM enables effective multilevel load balancing throughout the multiplex structure while keeping computational overhead low. Comprehensive theoretical analysis and experiments show that HGTM enhances task completion rates, improves execution utility, and reduces completion costs. The approach exhibits strong robustness and adaptability, particularly under increasingly dynamic and highly coupled operating conditions.

Industrial software systems underpin complex industrial platforms by integrating cross-disciplinary expertize and sophisticated workflows. Their inherent complexity generates substantial cognitive demands, necessitating contextual, adaptive, and personalized knowledge support aligned with dynamic tasks and evolving expertize. Conventional recommendation approaches struggle to address heterogeneous knowledge sources, dynamic user needs with intent drift, and the domain-specific semantics required in industrial software. To overcome these challenges, we propose a context-aware dialog-based knowledge recommendation (CADKR) model, powered by large language models (LLMs). CADKR fuses dynamic interaction context with domain knowledge through a novel recommendation network (RecNet), enabling robust generalization to unseen scenarios and adaptability to preference drift. For practical deployment, lightweight optimization strategies compress model size by up to 98% without compromising accuracy. A case study in a large chemical industrial park demonstrates the effectiveness of CADKR in enhancing industrial knowledge support, while application deployments in leading new energy vehicle enterprises and the world’s largest circular resource power plant have yielded an independent verification report, providing strong evidence of the proposed method’s practical value.11The report is available athttps://anonymous.4open.science/r/verification-report. Code and data are available athttps://anonymous.4open.science/r/CADKR-TCSS. To meet double-blind requirements, organization and personnel details are anonymized and will be disclosed after acceptance.

Determining the optimal number of clusters in cluster analysis without prior knowledge remains a critical and challenging task. Existing methods often depend on calculating clustering validity indices (CVIs), which increases complexity and may reduce efficiency. Furthermore, different CVIs frequently suggest varying optimal cluster numbers, complicating the selection process. To address these challenges, we propose a novel clustering algorithm, self-regulating possibilistic C-means (PCM) with high-density points (SR-PCM-HDP), which simplifies cluster number determination while improving clustering efficiency. First, the density-based knowledge extraction (DBKE) method is introduced to estimate an appropriate initial cluster number and identify high-density points. DBKE enhances the density peak clustering (DPC) algorithm by removing the need for a predefined density radius. Second, SR-PCM-HDP refines the clustering process by incorporating a parameter to balance the interactions between high-density points and cluster centers, reducing sensitivity to initial configurations and accelerating convergence. Third, the parameter adjustment mechanism in classical PCM is redefined to enable adaptive updates during SR-PCM-HDP iterations. This mechanism facilitates the gradual elimination of obsolete clusters and iterative cluster formation. The theoretical foundations of the SR-PCM-HDP cluster elimination mechanism are rigorously established. Experimental results validate the accuracy and effectiveness of SR-PCM-HDP in determining cluster numbers and ensuring clustering validity, particularly for datasets with overlapping or imbalanced distributions. Comparisons are conducted against 13 state-of-the-art algorithms, including fuzzy clustering, possibilistic clustering, and CVI-based cluster determination methods.

Multi-view attributed graphs (MVAGs) provide rich structural and attribute information, but existing clustering methods struggle to jointly exploit multi-view attributes and multiple graph structures. Moreover, they often focus on either visible view collaboration or hidden feature extraction, failing to capture the synergy between the two. To address these challenges, we propose ITF-MVFC (Multi-View Fuzzy Clustering with Intrinsic and Topological Features), a novel clustering model designed for MVAGs. ITF-MVFC first constructs proximity matrices from topological connections and then introduces a Double Visible-Hidden Feature Extraction (DVHFE) mechanism based on non-negative matrix factorization (NMF). This extracts both intrinsic and topological visible-hidden feature representations. To enhance sparsity and interpretability, we further employ network lasso regularization, enabling effective cooperative learning between intrinsic and topological views. Finally, a fuzzy clustering objective function is established to integrate these multi-view representations. Experiments on synthetic, real-world, and large size datasets show that ITF-MVFC consistently outperforms state-of-the-art clustering methods on both external metrics and internal validation indices across multiple datasets.

In current granular clustering algorithms, numeric representatives were selected by users or an ordinary strategy, which seemed simple; meanwhile, weight settings for granular data could not adequately express their structural characteristics. Aiming at these problems, in this study, a new scheme called a granular weighted kernel fuzzy clustering (GWKFC) algorithm is put forward. We propose the representative selection and granularity generation (RSGG) algorithm enlightened by the density peak clustering (DPC) algorithm. We build interval and triangular granular data on the strength of numeric representatives obtained by RSGG under the principle of justifiable granularity (PJG), in which we establish some combinations of functions and boundary constraints and prove their properties. Furthermore, we present a novel distance formula via the kernel function for granular data and design new weights to affect the coverage and specificity of granular data. In addition, based upon these factors, we come up with the GWKFC algorithm of granular clustering, and its performance with different granularity is assessed. To sum up, a macro framework involving granular modeling, granular clustering, and assessment has been set up. Lastly, the GWKFC algorithm and ten other granular clustering algorithms are compared by experiments on some artificial and UCI datasets together with datasets with large data or those of high dimensionality. It is found that the GWKFC algorithm can provide better granular clustering results by contrast with other algorithms. The originality is embodied as follows. First, we improve the previous density radius and present the RSGG algorithm to acquire numeric representatives. Second, we propose a new strategy to determine granular data boundaries and further obtain novel weights enlightened by the idea of volume. Lastly, we employ the kernel function to calculate the distance between granular data, which has a stronger spatial division ability than the previous Euclidean distance.

The introduction of domain knowledge opens new horizons to fuzzy clustering. Then knowledge-driven and data-driven fuzzy clustering methods come into being. To address the challenges of inadequate extraction mechanism and imperfect fusion mode in such class of methods, we propose the Knowledge-induced Multiple Kernel Fuzzy Clustering (KMKFC) algorithm. First, to extract knowledge points better, the Relative Density-based Knowledge Extraction (RDKE) method is proposed to extract high-density knowledge points close to cluster centers of real data structure, and provide initialized cluster centers. Moreover, the multiple kernel mechanism is introduced to improve the adaptability of clustering algorithm and map data to high-dimensional space, so as to better discover the differences between the data and obtain superior clustering results. Second, knowledge points generated by RDKE are integrated into KMKFC through a knowledge-influence matrix to guide the iterative process of KMKFC. Third, we also provide a strategy of automatically obtaining knowledge points, and thus propose the RDKE with Automatic knowledge acquisition (RDKE-A) method and the corresponding KMKFC-A algorithm. Then we prove the convergence of KMKFC and KMKFC-A. Finally, experimental studies demonstrate that the KMKFC and KMKFC-A algorithms perform better than thirteen comparison algorithms with regard to four evaluation indexes and the convergence speed.

Knowledge-based clustering algorithms can improve traditional clustering models by introducing domain knowledge to identify the underlying data structure. While there have been several approaches to clustering with the guidance of knowledge tidbits, most of them mainly focus on numeric knowledge without considering the uncertain nature of information. To capture the uncertainty of information, pure numeric knowledge tidbits are expanded to knowledge granules in this article. Then, two questions arise: how to obtain granular knowledge and how to use those knowledge granules in clustering. To the end, a novel knowledge extraction and granulation (KEG) method and a granular knowledge-based fuzzy clustering model are proposed in this study. First, inspired by the concept of natural neighbors, an automatic KEG is developed. In KEG, high-density points are filtered from the dataset and then merged with their natural neighbors to form several dense areas, i.e., granular knowledge. Furthermore, the granular knowledge expressed by interval or triangular numbers is leveraged into the clustering algorithm, which is the framework of fuzzy clustering with granular knowledge. To concretize this model into clustering algorithms, the classical fuzzy C-Means clustering algorithm has been selected to incorporate the granular knowledge produced by KEG. Then, the corresponding fuzzy C-Means clustering with interval knowledge granules (IKG-FCM) and triangular knowledge granules (TKG-FCM) are proposed. Experiments on synthetic and real-world datasets demonstrate that IKG-FCM and TKG-FCM always achieve better clustering performance with less time cost, especially on imbalanced data, compared with state-of-the-art algorithms.

Packet classification is crucial for the Internet to provide more value-added services and guaranteed quality of service. Besides hardware-based solutions, many software-based classification algorithms have been proposed. However, classifying at 10Gbps speed or higher is a challenging problem and it is still one of the performance bottlenecks in core routers. In general, classification algorithms face the same challenge of balancing between high classification speed and low memory requirements. This paper proposes a modified Recursive Flow Classification (RFC) algorithm, Bitmap-RFC, which significantly reduces the memory requirements of RFC by applying a bitmap compression technique. To speed up classifying speed, we experiment on exploiting the architectural features of a many-core and multithreaded architecture from algorithm design to algorithm implementation. As a result, Bitmap-RFC strikes a good balance between speed and space. It can not only keep high classification speed but also reduce memory space significantly.This paper investigates the main NPU software design aspects that have dramatic performance impacts on any NPU-based implementations: memory space reduction, instruction selection, data allocation, task partitioning, and latency hiding. We experiment with an architecture-aware design principle to guarantee the high performance of the classification algorithm on an NPU implementation. The experimental results show that the Bitmap-RFC algorithm achieves 10Gbps speed or higher and has a good scalability on Intel IXP2800 NP.

IP forwarding is one of the main bottlenecks in Internet backbone routers, as it requires performing the longest-prefix match at 10Gbps speed or higher. IPv6 forwarding further exacerbates the situation because its search space is quadrupled. We propose a high-performance IPv6 forwarding algorithm TrieC, and implement it efficiently on the Intel IXP2800 network processor (NPU). Programming the multi-core and multithreaded NPU is a daunting task. We study the interaction between the parallel algorithm design and the architecture mapping to facilitate efficient algorithm implementation. We experiment with an architecture-aware design principle to guarantee the high performance of the resulting algorithm.This paper investigates the main software design issues that have dramatic performance impacts on any NPU based implementation: memory space reduction, instruction selection, data allocation, task partitioning, latency hiding, and thread synchronization. In the paper, we provide insight on how to design an NPU-aware algorithm for high-performance networking applications. Based on the detailed performance analysis of the TrieC algorithm, we provide guidance on developing high-performance networking applications for the multi-core and multithreaded architecture.