Solving nonlinear equation systems with multiple roots is challenging due to complex basin structures, uneven root distributions, premature population convergence, and repeated search around already discovered roots. Although differential evolution (DE) algorithm has been widely applied to nonlinear equation solving due to its derivative-free global search capability, standard DE often lacks an effective mechanism for maintaining multiple search branches and reallocating search resources among different potential root regions. To address these issues, this paper proposes a hierarchical cluster-guided adaptive differential evolution (HCADE) algorithm. This method employs a neighborhood-based differential evolution strategy to guide individuals toward potential root regions while preserving local search diversity; introduces a success-history-based parameter adaptation mechanism to dynamically adjust the mutation factor and crossover probability, reducing the dependence on manually fixed parameters; in the later search stage, utilizes hierarchical clustering to analyze the spatial distribution of the population and classify individuals into promising clusters, non-promising clusters, and scattered individuals; on this basis, an adaptive migration mechanism reallocates individuals from low-contribution clusters to more promising regions, while an archive-based reinitialization strategy preserves discovered roots and releases population capacity for further exploration. Experimental results on benchmark nonlinear equation systems demonstrate that HCADE achieves competitive performance in terms of multiple-root detection, convergence stability, and robustness.

The multi-load automated guided vehicle (MLAGV), capable of carrying multiple jobs simultaneously, provides additional flexibility compared to single-load counterpart. Applying MLAGV into material handling systems is of significantly importance for promoting greening and efficiency in modern manufacturing workshop. However, the operational challenges arising from the integrated scheduling of production and MLAGV transportation within a flexible open shop environment have not yet been adequately addressed by existing research. To this end, the energy-aware flexible open shop scheduling problem with MLAGV is investigated in this paper. A mixed-integer programming model is constructed with the objective of simultaneously minimizing the makespan and the total energy consumption of the MLAGV system. To solve this, a graph reinforcement learning assisted multi-objective memetic algorithm is proposed. The learning mechanism is adopted to enhance the local search ability, where the solution state is represented via a graph attention network architecture integrated with problem-specific knowledge, and the action policy is obtained via a double dueling deep Q-network with prioritized experience replay. Through experiments against three existing algorithms and an exact solver, the proposed method demonstrate the superiority in comprehensive performance. A real-world case studies further validate the effectiveness of MLAGV and offer insights for managing flexible manufacturing shop floor.

In robotics control experiments, the balance between exploration and exploitation, as well as the accuracy of the advantage function estimation, are crucial factors that affect the effectiveness of policy optimization methods. To overcome these challenges, this paper proposes an adaptive adjustment of advantage estimation based on the policy loss and policy entropy algorithm (A3E-PLE), which can improve the exploratory capabilities of the proximal policy optimization (PPO) algorithm. Specifically, on the one hand, the policy loss is adjusted using a Gaussian distribution policy entropy to mitigate randomness and separate policy improvement from random noise, thereby improving exploration efficiency. On the other hand, to adapt flexibly to various training scenarios and further enhance the accuracy of advantage function estimation, the policy loss is incorporated into the advantage function estimation. This enables the algorithm to adaptively adjust according to changes in the strategy. Finally, the proposed reinforcement learning (RL) framework was validated using robot control simulations and complex decision-making environments. It is shown that A3E-PLE achieves higher learning efficiency and greater rewards compared to traditional generalized advantage estimation.

The autonomous underwater vehicle (AUV) serves as an ideal platform for replacing human operators in high-risk underwater operations, where high-precision trajectory tracking control is crucial for ensuring mission effectiveness. However, the time-varying dynamics caused by the complexity of the underwater environment present significant challenges to achieving high-precision trajectory tracking for AUVs. To address this challenge, a model-assisted deep reinforcement learning-based trajectory tracking method for an AUV with time-varying dynamics is presented in this article. Specifically, a novel state space is proposed, which replaces the absolute position of the agent with the relative position. This representation provides a more comprehensive description of the relationship between the AUV and the reference trajectory. The policy trained based on this state space can be easily transferred and applied to a different type of reference trajectory. Furthermore, by decomposing the reward function into three components, the sparse reward issue is effectively mitigated. The smoothness term within the reward function effectively suppresses abrupt changes in control commands, ensuring that the AUV maintains smooth navigation even under time-varying dynamics. Finally, an improved proximal policy optimization algorithm is proposed. The algorithm includes two critics that separately evaluate the value functions of actions under time-varying and static dynamics, and adaptively adjust their weights based on the intensity of the time-varying dynamics, effectively enhancing the policy’s disturbance rejection capability and robustness. Experimental results demonstrate that the proposed method maintains high-precision trajectory tracking across various time-varying dynamics, significantly outperforming other algorithms and validating its effectiveness.

This paper formulates a self-organized dynamic fencing problem for multiple AUVs under finite target-sensing range and bounded nonuniform acoustic communication delays. Here, self-organization means that the fence is generated by local interactions without assigning fixed angular slots, virtual leaders, or persistent vehicle roles. A minimal observer-assisted attraction-repulsion fencing controller is proposed for AUV implementation, comprising target-AUV radial attraction–repulsion, AUV–AUV distance attraction–repulsion computed from timestamp-aligned delayed neighbor states, a state-only target-motion observer, and a label-free bearing-coverage repulsion that acts only on oversized target-centered angular gaps. To address acoustic delay without delaying physical execution, each AUV stores its own state history and evaluates pairwise relative geometry at the timestamp carried by the received neighbor packet. The resulting command is applied at the current time. The analysis shows that timestamp alignment converts acoustic delay into a bounded geometric perturbation and establishes collision avoidance, radial confinement, angular-gap contraction, target tracking, and packet-range preservation on a locally order-consistent regular fencing interval. The theorem does not claim global entry from arbitrary non-enclosing configurations. Numerical simulations, including a five-degree-of-freedom ocean-current robustness test without current feedforward compensation and an evasive-target stress test with four rapid finite-acceleration turns, demonstrate self-organized entry and maintenance of compact convex-hull fencing in the tested cases.

As most of the digital image encryption algorithms are dependent with matrix theory, matrix equations are widely used in digital image encryption algorithms. Matrix inversion is a basic matrix equation operation, and how to effectively solve the matrix inversion problem has drawn considerable attention. However, previous works mainly focused on the static matrix inversion, and they are not suitable for modern time-varying problems solving. Zeroing neural network (ZNN) is a emerging systematic approach for solving time-varying problems, and it has been successfully applied in the dynamic matrix inversion. In order to enhance the performance of the existing models, this paper constructs a novel fuzzy adaptive ZNN (FA-ZNN) model, which incorporates segmented activation functions and an adaptive fuzzy dynamic convergence factor. Based on the constructed FA-ZNN model, a novel time-varying Hill cipher (NTVHC) with chaotic sequences scrambling and encryption for remote sensing images encryption is proposed. The proposed NTVHC algorithm utilizes the tangential-delay elliptic reflection cavity system (TD-ERCS) to generate two chaotic sequences for pixels displacement scrambling while constructing dynamic key matrix for image encryption. The superior performance of the constructed FA-ZNN model for dynamic key matrix inversion are validated by mathematical analysis and comparative simulation results with other models. Additionally, in subsequent practical applications, the model is used during the NTVHC decryption, which further verifies the feasibility of the proposed NTVHC encryption algorithm and the promising application prospects of the FA-ZNN model.

This paper investigates cooperative tracking control for virtually coupled multi-train systems subject to nonlinear running resistance, bounded time-varying resistance parameters, state constraints, and actuator saturation. The theoretical contribution is not the separate use of barrier Lyapunov functions, adaptive control, anti-windup compensation, or distributed cooperative control. Instead, the revised analysis establishes a coupled safety-and-boundedness certificate for the actual saturated closed-loop vector field. The closing-speed-aware spacing variable and actuator-authority condition support a first-exit proof of forward invariance, after which a composite Lyapunov analysis couples the saturation residual, anti-windup state, cooperative tracking error, and time-varying parameter-estimation error to establish uniform ultimate boundedness without persistent excitation. This proof architecture distinguishes the proposed controller from recent constrained train-control methods focused separately on velocity/input bounds, distance-oriented full-state barriers, or iteration-indexed learning. Numerical studies with heterogeneous trains, stronger time-varying aerodynamic perturbations, normalized actuator limits, tracking-bound verification, constrained baselines, a near-boundary safety-allocation case, and a quantitative one-factor-at-a-time parameter-sensitivity study are provided.

With the advancement of intelligence in Active Distribution Networks (ADNs), effective fault recovery methods have become increasingly crucial. In this study, a reconfiguration method combining the immune mechanism and Northern Goshawk Optimization algorithm (NGO) is proposed, aimed at swiftly restoring power post-fault, maximizing the recovery of lost power areas within ADN, and minimizing losses. Firstly, an identification model within the immune mechanism is crafted to precisely match failures in ADNs. Then, the successful matched failure types can be used to restore power supply by the direct invocation of the recovery strategy from the library of strategies. Secondly, the immune response of ADNs is modeled, known as the reconfiguration model. For faults beyond the recovery strategy library, NGO is leveraged to address distribution network failures, with restoration solutions integrated into the library. Additionally, a reversed learning approach and stochastic variation strategy enhance the robustness of algorithm, preventing it from converging to suboptimal solutions. Finally, through simulation experiments, it is demonstrated that the recovery scheme obtained using the algorithm can be used to recover failure as well as reduce network losses in an effective manner. When similar or identical faults recur, ADN failure recovery becomes swift and efficient.

With the proliferation of distributed energy resources and DC loads, DC microgrids have increasingly become a pivotal direction for the evolution of future power systems. Compared with conventional AC grids, the inherent absence of natural zero-crossing points and the short duration of fault transients in DC systems impose more stringent requirements on protection schemes, where traditional methods exhibit significant limitations in handling high-resistance faults and noise interference. To address these challenges, this paper proposes a DC microgrid fault diagnosis method based on dual-terminal information integrated with a combined Teager–CuSum criterion. The Teager energy operator is first utilized to enhance the transient features of current signals, followed by an improved CuSum algorithm for the real-time accumulation of fault features to achieve precise fault detection and classification. Finally, a simulation model is established on the MATLAB/Simulink platform to verify the performance of the proposed scheme. Simulation results demonstrate that the proposed diagnostic method can accurately identify various typical faults while maintaining high sensitivity and reliability even under conditions involving high resistance, communication delays, and noise interference.

Images captured in hazy environments experience gradient reduction due to the scattering of light by atmospheric particles, yet few existing dehazing methods utilize the gradients of hazy images to restore the visibility of the scene. In this paper, we propose an efficient dehazing method based on gradient line prior. By associating image gradients in atmospheric scattering model, we obtain a stable and simple prior, termed the gradient line prior (GLP), that is, in the corresponding hazy images normalized by atmospheric light, there is a linear relationship between the reciprocal of the gradients distributed across different regions of the hazy image plane and the corresponding ratio of pixel intensity to the gradient. For accurate estimation of the transmission map, its refinement is realized through the analysis of the distribution characteristics of pixels in three channels. Experimental results demonstrate that, compared to different dehazing methods, our approach exhibits good detail enhancement and color restoration performance.

Ocean-aware salient object detection (OA-SOD) aims to identify and highlight the most visually distinctive regions in complex and variable underwater imagery under challenging maritime environments, furnishing essential visual cues for underwater environmental perception and large-scale maritime monitoring as well as autonomous operational tasks. Despite the dominance of deep learning-based approaches in OA-SOD, existing techniques remain constrained by inherent limitations, including insufficient multi-scale feature adaptation and blurred saliency boundaries, thereby severely undermining predictive accuracy and robustness. In this study, we propose a robust Bifurcated Interactive Fusion Network (BIFNet) for OA-SOD in maritime environments. The proposed BIFNet contains three primary components, including Hybrid Bifurcated Encoder (HBE), Feature Interactive Boosting Module (FIBM), and Differential Fusion Decoder (DFD). Specifically, HBE is introduced to achieve comprehensive extraction of local details and global contextual features from complex underwater scenarios. FIBM is developed to facilitate cross-scale feature interaction and integration, enhancing the representation of salient objects while suppressing background interference. DFD is designed to perform layer-wise differential operations, enabling progressive resolution restoration and interactive fusion of multi-stage encoder features. Extensive experiments on several popular OA-SOD datasets demonstrate that our proposed BIFNet outperforms state-of-the-art competitors across various evaluation metrics. The source code is available at https://github.com/jixun-dmu/BIFNet.

Nowadays, information security becomes increasing important, and cryptography is an indispensable part of information security. Typically, the encryption algorithms are implemented through performing various operations on plaintext with a secret key to achieve information hiding. Based on the existing Tangent-Delay Ellipse Reflecting Cavity-map System (TD-ERCS) chaotic system and the Traditional Hill Cipher (THC) with a time-invariant key matrix, a Time-Varying Hill Cipher (TVHC) with a time-variant key matrix is proposed in this work. As an effective method in solving time-varying problems, the Zeroing Neural Network (ZNN) is used to effective find the Time-Variant Inversion Key Matrix (TVIKM) for the TVHC decryption process. Moreover, a Novel Fix-time Convergence Fuzzy ZNN (NFCF-ZNN) with superior convergence and robustness is constructed for quickly solving the TVIKM of the TVHC decryption process. The convergence and robustness of NFCF-ZNN for solving TVKIM in the absence and presence of noise are both demonstrated through rigorous mathematical derivation and comparative simulation experiments. Additionally, the successful simulation experiments of the proposed TVHC in grayscale and RGB color images encryption and decryption further validates its effectiveness in practical applications.

Visual simultaneous localization and mapping in indoor dynamic environments remains challenging because moving objects introduce unreliable correspondences, whilst removing dynamic feature points often leaves insufficient static features in low-texture regions. This paper proposes a robust visual SLAM framework that combines semantic-geometric feature filtering with texture-aware feature compensation to improve pose estimation under dynamic interference. The framework first identifies potentially dynamic regions through pixel-level semantic segmentation and removes features associated with highly dynamic objects. To reduce over-filtering and address semi-static objects, depth variation and multi-view geometric consistency are further used to distinguish static and moving feature points across consecutive frames. After dynamic filtering, a learned local feature extractor is introduced to improve descriptor discriminability and feature density in reliable static regions. Two additional modules, semantic confidence weighting and static region feature compensation, adaptively adjust feature extraction thresholds so that low-texture but geometrically useful areas can contribute more stable correspondences. The proposed system is implemented within a visual SLAM pipeline and evaluated on public dynamic RGB-D benchmarks, including TUM and Bonn sequences. Experimental results indicate that the method improves localization robustness in high-dynamic scenarios and reduces trajectory error compared with conventional ORB-based SLAM and several dynamic SLAM baselines. The study demonstrates the potential of combining semantic priors, geometric verification and adaptive feature enhancement for dynamic indoor localization.

Transfer learning has proved effective in cross-domain prediction of the wastewater treatment process (WWTP) by leveraging labeled data from related source domains and unlabeled target data. However, access to original data is not always feasible in practical scenarios due to the demand for data privacy and security, which can make transfer learning methods that aligning distributions utilizes data ineffective. Federated learning is an emerging technology for data privacy and security but requires labeled target data, which is time-consuming. To address these challenges, in this paper, we propose Dynamic Bidirectional Federated Transfer Learning (DBFTL) by combining transfer learning and federated learning, which is the first multi-source domains unsupervised transfer learning framework for privacy-preserving prediction. DBFTL transfers source knowledge to the target domain by fusing source models as the target model with a dynamic weight calculated through the reconstruction error of target data on source models, which is regarded as a similarity of the source domain and target domain. Simultaneously, DBFTL transfers target knowledge to source domains by integrating the target encoder into source models as a regularization term to reduce the domain discrepancy, which is calculated by the distance between the representation features of source data obtained in the source encoder and those in the target encoder. Therefore, iterative bidirectional knowledge transfer achieves the prediction target model learning without compromising privacy security. To validate the effectiveness of DBFTL, we conduct prediction experiments on four WWTPs.

Heterogeneous graph neural networks (HGNN) can capture heterogeneous semantic information in heterogeneous networks, learn the low-dimensional embedding vectors, and use them for downstream tasks. The selection of meta-paths is always the focus of HGNN. Existing HGNN models often employ random selections of meta-paths or utilize all meta-paths with a fixed maximum number of hops, thereby overlooking significant heterogeneous semantic information of graphs and struggling to effectively leverage non-redundant information. To this end, a new Monte Carlo tree search-based heterogeneous graph neural network (MCTS-HGNN) model is developed to search for the appropriate set of meta-paths in heterogeneous graphs automatically, thus overcoming the difficulty of meta-path selection. Subsequently, the meta-path set is decomposed based on aggregation objects and independently applied to a subset of meta-paths by using a customized transformer-based semantic aggregation module, and then the diverse semantic information from meta-paths can be effectively utilized. Furthermore, the information from the meta-path subset is integrated by the graph-level transformer to achieve a comprehensive heterogeneous graph embedding. The learned embedding is evaluated via the downstream task of the heterogeneous graph. Finally, the ablation experiments validate the effectiveness of the module designed for the MCTS-HGNN. The experimental results demonstrate that the MCTS-HGNN outperforms state-of-the-art baselines across all evaluation metrics.

Due to the special characteristics of memristor, the synchronization problem of memristor-based chaotic systems has shown great importance and potential for application in both theoretical and practical fields. Zeroing neural network (ZNN) has always been highly regarded as an effective method to solve the synchronization problem of chaotic systems. However, previous ZNN models have rarely focused on solving the synchronization problem of memristor-based chaotic systems. Based on this, this paper proposes a novel fixed-time convergence robust zeroing neural network (FTCRZNN) model to solve the synchronization problem of memristor-based chaotic systems. The proposed FTCRZNN model has excellent fixed-time convergence and robustness while successfully completing synchronization tasks. The fixed-time convergence and anti-interference ability against external noise of the FTCRZNN model in solving the synchronization problems of chaotic systems are all validated by rigorous mathematical analysis. Moreover, comparative numerical experiments of the proposed FTCRZNN model with other models for the synchronization of memristor-based simplest chaotic systems and four-dimensional memristor-based L & uuml; hyper-chaotic system, as well as the demonstration based on a field programmable gate array (FPGA) further validates the faster convergence speed, higher accuracy and practical application value of the proposed FTCRZNN model.

With the exploitation of marine resources and the development of the marine economy, the realization of high-quality underwater images is crucial for underwater exploration applications. However, the complex aquatic environment often introduces severe visual degradation, including reduced contrast, color distortion, and haze-like effects. To overcome these difficulties, we propose a fusion of multiple feature lines to use underwater image enhancement. Specifically, we observe that the structure-, gradient-, and pixel-based information of underwater hazy images shows uniform surface reflectance within localized areas and exhibits a linear correlation between their structure, gradient, and pixel components and water light, allowing us to reformulate transmission estimation as a feature line construction problem. Given the complexity and variability of underwater scenes, relying on a single feature can lead to inaccurate transmission estimates. To overcome this limitation, we integrate multifeature fusion, leveraging structure-, gradient-, and pixel-based information to enhance the estimation process. Comprehensive evaluations across multiple benchmark data sets confirm that our approach demonstrates high efficacy in the restoration of image color and contrast while achieving greater robustness than existing approaches. The proposed algorithm provides a significant improvement in visual quality, making it well suited for practical underwater imaging applications.

The complexity of neural dynamics heavily depends on the nonlinear activation functions, and a mixed-bipower activation function (MBPAF) with adjustable parameters is designed for the memristive Hopfield neural network (MHNN) to generate complex hyper-chaotic behaviors. Based on the designed MBPAF, a novel MBPAF-memristive Hopfield neural network (MBPAF-MHNN) model is proposed. The complex dynamics of the proposed MBPAF-MHNN model are validated through numerical analyses and further verified via FPGA implementation. Finally, a robust image encryption scheme is designed based on the MBPAF-MHNN model, featuring a plaintext-related “Diffusion-Permutation-Diffusion" architecture with DNA-based operations.

Zeroing neural networks (ZNNs) have emerged as powerful tools for solving time-varying problems, in which the constructed error-zeroing dynamics play a pivotal role in dynamic system computation. Real-time performance and robustness are widely recognized as key criteria for evaluating ZNN effectiveness. With the deepening of research, ZNN design paradigms have evolved from single-performance-driven improvements toward task-oriented cooperative optimization, while research focus has expanded from localized structural innovations to unified, cross-scenario, and transferable modeling frameworks. This paper provides a comprehensive review of the evolutionary trajectory, cooperative optimization designs, and representative applications of ZNNs from the perspective of practical technical pathways, with particular emphasis on several state-of-the-art optimization strategies. Finally, the challenges and future research directions of this field are discussed, aiming to offer theoretical insights for cross-scenario unified modeling and efficient deployment of ZNNs.

In this paper, a method of model predictive control for load frequency control is proposed. The proposed method considers the terminal state into the cost function, which can accelerate convergence speed. And it also can address the realistic constraints. Firstly, a continuous state space model for LFC system is constructed. Because the MPC controller worked on discrete time, the continuous state space model is transformed into discrete state space model. Secondly, due to the quadratic programming is used in this paper to solve the optimal control sequence, the formula derivation procedure is presented in detail. Then, considering the constraints in real LFC system, the constraints matrix is also given. In the end, the simulation in Simulink verifies the effectiveness of the proposed method.