Vision-language pre-training models (VLPs) demonstrate strong multimodal understanding and zero-shot generalization, yet remain vulnerable to adversarial examples, raising concerns about their reliability. Recent work, Test-Time Counterattack (TTC), improves robustness by generating perturbations that maximize the embedding deviation of adversarial inputs using PGD, pushing them away from their adversarial representations. However, due to the fundamental difference in optimization objectives between adversarial attacks and counterattacks, generating counterattacks solely based on gradients with respect to the adversarial input confines the search to a narrow space. As a result, the counterattacks could overfit limited adversarial patterns and lack the diversity to fully neutralize a broad range of perturbations. In this work, we argue that enhancing the diversity and coverage of counterattacks is crucial to improving adversarial robustness in test-time defense. Accordingly, we propose Directional Orthogonal Counterattack (DOC), which augments counterattack optimization by incorporating orthogonal gradient directions and momentum-based updates. This design expands the exploration of the counterattack space and increases the diversity of perturbations, which facilitates the discovery of more generalizable counterattacks and ultimately improves the ability to neutralize adversarial perturbations. Meanwhile, we present a directional sensitivity score based on averaged cosine similarity to boost DOC by improving example discrimination and adaptively modulating the counterattack strength. Extensive experiments on 16 datasets demonstrate that DOC improves adversarial robustness under various attacks while maintaining competitive clean accuracy.

Diffusion models have demonstrated strong capabilities in generating high-fidelity 3D human poses, yet their iterative nature and multi-hypothesis requirements incur substantial computational cost. In this paper, we propose an efficient diffusion-based 3D human pose estimation framework with a Hierarchical Temporal Pruning (HTP) strategy, which dynamically prunes redundant pose tokens across both frame and semantic levels while preserving critical motion dynamics. HTP operates in a staged, top-down manner: (1) Temporal Correlation-Enhanced Pruning (TCEP) identifies essential frames by analyzing inter-frame motion correlations through adaptive temporal graph construction; (2) Sparse-Focused Temporal MHSA (SFT MHSA) leverages the resulting frame-level sparsity to reduce attention computation, focusing on motion-relevant tokens; and (3) Mask-Guided Pose Token Pruner (MGPTP) performs fine-grained semantic pruning via clustering, retaining only the most informative pose tokens. Experiments on Human3.6M and MPI-INF-3DHP show that HTP reduces training MACs by 38.5%, inference MACs by 56.8%, and improves inference speed by an average of 81.1% compared to prior diffusion-based methods, while achieving state-of-the-art performance.

While adversarial training is an effective defense method against adversarial attacks, it notably increases the training cost. To this end, fast adversarial training (FAT) is presented for efficient training and has become a hot research topic. However, FAT suffers from catastrophic overfitting, which leads to a performance drop compared with multi-step adversarial training. However, the cause of catastrophic overfitting remains unclear and lacks exploration. In this paper, we present an example taxonomy in FAT, which suggests that catastrophic overfitting is correlated with the imbalance between the inner and outer optimization in FAT. Furthermore, we investigated the impact of varying degrees of training loss, revealing a correlation between training loss and catastrophic overfitting. Based on these observations, we redesign the loss function in FAT with the proposed dynamic label relaxation to concentrate the loss range and reduce the impact of misclassified examples. Meanwhile, we introduce batch momentum initialization to enhance diversity and prevent catastrophic overfitting in an efficient manner. Furthermore, we also propose Catastrophic Overfitting aware Loss Adaptation (COLA), which employs a separate training strategy for examples based on their loss degree. Our proposed method, named example taxonomy aware FAT (ETA), establishes an improved paradigm for FAT. Experiment results demonstrate that our ETA achieves higher robust accuracy than all other evaluated methods. Comprehensive experiments on four standard datasets demonstrate the competitiveness of our method. The source code and model checkpoints will be publicly released.

This article introduces a learning-based model predictive control (MPC) framework that leverages Gaussian mixture models (GMMs) to address dynamic system uncertainties effectively. To address the limitations of traditional MPC methods in handling system disturbances and uncertainties, we integrate GMM into the MPC framework to model and account for these disturbances probabilistically. By reformulating the chance constraints within this framework, the proposed approach provides high-probability safety guarantees. Specifically, GMM can capture complex disturbance distributions in dynamic systems compared with traditional Gaussian processes, thereby enabling more precise prediction and optimization within the MPC loop. This ensures that the resulting control strategies not only satisfy safety constraints but also enhance system performance. Experimental evaluations demonstrate that the proposed method achieves superior performance in satisfying high-probability safety requirements while enhancing the overall robustness of the system. Compared to conventional MPC approaches, the proposed method can effectively tackle the challenges posed by uncertainties, ensuring stability and safety under diverse conditions. This approach has broad applications in domains that require robust control under uncertainties, including autonomous driving, robotic manipulation, and other complex engineering systems.

This paper proposes a novel dual-mode dynamic event-triggered control framework designed specifically for nonlinear cyber-physical systems (CPS) subject to constraints and bounded disturbances. The framework addresses critical challenges in balancing system performance, computation efficiency, and communication overhead. To achieve this, two distinct control modes are developed based on the system state’s location relative to the terminal set. When the system state lies outside the terminal set, Mode 1 is activated. This mode implements an event-triggered model predictive control approach, combining a dynamic threshold with a PID-based triggering mechanism. These features notably reduce the frequency of triggering events while also lowering computation and communication costs. In contrast, Mode 2 becomes active when the system state lies within the terminal set. This mode employs an event-triggered feedback control approach aimed at further reducing communication costs while maintaining control efficiency. In addition, rigorous theoretical analysis is conducted to establish the recursive feasibility, stability, and exclusion of Zeno behavior within the proposed framework. Finally, numerical simulations are performed to validate the superiority of the proposed method.

This work proposes a variant of Colored Traveling Salesman Problem (CTSP) called Capacitated Colored-traveling-salesman Problem with Time-windows (CCPT), which comes from time-sensitive logistics applications. CCPT is first formulated via mathematical programming formulations, and an Elite-guided Memetic Algorithm (EMA) is developed to tackle it. EMA is able to preserve an active archive of elites during an evolution process. It comprises three schemes, i.e., neighborhood-list-2-opt, relocation move, and cross-arc exchange. They are organized in a variable neighborhood descent framework to optimize a specific high-quality individual. Ablation studies fully show their importance for EMA’s performance. 28 CCPT cases are designed based on representative traveling salesman problem instances to conduct benchmark tests. The statistical comparison shows that EMA is significantly better than Variable Neighborhood Search (VNS), Delaunay-triangulation-based VNS, local search, and memetic algorithm in over 85% of the cases. It achieves faster convergence to the solutions than its competitors.Note to Practitioners—This work is motivated by practical needs for distribution logistics with time-sensitive requirements. A capacitated colored-traveling-salesman problem with time-windows is modeled and can be applied to time-sensitive transportation tasks with multiple goods. An elite-guided memetic algorithm is developed to tackle this problem. It executes the local optimization on a specific high-quality solution during the search process. Extensive comparisons demonstrate that the proposed algorithm can provide decision-makers with significantly better routes than other state-of-the-art algorithms.

Einstein Würfelt Nicht(EWN) is a stochastic game involving random information and uncertainty. Due to inherent randomness, many algorithms struggle to effectively solve EWN, and their level of play requires enhancement. In this article, a novel belief state-based upper confidence bound for trees (BS-UCT) algorithm is introduced for the EWN game. The algorithm addresses the challenges posed by random information in EWN by maintaining a set of belief states to estimate the impact of dice rolls, effectively improving the efficiency of Monte Carlo Tree Search under uncertainty. We also propose a self-playing method of warm-start reinforcement learning with an improved value network structure, using a pretrained model to generate high-quality data and incorporating a coordinate attention mechanism to improve feature processing. Finally, an efficient lock-free parallel search algorithm is presented, enabling rooted parallel tree search and significantly improving the search efficiency of BS-UCT during simulation. The experimental results show that the BS-UCT algorithm has an advantage over other baseline methods, with 89%, 70%, 74%, and 64% win rates for random, beta pruning, normal UCT, and quick neural network tree search (QNNTS) algorithm, respectively, highlighting its effectiveness in the processing of random information and achieving high performance in EWN.

Adversarial training has achieved remarkable advancements in defending against adversarial attacks. Among them, fast adversarial training (FAT) is gaining attention for its ability to achieve competitive robustness with fewer computing resources. Existing FAT methods typically employ a uniform strategy that optimizes all training data equally without considering the influence of different examples, which leads to an imbalanced optimization. However, this imbalance remains unexplored in the field of FAT. In this paper, we conduct a comprehensive study of the imbalance issue in FAT and observe an obvious class disparity regarding their performances. This disparity could be embodied from a perspective of alignment between clean and robust accuracy. Based on the analysis, we mainly attribute the observed misalignment and disparity to the imbalanced optimization in FAT, which motivates us to optimize different training data adaptively to enhance robustness. Specifically, we take disparity and misalignment into consideration. First, we introduce self-knowledge guided regularization, which assigns differentiated regularization weights to each class based on its training state, alleviating class disparity. Additionally, we propose self-knowledge guided label relaxation, which adjusts label relaxation according to the training accuracy, alleviating the misalignment and improving robustness. By combining these methods, we formulate the Self-Knowledge Guided FAT (SKG-FAT), leveraging naturally generated knowledge during training to enhance the adversarial robustness without compromising training efficiency. Extensive experiments on four standard datasets demonstrate that the SKG-FAT improves the robustness and preserves competitive clean accuracy, outperforming the state-of-the-art methods. Code and checkpoints are available at SFG-FAT Code Implementation.

Vein recognition technologies have become one of the primary solutions for high-security identification systems. However, the issue of biometric information leakage can still pose a serious threat to user privacy and anonymity. Currently, there is no cancelable biometric template generation scheme specifically designed for vein biometrics. Therefore, this paper proposes an innovative cancelable vein biometric generation scheme: ColorVein. Unlike previous cancelable template generation schemes, ColorVein does not destroy the original biometric features and introduces additional color information to grayscale vein images. This method significantly enhances the information density of vein images by transforming static grayscale information into dynamically controllable color representations through interactive colorization. ColorVein allows users/administrators to define a controllable pseudo-random color space for grayscale vein images by editing the position, number, and color of hint points, thereby generating protected cancelable templates. Additionally, we propose a new secure center loss to optimize the training process of the protected feature extraction model, effectively increasing the feature distance between enrolled users and any potential impostors. Finally, we evaluate ColorVein’s performance on all types of vein biometrics, including recognition performance, unlinkability, irreversibility, and revocability, and conduct security and privacy analyses. ColorVein achieves competitive performance compared with state-of-the-art methods.

Security concerns in large-scale networked environments are becoming increasingly critical. To further improve the algorithm security from the design perspective of decentralized optimization algorithms, we introduce a new measure: Privacy Leakage Frequency (PLF), which reveals the relationship between communication and privacy leakage of algorithms, showing that lower PLF corresponds to lower privacy budgets. Based on such assertion, a novel differentially private decentralized primal-dual algorithm named DP-RECAL is proposed to take advantage of operator splitting method and relay communication mechanism to experience less PLF so as to reduce the overall privacy budget. To the best of our knowledge, compared with existing differentially private algorithms, DP-RECAL presents superior privacy performance and communication complexity. In addition, with uncoordinated network-independent stepsizes, we prove the convergence of DP-RECAL for general convex problems and establish a linear convergence rate under the metric subregularity. Evaluation analysis on least squares problem and numerical experiments on real-world datasets verify our theoretical results and demonstrate that DP-RECAL can defend some classical gradient leakage attacks.

This article proposes an extended zero-gradient-sum (EZGS) approach for solving constrained distributed optimization with free initialization and desired convergence properties. A Newton-based continuous-time algorithm is first designed for general constrained optimization, which is adapted to handle inequality constraints by using log-barrier penalty functions. Then, a general class of EZGS dynamics is developed to address equation-constrained distributed optimization, where an auxiliary dynamics is introduced to ensure the final ZGS property from any initialization. It is demonstrated that for typical consensus protocols and auxiliary dynamics, the proposed EZGS dynamics can achieve the performance with exponential/finite/fixed/prescribed-time (PT) convergence. Particularly, the nonlinear consensus protocols for finite-time EZGS algorithms allow for heterogeneous power coefficients. Significantly, the proposed PT EZGS dynamics is continuous, uniformly bounded, and capable of reaching the optimal solution in a single stage. Furthermore, the barrier method is employed to handle the inequality constraints effectively. Finally, the efficiency and performance of the proposed algorithms are validated through numerical examples, highlighting their superiority over existing methods. In particular, by selecting appropriate protocols, the proposed EZGS dynamics can achieve desired convergence performance.

In this paper, we address a novel and comprehensive social welfare maximization (SWM) problem for the optimal energy management in a smart grid. The objective is to maximize the total social welfare of dispatchable devices in the smart grid while satisfying certain constraints. Each device in the smart grid is required to meet its local power constraints, and the system as a whole maintains supply-demand balance, taking into account transmission losses and stochastic output power. To facilitate distributed algorithm design, we initially transform the SWM problem into an equivalent dual problem, which is a distributed composite optimization problem. Subsequently, a novel fully distributed proximal alternating direction method of multipliers (PADMM) is proposed, where each agent can autonomously select non-coordinated step size parameters based solely on local information, independent of other agents and the network structure. Detailed convergence analysis is provided, and a worst-case$\mathcal{O}(1/k)$convergence rate is established in the non-ergodic sense. Finally, several numerical experiments are conducted to confirm the effectiveness of the proposed algorithm.

A colored traveling salesman problem (CTSP) is a generalization of the well-known multiple traveling salesman problem, which introduces colors to distinguish the accessibility of its cities to salesmen. This work proposes a city/customer-centric model called cumulative capacitated CTSP (C2-CTSP) to tackle some practical problems with fast response requirements. Its hypergraph and mathematical programming formulations are developed for the first time. A general variable neighborhood search (GVNS) metaheuristic is designed to solve it. Specifically, greedy backtracking is proposed to initialize a solution taking into account the cumulative cost and two constraints including colors and capacities. Next, 2-swap, reinsertion, and double-bridge operations are randomly selected and carried out to execute the perturbation. Moreover, neighborhood-list-2-opt, relocation move, and generalized partition crossover are organized as variable neighborhood descent to constitute the local search for better solutions. Extensive experiments are conducted to compare the proposed GVNS with four genetic algorithms, two hybrid ant colony systems, two variable neighborhood search methods, and a perturb-based local search in 20 regular and random cases. The statistical results demonstrate that GVNS is superior to all competitors tuned by irace package in terms of both search ability and convergence rate. In addition, the study of six GVNS variants lacking different operators validates the significant role of each corresponding operator in GVNS's outstanding performance.

In this article, we establish the local and global exponential convergence of a primal-dual dynamics (PDD) for solving equality-constrained optimization problems without strong convexity and full row rank assumption on the equality constraint matrix. Under the metric subregularity of Karush-Kuhn-Tucker (KKT) mapping, we prove the local exponential convergence of the dynamics. Moreover, we establish the global exponential convergence of the dynamics in an invariant subspace under a technically designed condition which is weaker than strong convexity. As an application, the obtained theoretical results are used to show the exponential convergence of several existing state-of-the-art primal-dual algorithms for solving distributed optimization without strong convexity. Finally, we provide some experiments to demonstrate the effectiveness of our results.

The application of neural network models to solve combinatorial optimization has recently drawn much attention and shown promising results in dealing with similar problems, like Travelling Salesman Problem. The neural network allows to learn solutions based on given problem instances, using reinforcement learning or supervised learning. In this paper, we present a novel end-to-end method to solve routing problems. In specific, we propose a gated cosine-based attention model (GCAM) to train policies, which accelerates the training process and the convergence of policy. Extensive experiments on different scale of routing problems show that the proposed method can achieve faster convergence of the training process than the state-of-the-art deep learning models while achieving solutions of the same quality.

This article studies the finite-time (FT) convergence of a fast primal-dual gradient dynamics (PDGD), called FT-PDGD, for solving constrained optimization with general constraints and cost functions. Based on the nonsmooth analysis and augmented Lagrangian function, sufficient conditions are established for FT-PDGD to enable the realization of primal-dual optimization in FT. A specific class of nonsmooth sign-preserving functions is defined and analyzed for ensuring FT stability. Particularly, the matrix of linear equations is not required to have a full-row rank and the cost function is not necessary to be strictly convex. By introducing auxiliary variables for general linear inequality constraints, reduced sufficient conditions are further derived for the optimization with linear equality and inequality constraints after transformation. In addition, by the nonsmooth analysis, the switching dynamics evolved in both primal and dual variables are carefully investigated and the upper bound on the convergence time is explicitly provided. Moreover, as applications of FT-PDGD, several FT convergent distributed algorithms are designed to solve distributed optimization with separated and coupled linear equations, respectively. Finally, two case studies are conducted to show the performance of the proposed algorithms.

Neural network-based models have been implemented to predict various health indicators of asphalt pavement using pavement historical detection data. Unfortunately, their accuracy and reliability are not acceptable owing to their shallow architecture. To solve the issue, this study proposed an improved Transformer network to predict asphalt pavement health, called the Transformer with forward and reversed time series (Transformer FRTS). In terms of the input data, Transformer FRTS uses a new data form, so-called the random difference time series, to reduce the time dependency of the network prediction. In terms of the network architecture, the proposed network uses its encoder and decoder to obtain the data association from the forward and reverse time series. In addition, Transformer FRTS uses a post-processing decision criterion to improve the accuracy and reliability of prediction. The numerical experiment using the detection data from RIOHTrack full-scale track demonstrates that the proposed network has state-of-the-practice performance in asphalt pavement health prediction.

This article investigates the finite-time and fixed-time synchronization for memristive neural networks (MNNs) with mixed time-varying delays under the adaptive aperiodically intermittent adjustment strategy. Different from previous works, this article first employs the aperiodically intermittent adjustment feedback control and adaptive control to drive the MNNs to achieve synchronization in finite time and fixed time. First of all, according to the theories of set-valued mappings and differential inclusions, the error MNNs is derived, and its finite-time and fixed-time stability problems are discussed by applying the Lyapunov function method and some LMI techniques. Moreover, by meticulously designing an effective aperiodically intermittent adjustment with adaptive updating law, sufficient conditions that guarantee the finite-time and fixed-time synchronization of the drive-response MNNs are obtained, and the settling time is explicitly estimated. Finally, three numerical examples are provided to illustrate the validity of the obtained theoretical results.

In this paper, some efficient criteria for finite-time consensus of a class of nonsmooth opinion dynamics over a digraph are established. The lower and upper bounds on the finite settling time are obtained based respectively on the maximal and minimal cut capacity of the digraph. By using tools of the nonsmooth theory and algebraic graph theory, the Carathéodory and Filippov solutions of nonsmooth opinion dynamics are analyzed and compared in detail. In the sense of Filippov solutions, the dynamic consensus is demonstrated without a leader and the finite-time bipartite consensus is also investigated in a signed digraph correspondingly. To achieve a predetermined consensus, a leader agent is introduced to the considered agent networks. As an application, the nonsmooth compartmental dynamics in the presence of a leader is embedded in the proposed continuous-time protocol to solve the distributed optimization problems over an unbalanced digraph. The convergence to the optimal solution by using the proposed distributed algorithm is guaranteed with appropriately selected parameters. To verify the effectiveness of the proposed protocols, three numerical examples are performed.

The safety and stability of modern power systems are undergoing various challenges, introduced by the integration of fluctuating renewable generation. In this paper, we present a hierarchical model predictive power dispatch and control strategy for a class of modern power systems with price-elastic controllable loads (CLs) in energy Internet. In the upper-level optimization, a generalized multiperiod economic dispatch (GMPED) problem is organized within an electricity market environment aiming at maximizing the social welfare. Specifically, the price-elastic CLs are aggregated in controllable load aggregators (CLAs) to participate in the market competition. A novel utility function of the price-elastic CLAs is proposed for market demand response. By solving GMPED, the power setpoints of plants over the further periods are produced, as well as the real-time price for the optimal response of price-elastic CLAs. In the second-level operation, two types of model predictive control-based controllers for both the supply and demand sides are designed for power tracking control by considering the model of the power system and aggregated thermostatically controlled loads. Finally, two case studies are performed on the IEEE 14- and 39-bus system, respectively, which shows that the system-frequency deviation and system cost are reduced significantly with the proposed methods.

In this paper, we study a special class of distributed convex optimization problems-distributed parametric consensus optimization problem (DPCOP), for which a two-stage optimization method including primal decomposition and distributed consensus is provided. Different from traditional distributed optimization problems driving all the local states to a common value, DPCOP aims to solve a system-wide problem with partial common parameters shared amongst local agents in a distributed way. To relax the restriction on the topology, a distributed projected subgradient method is applied in distributed consensus stage to achieve the consensus of local estimated parameters, while the subgradients can be obtained by solving a multiparametric problem locally. For a special class of DPCOPs, a discrete-time distributed algorithm with exponential rate of convergence is provided. Furthermore, the proposed two-stage optimization method is applied to a distributed model predictive consensus problem in order to reach an optimal output consensus at equilibrium points for all agents. The stability analysis for the proposed algorithm is further given. Two case studies on a heterogenous multiagent system with high-order integrator dynamics are provided to verify the effectiveness of proposed methods.

A compound control strategy is proposed for frequency regulation of source-grid-load systems in which power sources, power grids, and loads are all participating in the process. Here, power sources are conventional thermal generators, including new energy power generations, and loads are composed of energy storage units (ESUs) and grid-friendly appliances (GFAs). The proposed control scheme includes two levels of operations, with the upper level to be a model predictive control (MPC) for generators and the lower level to be a distributed leader-following consensus control strategy for multiple ESUs. For new energy power generations, the power outputs are restricted on a constant value during a sampling period based on a predicted generating curve. GFAs respond to the system frequency by regulating their active power consumption. Simulations on a single power system and three interconnected area power systems are provided to verify the effectiveness of the proposed compound control strategy.