Hierarchical Algorithm Research Articles

Hierarchical Membrane Computing Algorithms for Optimizing Customer-to-Green-Manufacturer Decision-Making in Industrial Internet Platforms

This paper proposes a dynamic membrane algorithm (DMA)-oriented computing framework designed to optimize decision-making in Customer-to-Green-Manufacturer (C2GM) operations on industrial internet platforms. Unlike traditional methods that focus solely on economic metrics, the DMA integrates membrane computing principles with evolutionary optimization techniques and incorporates green manufacturing objectives (e.g., energy efficiency, waste reduction, carbon footprint). By doing so, it dynamically aligns customer demands with manufacturing capabilities in real time, ensuring both operational efficiency and environmental stewardship. The DMA facilitates parallel and hierarchical processing of complex decision tasks, mapping evolutionary rules and manufacturing operations into a structured membrane system that accelerates convergence and improves scalability. Experimental evaluations—both in controlled simulations and a real-world case study of C2GM operations in Yiwu—demonstrate that the DMA not only achieves faster and more stable convergence than genetic algorithms but also supports greener production processes. This integrated approach thus enhances strategic decision-making, offering a sustainable pathway for advancing industrial internet ecosystems and global supply chains.

Adaptive Clustering Hierarchical PBFT Algorithm for Secure and Efficient Blockchain-Based IoT Edge Computing

Adaptive Clustering Hierarchical PBFT Algorithm for Secure and Efficient Blockchain-Based IoT Edge Computing

Design of multi-innovation hierarchical fractional adaptive algorithm for generalized bilinear-in-parameter system using the key term separation principle

This paper mainly studies the issue of fractional parameter identification of generalized bilinear-in-parameter system(GBIP) with colored noise. Hierarchical fractional least mean square algorithm based on the key term separation principle(K-HFLMS) and multi-innovation hierarchical fractional least mean square algorithm based on the key term separation principle (K-MHFLMS) are presented for the effective parameter estimation of GBIP system. The K-MHFLMS expands the scalar innovation into the vector innovation by making full use of the system input and output data information at each recursive step. The detailed performance analyses of the K-MHFLMS strategy are compared with the K-HFLMS algorithm for GBIP identification model based on the Fitness metrics, the mean square error metrics and the average predicted output error. The effectiveness and reliability of K-HFLMS and K-MHFLMS algorithms are further verified through the simulation experimentation under different noise variances, fractional orders and innovation lengths, and the K-MHFLMS yields faster convergence speed than the K-HFLMS by increasing the innovation length.

Regularized X‐FEM Modeling of Arbitrary 3D Interacting Crack Networks

ABSTRACTAn extension to the Regularized eXtended Finite Element Method (RX‐FEM) is proposed that allows arbitrary 3D cracks through a novel hierarchical enrichment algorithm. The technique avoids geometric consideration of how a crack cuts elements or intersects other cracks. Each crack is described separately in terms of its sign distance function and regularized step function, which are only recorded for nodes in the region where the gradient of the regularized step function is non‐zero. The algorithm creates a set of superimposed nodes, referred to as node twins, and elements, referred to as twinned elements, for each crack and determines the connectivity of the element twins using the involved crack indices. The displacement jump is calculated between each pair of element twins corresponding to the same crack, and a cohesive zone model (CZM) is formulated for each pair of twins to model crack opening. Following the theory for the novel method, several examples are presented that illustrate capabilities of the new method that the traditional RX‐FEM formulation lacked. A quasi‐2D example of offset crack propagation is considered and successfully compared with published results. Additionally, two 3D examples involving perpendicularly intersecting cracks are considered, illustrating the intersection of two crack fronts and correct partitioning of the domain into eight fragments due to three crossing cracks, respectively.

Dynamic Hierarchical Optimization for Train-to-Train Communication System

To enhance the operational efficiency of high-speed trains (HSTs), Train-to-Train (T2T) communication has received considerable attention. This paper introduces a T2T cooperative communication model that allows direct information exchange between HSTs, enhancing communication efficiency and system performance. The model incorporates a mix of dynamic and static nodes, and within this framework, we have developed a novel Dynamic Hierarchical Algorithm (DHA) to optimize communication paths. The DHA combines the stability of traditional algorithms with the flexibility of machine learning to adapt to changing network topologies. Furthermore, a communication link quality assessment function is proposed based on stochastic network calculus, which accounts for channel randomness, allowing for a more precise adaptation to the actual channel environment. Simulation results demonstrate that DHA has superior performance in terms of optimization time and effect, particularly in large-scale and highly dynamic network environments. The algorithm’s effectiveness is validated through comparative analysis with traditional and machine learning-based approaches, showing significant improvements in optimization efficiency as the network size and dynamics increase.

Anti‐Leakage Method of Sensitive Information of Network Documents Based on Differential Privacy Model

ABSTRACTThis article proposes a method for preventing sensitive information leakage in network documents based on differential privacy models to ensure the security of sensitive information in network documents. Based on the definition of differential privacy and its Laplace mechanism, a differential privacy model was constructed to prevent sensitive information leakage in network documents. Using differential privacy based Laplace mechanism to protect the sensitive information dataset of network documents, and inputting the sensitive information dataset of network documents into the differential privacy model, the sensitive information in network documents is generalized and perturbed, and Laplace noise is added after transformation and compression to prevent leakage. Using roulette wheel sampling technology to sample and sort the original histograms of sensitive data in network documents, using a hierarchical partitioning algorithm to group the sorted histograms, and adding Laplace noise to the groups based on differential confidentiality Laplace mechanism to achieve leak prevention when publishing sensitive messages in network documents. The experimental results show that this method can ensure the security of sensitive information data in network documents and prevent sensitive information leakage in network documents. There is no data loss during the data conversion and compression process of sensitive information. At the same time, the protection effect of sensitive information is less affected by the amount of data, and the loss rate of sensitive information is lower.

A digital twin-driven pre-grasp path planning method for robotic deep-frame grasping of disordered workpieces

In a sheet metal parts welding shop, traditional robot path-planning methods prove inadequate for achieving automatic robot loading and unloading of disordered workpieces in the deep material frames. Therefore, this paper proposes a robotic motion planning framework in Deep-frame Disordered Workpiece Grasping (DDWG), ensuring efficient automatic loading and unloading tasks with high efficiency and collision-free operations. In conjunction with the actual DDWG scenario, an Oriented Bounding Boxes (OBB) based hierarchical enclosing box algorithm is used for collision detection. Further, this paper proposes a two-segment Middle Pre-Grasp Rapidly-exploring Random Tree (MPG-RRT) algorithm for path planning, utilizing pre-grasp point (middle point) guidance. In the DDWG process, a pre-adjustable pre-grasp point is introduced to expand the two random trees toward the intermediate points. Additionally, a probabilistic goal bias and a goal gravity strategy are incorporated with an adaptive gravity step size at each exploring stage to guide the expansion of random trees toward the goal point direction and to optimize paths by removing redundant nodes. Finally, an existing digital twins-driven robotic production line is reconfigured to simulate motion planning in two DDWG scenarios, which validates the effectiveness and superiority of the proposed method.

Real-Time Orbit Determination of Micro-Nano Satellite Using Robust Adaptive Filtering.

Low-performing GPS receivers, often used in challenging scenarios such as attitude maneuver and attitude rotation, are frequently encountered for micro-nano satellites. To address these challenges, this paper proposes a modified robust adaptive hierarchical filtering algorithm (named IARKF). This algorithm leverages robust adaptive filtering to dynamically adjust the distribution of innovation vectors and employs a fading memory weighted method to estimate measurement noise in real time, thereby enhancing the filter's adaptability to dynamic environments. A segmented adaptive filtering strategy is introduced, allowing for flexible parameter adjustment in different dynamic scenarios. A micro-nano satellite equipped with a miniaturized dual-frequency GPS receiver is employed to demonstrate precise orbit determination capabilities. On-orbit GPS data from the satellite, collected in two specific scenarios-slow rotation and Earth-pointing stabilization-are analyzed to evaluate the proposed algorithm's ability to cope with weak GPS signals and satellite attitude instability as well as to assess the achievable orbit determination accuracy. The results show that, compared to traditional Extended Kalman Filters (EKF) and other improved filtering algorithms, the IARKF performs better in reducing post-fit residuals and improving orbit prediction accuracy, demonstrating its superior robustness. The three-axes orbit determination internal consistency precision can reach the millimeter level. This work explores a feasible approach for achieving high-performance orbit determination in micro-nano satellites.

AI Dermatochroma Analytica (AIDA): Smart Technology for Robust Skin Color Classification and Segmentation

Traditional methods for skin color classification, such as visual assessments and conventional image classification, face limitations in accuracy and consistency under varying conditions. To address this, we developed AI Dermatochroma Analytica (AIDA), an unsupervised learning system designed to enhance dermatological diagnostics. AIDA applies clustering techniques to classify skin tones without relying on labeled data, evaluating over twelve models, including K-means, density-based, hierarchical, and fuzzy logic algorithms. The model’s key feature is its ability to mimic the process clinicians traditionally perform by visually matching the skin with the Fitzpatrick Skin Type (FST) palette scale but with enhanced precision and accuracy using Euclidean distance-based clustering techniques. AIDA demonstrated superior performance, achieving a 97% accuracy rate compared to 87% for a supervised convolutional neural network (CNN). The system also segments skin images into clusters based on color similarity, providing detailed spatial mapping aligned with dermatological standards. This segmentation reduces the uncertainty related to lighting conditions and other environmental factors, enhancing precision and consistency in skin color classification. This approach offers significant improvements in personalized dermatological care by reducing reliance on labeled data, improving diagnostic accuracy, and paving the way for future applications in diverse dermatological and cosmetic contexts.

Finite-Time Resource Allocation Algorithm for Networked Fractional Nonlinear Agents

This paper investigates finite-time resource allocation problems (RAPs) for uncertain nonlinear fractional-order multi-agent systems (FOMASs), considering global equality and local inequality constraints. Each agent is described by high-order dynamics with multiple-input multiple-output and only knows its local objective function. Due to the characteristics of dynamic systems, the outputs of agents are inconsistent with their inputs, making it challenging to satisfy the inequality constraints when solving RAPs. To address this complex optimization control problem, a novel hierarchical algorithm is proposed, consisting of a distributed estimator and a local controller. Specifically, the distributed estimator is established by adopting the ϵ-exact penalty function and the gradient descent method. This estimator enables the system states to reach the optimal solution of RAPs within a finite time. Furthermore, the local controller is presented based on the fractional-order tracking differentiator and adaptive neural control approach. Under this controller, the system states are slaved to track the optimal signals generated by the estimator within a finite time. In both the estimator and controller algorithms, the finite-time stability is uniformly guaranteed with the help of Lyapunov functions. Finally, the effectiveness of our algorithm is demonstrated through three simulation examples.

Novel algorithm for non-invasive estimation of left atrial pressure in patients with atrial fibrillation.

Determining elevated left atrial (LA) pressure is crucial in patients with atrial fibrillation (AF), yet non-invasive estimation using echocardiography remains unclear. This study aimed to identify useful echocardiographic indices for identifying elevated LA pressure in patients with AF. Patients with paroxysmal or persistent AF referred for catheter ablation at two tertiary hospitals were prospectively enrolled. Mean LA pressure was measured immediately after transseptal puncture. Elevated mean LA pressure was defined as ≥15 mmHg. Transthoracic echocardiography was performed to acquire the guideline-recommended parameters. A total of 176 patients were included, and 63 (36%) patients had a mean LA pressure ≥15 mmHg. Patients with elevated LA pressure had more frequent hypertension, larger LA, higher septal E/e', and worse LA strain than the remaining patients. The correlations between mean LA pressure and each echocardiographic parameter were weak. Septal E/e' ratio showed the best correlation with mean LA pressure (r = 0.351, P < 0.001), and septal E/e' ratio ≥11 was the best parameter (area under the curve = 0.7, sensitivity = 65%, specificity = 73%, accuracy = 70%) to identify elevated mean LA pressure. A hierarchical algorithm consisting of septal E/e' ratio, LA reservoir strain, and LA volume index improved identification of patients with elevated mean LA pressure (sensitivity = 61%, specificity = 91%, accuracy = 80%). In patients with AF, the septal E/e' ratio was the best single parameter for identifying elevated mean LA pressure. A hierarchical algorithm combining the septal E/e' ratio, LA reservoir strain, and LA volume index helps identify elevated LA pressure in patients with AF.

Hierarchical Heuristic Species Delimitation Under the Multispecies Coalescent Model with Migration.

The multispecies coalescent (MSC) model accommodates genealogical fluctuations across the genome and provides a natural framework for comparative analysis of genomic sequence data from closely related species to infer the history of species divergence and gene flow. Given a set of populations, hypotheses of species delimitation (and species phylogeny) may be formulated as instances of MSC models (e.g., MSC for 1 species versus MSC for 2 species) and compared using Bayesian model selection. This approach, implemented in the program bpp, has been found to be prone to over-splitting. Alternatively, heuristic criteria based on population parameters (such as population split times, population sizes, and migration rates) estimated from genomic data may be used to delimit species. Here, we develop hierarchical merge and split algorithms for heuristic species delimitation based on the genealogical divergence index (gdi) and implement them in a Python pipeline called hhsd. We characterize the behavior of the gdi under a few simple scenarios of gene flow. We apply the new approaches to a dataset simulated under a model of isolation by distance as well as 3 empirical datasets. Our tests suggest that the new approaches produced sensible results and were less prone to oversplitting. We discuss possible strategies for accommodating paraphyletic species in the hierarchical algorithm, as well as the challenges of species delimitation based on heuristic criteria.

Hierarchical simplicial manifold learning.

Learning global structures, i.e. topological properties, inherent in complex data is an essential yet challenging task that spans across various scientific and engineering disciplines. A fundamental approach is to extract local data representations and use them to assemble the global structure. This conjunction of local and global operations catalyzes the integration of tools from algebraic and computational topology with machine learning. In this article, we propose a hierarchical simplicial manifold learning algorithm, constituted by nested clustering and topological reduction, for constructing simplicial complexes and decoding their topological properties. We show that the learned complex possesses the same topology as the original embedding manifold from which the data were sampled. We demonstrate applicability, convergence, and computational efficiency of the algorithm on both synthetic and real-world data.

Parameter estimation in solar power plant systems: a comparative study of recursive and iterative techniques

The development of a dynamic model for a popular implemented solar power plant is a critical task for power engineers aiming to enhance the plant’s performance and reliability. In this study, we utilized the prediction error method (PEM), a robust algorithm for system identification, to capture the plant’s operational characteristics with precision. Additionally, we employed both recursive and hierarchical algorithms to identify the system parameters effectively. The results from each identification method are rigorously quantified and analyzed, allowing for a detailed comparison of their performance. This comprehensive evaluation not only highlights the strengths and weaknesses of each approach, but also provides valuable insights into their practical applications in the context of solar power systems.

System architecture optimization strategies: dealing with expensive hierarchical problems

Abstract Choosing the right system architecture for the problem at hand is challenging due to the large design space and high uncertainty in the early stage of the design process. Formulating the architecting process as an optimization problem may mitigate some of these challenges. This work investigates strategies for solving system architecture optimization (SAO) problems: expensive, black-box, hierarchical, mixed-discrete, constrained, multi-objective problems that may be subject to hidden constraints. Imputation ratio, correction ratio, correction fraction, and max rate diversity metrics are defined for characterizing hierarchical design spaces. This work considers two classes of optimization algorithms for SAO: multi-objective evolutionary algorithms such as NSGA-II, and Bayesian optimization (BO) algorithms. A new Gaussian process kernel is presented that enables modeling hierarchical categorical variables, extending previous work on modeling continuous and integer hierarchical variables. Next, a hierarchical sampling algorithm that uses design space hierarchy to group design vectors by active design variables is developed. Then, it is demonstrated that integrating more hierarchy information in the optimization algorithms yields better optimization results for BO algorithms. Several realistic single-objective and multi-objective test problems are used for investigations. Finally, the BO algorithm is applied to a jet engine architecture optimization problem. This work shows that the developed BO algorithm can effectively solve the problem with one order of magnitude less function evaluations than NSGA-II. The algorithms and problems used in this work are implemented in the open-source Python library SBArchOpt.

Identification of movie encoding neurons enables movie recognition AI

Natural visual scenes are dominated by spatiotemporal image dynamics, but how the visual system integrates "movie" information over time is unclear. We characterized optic tectal neuronal receptive fields using sparse noise stimuli and reverse correlation analysis. Neurons recognized movies of ~200-600 ms durations with defined start and stop stimuli. Movie durations from start to stop responses were tuned by sensory experience though a hierarchical algorithm. Neurons encoded families of image sequences following trigonometric functions. Spike sequence and information flow suggest that repetitive circuit motifs underlie movie detection. Principles of frog topographic retinotectal plasticity and cortical simple cells are employed in machine learning networks for static image recognition, suggesting that discoveries of principles of movie encoding in the brain, such as how image sequences and duration are encoded, may benefit movie recognition technology. We built and trained a machine learning network that mimicked neural principles of visual system movie encoders. The network, named MovieNet, outperformed current machine learning image recognition networks in classifying natural movie scenes, while reducing data size and steps to complete the classification task. This study reveals how movie sequences and time are encoded in the brain and demonstrates that brain-based movie processing principles enable efficient machine learning.

A Clinical Care Algorithm for Detecting Progression in Multiple Sclerosis: RetratEMos Project.

The diagnosis of secondary progressive multiple sclerosis (SPMS) is often established retrospectively leading to a delay in detection. This work presents a clinical care algorithm that aims to facilitate the recognition of the secondary progressive phase of the disease, analyzing its usefulness and the feasibility of its implementation in routine clinical practice. The algorithm was developed in four phases: 1) choice of validated diagnostic tools for the detection of progression; 2) assessment of these tools based on experience of use, applicability, time consumed, perceived usefulness and suitability for a profile of a patient in transition to SPMS; 3) framework and final sequence of application; 4) feasibility evaluation through application in clinical practice. A hierarchical algorithm was developed with an initial screening phase to detect warning signs and establish suspicion of progression (which included the tests "Your Multiple Sclerosis (Your MS)," "MSProDiscuss," and "Nomogram") and a second phase conditional on a positive result in the first, including a functional examination with the Symbol Digit Modalities Test (SDMT), 9-Hole Peg Test (9-HPT), and Timed 25-Foot Walk (T25FW) tools. The algorithm was applied to 373 patients with Expanded Disability Status Scale (EDSS) ≥ 2. The mean time spent per patient in the screening was eight minutes and 20.4 minutes for the complete algorithm. The perceived usefulness of the process by the neurologists was 3.1 (range of 1-4, with 4 being the maximum). In 46% of the cases, the algorithm detected the need for additional functional exploration. From our experience, this clinical care algorithm is effective and feasible for detecting progression in MS, although its implementation requires proper organization and can be uneven depending on the resources of each center.

How to arrange the robotic environment? Leveraging experience in both motion planning and environment optimization.

This study presents an experience-based hierarchical-structure optimization algorithm to address the robotic system environment design problem, which combines motion planning and environment arrangement problems together. The motion planning problem, which could be defined as a multiple-degree-of-freedom (m-DOF) problem, together with the environment arrangement problem, which could be defined as a free DOF problem, is a high-dimensional optimization problem. Therefore, the hierarchical structure was established, with the higher layer solving the environment arrangement problem and lower layer solving the problem of motion planning. Previously planned trajectories and past results for this design problem were first constructed as datasets; however, they cannot be seen as optimal. Therefore, this study proposed an experience-reuse manner, which selected the most "useful" experience from the datasets and reused it to query new problems, optimize the results in the datasets, and provide better environment arrangement with shorter path lengths within the same time. Therefore, a hierarchical structural caseGA-ERTC algorithm was proposed. In the higher layer, a novel approach employing the case-injected genetic algorithm (GA) was implemented to tackle optimization challenges in robot environment design, leveraging experiential insights. Performance indices in the arrangement of the robot system's environment were determined by the robotic arm's motion and path length calculated using an experience-driven random tree (ERT) algorithm. Moreover, the effectiveness of the proposed method is illustrated with the 12.59% decrease in path lengths by solving different settings of hard problems and 5.05% decrease in easy problems compared with other state-of-the-art methods in three small robots.

A Time-Critical Low Complexity Distributed Self Organizing Hierarchical Particle Swarm Optimization Algorithm for Wireless Sensor Networks

A Time-Critical Low Complexity Distributed Self Organizing Hierarchical Particle Swarm Optimization Algorithm for Wireless Sensor Networks

Wave effect of gravitational waves intersected with a microlens field II: An adaptive hierarchical tree algorithm and population study

Wave effect of gravitational waves intersected with a microlens field II: An adaptive hierarchical tree algorithm and population study