Hyperspectral image-anomaly detection (HSI-AD) has become one of the research hotspots in the field of remote sensing. Because HSI’s features of integrating image and spectrum provide a considerable data basis for abnormal object detection, HSI-AD has a huge application potential in HSI analysis. It is difficult to effectively extract a large number of nonlinear features contained in HSI data using traditional machine learning methods, and deep learning has incomparable advantages in the extraction of nonlinear features. Therefore, deep learning has been widely used in HSI-AD and has shown excellent performance. This review systematically summarizes the related reference of HSI-AD based on deep learning and classifies the corresponding methods into performance comparisons. Specifically, we first introduce the characteristics of HSI-AD and the challenges faced by traditional methods and introduce the advantages of deep learning in dealing with these problems. Then, we systematically review and classify the corresponding methods of HSI-AD. Finally, the performance of the HSI-AD method based on deep learning is compared on several mainstream data sets, and the existing challenges are summarized. The main purpose of this article is to give a more comprehensive overview of the HSI-AD method to provide a reference for future research work.

The Traveling Salesman Problem (TSP) is a classic combinatorial optimization problem with broad applications in logistics and smart agriculture. However, despite significant progress in Transformer-based deep reinforcement learning methods, two major challenges remain. First, standard linear embedding layers struggle to capture dynamic local geometric relationships between nodes. Second, the quadratic complexity of self-attention in the decoder hinders efficiency in large-scale TSP instances. To address these issues, this paper proposes a Dynamic Topology-Aware Linear Attention Network (DTALAN). The encoder employs a Channel-aware Topological Refinement Graph Convolution (CTRGC) module to model local geometric structures and a Global Attention Mechanism (GAM) for adaptive feature recalibration. The decoder introduces a temporal locality-aware attention mechanism that focuses only on recently visited nodes, reducing self-attention complexity from quadratic to linear while preserving solution quality. The policy network is trained using the REINFORCE algorithm with baseline and the Adam optimizer. Experiments on random instances and the TSPLIB benchmark show that DTALAN outperforms leading deep reinforcement learning methods in both optimality gap and inference efficiency. For TSP100, it achieves an optimality gap of 0.55%, producing near-optimal solutions. Ablation studies confirm that both the improved CTRGC and enhanced GAM modules are essential to these results.

As a classic NP-hard problem, the Traveling Salesman Problem (TSP) exhibits exponentially increasing complexity with node quantity, making optimal solutions difficult for large-scale instances. Traditional exact and heuristic algorithms still struggle to balance computational cost with global optimality. Recently, deep learning has enabled end-to-end sequence modeling for TSP, yet existing models face limitations in global feature modeling, cross-scale generalization, and decoding stability. To address these issues, this study proposes a multi-scale deep optimization model based on an encoder-decoder architecture. In the encoding phase, an Exponential Moving Average (EMA) mechanism enhances global spatial correlation via multi-scale feature smoothing and dynamic weighting while suppressing feature noise. In the decoding phase, a Triplet-Reasoning attention mechanism captures high-order spatial dependencies through three-branch interaction (node, edge, path), balancing local coherence with global optimization. Additionally, a dynamic sampling strategy mitigates training-inference distribution shifts to improve generalization. Experimental results on benchmark datasets show that the proposed model outperforms mainstream deep learning methods in path length and optimality gap, demonstrating superior stability and global optimality, particularly on medium and large-scale instances. This work validates the effectiveness of the multi-scale EMA and Triplet-Reasoning mechanisms, providing a new direction for deep learning-based graph optimization research.

Uncertainty in travel and service times poses significant challenges for vehicle routing in logistics systems. This paper proposes a stochastic model predictive control (SMPC) strategy to manage a Vehicle Routing Problem with time windows (VRPTW) under stochastic service times with correlation across customers. The approach combines a dynamic optimization model with single and joint chance constraints and a forecasting tool for updating travel plans as new information becomes available. A deterministic reformulation of the stochastic constraints is developed so that the problem can be solved via mixed-integer programming. The aim of this paper is to demonstrate that the SMPC strategy can maintain a high level of time-window reliability (meeting customer time windows with high probability) at a reasonable cost by re-optimizing routes over a moving horizon. In numerical case studies, the SMPC approach achieves the desired reliability levels while incurring only modest increases in total cost, and it flexibly adjusts the cost–risk tradeoff by switching between single and joint chance constraints. These results illustrate the potential of the proposed method for real-time distribution routing under uncertainty and highlight the novel contribution of integrating chance-constrained optimization with Model Predictive Control in a VRPTW context.