Partially View-aligned Clustering (PVC) addresses the challenge of partial view alignment in multi-view learning by leveraging complementary and consistent information. While existing PVC methods show promise, most rely on distance-based strategies that are sensitive to view-specific details and noise, limiting their robustness. In this work, we propose a novel view alignment strategy that reformulates the alignment task as an anomaly detection problem. Rather than learning a view-alignment matrix that enforces strict one-to-one correspondences across views, we adopt a progressive approach to identify well-aligned samples. Specifically, we sample subsets of data by generating random view combinations from unaligned samples and propose an anomaly combination detection module to evaluate the alignment consistency of these combinations. In addition, our progressive training framework alternates between updating model parameters and selecting high-confidence view combinations for subsequent optimization. By reformulating view alignment as an anomaly detection task, our approach provides a more robust and effective solution to partial view alignment. Experiments on benchmark datasets demonstrate that our method outperforms state-of-the-art approaches in the PVC problem.

Combinatorial optimization problems (COPs) are fundamental to many real-world applications where efficiently producing high-quality solutions is critical. Recent advances in diffusion-based non-autoregressive models have reformulated solving COPs as a generative process, achieving promising results. However, almost all of these methods still suffer from accumulated errors and high inference costs due to the multi-step stochastic denoising process. To address these issues, we propose EFLOCO, an efficient discrete flow matching method for solving COPs, learning structured and deterministic solution trajectories. EFLOCO replaces noise-driven updates with smooth and guided transitions, thereby improves inference stability and quality. Furthermore, we introduce an adaptive time-step scheduler that makes more efforts in critical transition regions, yielding strong performance under few-step constraints. Experiments on standard Traveling Salesman Problems (TSPs) and Asymmetric TSPs (ATSPs) show that our method consistently outperforms both learning-based and heuristic baselines in terms of solution quality and inference speed.

The Vehicle Routing Problem (VRP) is a critical combinatorial optimization problem with wide-reaching real-world applications, particularly in logistics, transportation. While neural network-based VRP solvers have shown impressive results on test instances similar to training data, their performance often degrades when faced with varying scales and unseen distributions, limiting their practical applicability. To overcome these limitations, we introduce DGL (Dynamic Global-Local Information Aggregation), a novel model that combines global and local information to effectively solve VRPs. DGL dynamically adjusts local node selections within a localized range, capturing local invariance across problems of different scales and distributions, thereby enhancing generalization. At the same time, DGL integrates global context into the decision-making process, providing richer information for more informed decisions. Additionally, we propose a replacement-based self-improvement learning framework that leverages data augmentation and random replacement techniques, further enhancing DGL's robustness. Extensive experiments on synthetic datasets, benchmark datasets, and real-world country map instances demonstrate that DGL achieves state-of-the-art performance, particularly in generalizing to large-scale VRPs and real-world scenarios. These results showcase DGL's effectiveness in solving complex, realistic optimization challenges and highlight its potential for practical applications.

Recent studies exploited Large Language Models (LLMs) to autonomously generate heuristics for solving Combinatorial Optimization Problems (COPs), by prompting LLMs to first provide search directions and then derive heuristics accordingly. However, the absence of task-specific knowledge in prompts often leads LLMs to provide unspecific search directions, obstructing the derivation of well-performing heuristics. Moreover, evaluating the derived heuristics remains resource-intensive, especially for those semantically equivalent ones, often requiring omissible resource expenditure. To enable LLMs to provide specific search directions, we propose the Hercules algorithm, which leverages our designed Core Abstraction Prompting (CAP) method to abstract the core components from elite heuristics and incorporate them as prior knowledge in prompts. We theoretically prove the effectiveness of CAP in reducing unspecificity and provide empirical results in this work. To reduce computing resources required for evaluating the derived heuristics, we propose few-shot Performance Prediction Prompting (PPP), a first-of-its-kind method for the Heuristic Generation (HG) task. PPP leverages LLMs to predict the fitness values of newly derived heuristics by analyzing their semantic similarity to previously evaluated ones. We further develop two tailored mechanisms for PPP to enhance predictive accuracy and determine unreliable predictions, respectively. The use of PPP makes Hercules more resource-efficient and we name this variant Hercules-P. Extensive experiments across four HG tasks, five COPs, and eight LLMs demonstrate that Hercules outperforms the state-of-the-art LLM-based HG algorithms, while Hercules-P excels at minimizing required computing resources. In addition, we illustrate the effectiveness of CAP, PPP, and the other proposed mechanisms by conducting relevant ablation studies.

To address the weight coupling problem, certain studies introduced few-shot Neural Architecture Search (NAS) methods, which partition the supernet into multiple sub-supernets. However, these methods often suffer from computational inefficiency and tend to provide suboptimal partitioning schemes. To address this problem more effectively, we analyze the weight coupling problem from a novel perspective, which primarily stems from distinct modules in succeeding layers imposing conflicting gradient directions on the preceding layer modules. Based on this perspective, we propose the Gradient Contribution (GC) method that efficiently computes the cosine similarity of gradient directions among modules by decomposing the Vector-Jacobian Product during supernet backpropagation. Subsequently, the modules with conflicting gradient directions are allocated to distinct sub-supernets while similar ones are grouped together. To assess the advantages of GC and address the limitations of existing Graph Neural Architecture Search methods, which are limited to searching a single type of Graph Neural Networks (Message Passing Neural Networks (MPNNs) or Graph Transformers (GTs)), we propose the Unified Graph Neural Architecture Search (UGAS) framework, which explores optimal combinations of MPNNs and GTs. The experimental results demonstrate that GC achieves state-of-the-art (SOTA) performance in supernet partitioning quality and time efficiency. In addition, the architectures searched by UGAS+GC outperform both the manually designed GNNs and those obtained by existing NAS methods. Finally, ablation studies further demonstrate the effectiveness of all proposed methods.

Recent advances in neural models have shown considerable promise in solving Traveling Salesman Problems (TSPs) without relying on much hand-crafted engineering. However, while non-autoregressive (NAR) approaches benefit from faster inference through parallelism, they typically deliver solutions of inferior quality compared to autoregressive ones. To enhance the solution quality while maintaining fast inference, we propose DEITSP, a diffusion model with efficient iterations tailored for TSP that operates in a NAR manner. Firstly, we introduce a one-step diffusion model that integrates the controlled discrete noise addition process with self-consistency enhancement, enabling optimal solution prediction through simultaneous denoising of multiple solutions. Secondly, we design a dual-modality graph transformer to bolster the extraction and fusion of features from node and edge modalities, while further accelerating the inference with fewer layers. Thirdly, we develop an efficient iterative strategy that alternates between adding and removing noise to improve exploration compared to previous diffusion methods. Additionally, we devise a scheduling framework to progressively refine the solution space by adjusting noise levels, facilitating a smooth search for optimal solutions. Extensive experiments on real-world and large-scale TSP instances demonstrate that DEITSP performs favorably against existing neural approaches in terms of solution quality, inference latency, and generalization ability.

Multimodal models leverage complementary information across modalities to enrich feature representations. While visual information shows potential in representing structure for some combinatorial optimization problems (COPs), its application to complex scheduling like the Flexible Job Shop Scheduling Problem (FJSP) remains underexplored. Current learning-based FJSP solvers predominantly rely on handcrafted state features. This dependence can lead to inconsistencies and may not fully capture the problem's intricate dynamics. Crucially, these methods overlook visual modalities. Visual representations offer a distinct advantage by inherently capturing the global topological structure and complex resource interactions within the FJSP state. Unlike localized handcrafted features, this holistic, structural view provides a richer foundation for understanding scheduling complexity and making informed decisions. To overcome these limitations by leveraging visual information-known for representing topological structures and providing richer state representations-we introduce the AO-framework. This multimodal feature fusion approach enhances handcrafted state features by integrating insights from visual data. Our core contribution is a novel fusion mechanism utilizing orthogonal projection and local attention. Unlike traditional methods that often rely on simple concatenation of visual data, our method uniquely reduces redundancy by projecting global image-derived features onto local handcrafted features. This process extracts distinct information inherent to the visual modality, significantly improving the quality and complementarity of the resulting state features and enabling more informed scheduling decisions. To our knowledge, the AO-framework represents the first multimodal framework applied to scheduling problems, demonstrating the significant potential of visual information in this domain. Extensive experiments across various FJSP solvers and datasets confirm that our framework yields substantial enhancements in solution quality, decision-making capabilities, and generalization.

The rise of smart manufacturing under Industry 4.0 introduces mass customization and dynamic production, demanding more advanced and flexible scheduling techniques. The flexible job-shop scheduling problem (FJSP) has attracted significant attention due to its complex constraints and strong alignment with real-world production scenarios. Current deep reinforcement learning (DRL)-based approaches to FJSP predominantly employ constructive methods. While effective, they often fall short of reaching (near-)optimal solutions. In contrast, improvement-based methods iteratively explore the neighborhood of initial solutions and are more effective in approaching optimality. However, the flexible machine allocation in FJSP poses significant challenges to the application of this framework, including accurate state representation, effective policy learning, and efficient search strategies. To address these challenges, this paper proposes a $\textbf{M}$emory-enhanced $\textbf{I}$mprovement $\textbf{S}$earch framework with he$\textbf{t}$erogeneous gr$\textbf{a}$ph $\textbf{r}$epresentation—$\textit{MIStar}$. It employs a novel heterogeneous disjunctive graph that explicitly models the operation sequences on machines to accurately represent scheduling solutions. Moreover, a memory-enhanced heterogeneous graph neural network (MHGNN) is designed for feature extraction, leveraging historical trajectories to enhance the decision-making capability of the policy network. Finally, a parallel greedy search strategy is adopted to explore the solution space, enabling superior solutions with fewer iterations. Extensive experiments on synthetic data and public benchmarks demonstrate that $\textit{MIStar}$ significantly outperforms both traditional handcrafted improvement heuristics and state-of-the-art DRL-based constructive methods.

With the widespread adoption of Internet Protocol (IP) communication technology and web-based platforms, cloud manufacturing has become a significant hallmark of Industry 4.0. Integrating graph algorithms into these web-enabled environments is crucial as they facilitate the representation and analysis of complex relationships in manufacturing processes, enabling efficient decision-making and adaptability in dynamic environments. As a key scheduling problem in cloud manufacturing, the flexible job-shop scheduling problem (FJSP) finds extensive applications in real-world scenarios. However, traditional FJSP-solving methods struggle to meet the efficiency and adaptability demands of cloud manufacturing due to generalization issues and excessive computational time, while reinforcement learning-based methods fail to learn relationships between FJSP nodes, such as interactions between operations of different jobs, leading to limited interpretability and performance. To address these issues, we propose a dual operation aggregation graph neural network (GNN) for solving FJSP. Specifically, we decouple the disjunctive graph into two distinct graphs, reducing graph density and clarifying relationships between machines and operations, thus enabling more effective aggregation and understanding by neural networks. We develop two distinct graph aggregation methods to minimize the influence of non-critical machine and operation nodes on decision-making while enhancing the model's ability to account for long-term benefits. Additionally, to achieve more accurate multi-objective estimation and mitigate reward sparsity, we design a reward function that simultaneously considers machine efficiency, schedule balance, and makespan minimization. Extensive experimental results on well-known datasets demonstrate that our model outperforms state-of-the-art models and exhibits excellent generalization capabilities, effectively addressing the challenges of cloud manufacturing.

OBJECTIVE: Considering the radiation hazard of X-ray, safer, more convenient and cost-effective ultrasound methods are gradually becoming new diagnostic approaches for scoliosis. For ultrasound images of spine regions, it is challenging to accurately identify spine regions in images due to relatively small target areas and the presence of a lot of interfering information. Therefore, we developed a novel neural network that incorporates prior knowledge to precisely segment spine regions in ultrasound images. MATERIALS AND METHODS: We constructed a dataset of ultrasound images of spine regions for semantic segmentation. The dataset contains 3136 images of 30 patients with scoliosis. And we propose a network model (ICPPNet), which fully utilizes inter-class positional prior knowledge by combining an inter-class positional probability heatmap, to achieve accurate segmentation of target areas. RESULTS: ICPPNet achieved an average Dice similarity coefficient of 70.83% and an average 95% Hausdorff distance of 11.28 mm on the dataset, demonstrating its excellent performance. The average error between the Cobb angle measured by our method and the Cobb angle measured by X-ray images is 1.41 degrees, and the coefficient of determination is 0.9879 with a strong correlation. DISCUSSION AND CONCLUSION: ICPPNet provides a new solution for the medical image segmentation task with positional prior knowledge between target classes. And ICPPNet strongly supports the subsequent reconstruction of spine models using ultrasound images.

The traveling salesman problem (TSP) is a well-known combinatorial optimization problem (COP) with broad real-world applications. Recently, neural networks (NNs) have gained popularity in this research area because as shown in the literature, they provide strong heuristic solutions to TSPs. Compared to autoregressive neural approaches, nonautoregressive (NAR) networks exploit the inference parallelism to elevate inference speed but suffer from comparatively low solution quality. In this article, we propose a novel NAR model named NAR4TSP, which incorporates a specially designed architecture and an enhanced reinforcement learning (RL) strategy. To the best of our knowledge, NAR4TSP is the first TSP solver that successfully combines RL and NAR networks. The key lies in the incorporation of NAR network output decoding into the training process. NAR4TSP efficiently represents TSP-encoded information as rewards and seamlessly integrates it into RL strategies, while maintaining consistent TSP sequence constraints during both training and testing phases. Experimental results on both synthetic and real-world TSPs demonstrate that NAR4TSP outperforms five state-of-the-art (SOTA) models in terms of solution quality, inference speed, and generalization to unseen scenarios.

Neural construction models have shown promising performance for Vehicle Routing Problems (VRPs) by adopting either the Autoregressive (AR) or Non-Autoregressive (NAR) learning approach. While AR models produce high-quality solutions, they generally have a high inference latency due to their sequential generation nature. Conversely, NAR models generate solutions in parallel with a low inference latency but generally exhibit inferior performance. In this paper, we propose a generic Guided Non-Autoregressive Knowledge Distillation (GNARKD) method to obtain high-performance NAR models having a low inference latency. GNARKD removes the constraint of sequential generation in AR models while preserving the learned pivotal components in the network architecture to obtain the corresponding NAR models through knowledge distillation. We evaluate GNARKD by applying it to three widely adopted AR models to obtain NAR VRP solvers for both synthesized and real-world instances. The experimental results demonstrate that GNARKD significantly reduces the inference time (4-5 times faster) with acceptable performance drop (2-3%). To the best of our knowledge, this study is first-of-its-kind to obtain NAR VRP solvers from AR ones through knowledge distillation.

Brain tumor segmentation (BTS) has been studied from handcrafted engineered features to conventional machine learning (ML) methods, followed by the cutting-edge deep learning approaches. Each recent approach has attempted to overcome the challenges of previous methods and brought conveniences in efficacy, throughput, computation, explainability, investigation, and interpretability. Recently, deep learning (DL) algorithms show excellent performance regarding diverse fields, including image process, computer vision, health analytics, autonomous vehicles, and natural language processes; however, ultimately impediment in making the artificial intelligence explainable and interpretable to clinicians while dealing with critical health informatics and radiomics. Besides the sophisticated deep learning models for brain tumor segmentation, notorious notions like explainability, investigation, trust, and interpretability of DL raised significant concerns for clinicians in their domains. Among many DL methods, the neuro-symbolic learning (NSL) concept has gained more attention as it can contribute to explainable and interpretable AI. In the current study, we survey the prominent approaches, from handcrafted engineering conventional ML to deep learning algorithms, highlight the challenges in DL algorithms, and propose NSL architectures for BTS. Compared to existing surveys, our study not only outlines handcrafted to DL methods for BTS but also proposed explainable and interpretable pipelines appropriate for clinical practices. Our study can better facilitate novice learners in explainable AI and propose efficient, robust, interpretable DL models to facilitate the diagnosis, prognosis, and treatment of BTS.

Cartesian Genetic Programming (CGP) has often been applied for Neural Architecture Search (NAS). However, the performance of CGP is less than ideal when searching for architectures with limited computing resources. To better facilitate NAS with limited computing resources, this paper proposes a crossover operator, a light-weighted age mechanism, and two adaptive mutation operators as the novel components in our Efficient Cartesian Genetic Programming (ECGP) method. To assess the performance of ECGP, we conduct extensive experiments on three text classification task datasets. The experimental results demonstrate that ECGP outperforms other NAS methods, requiring only hundreds of fitness evaluations to find architectures with competitive accuracy compared with human-designed models. Additionally, the ECGP-evolved architectures are shown as converging fast and stably, and having high-level transferability with merely a 1-2% accuracy drop. Ablation studies demonstrate the effectiveness of the proposed operators and age mechanism, and identify GRU as the most critical function in the text classification task. Finally, we summarize three design principles observed from the ECGP-evolved architectures that are in line with human-design strategies. To the best of our knowledge, this work introduces the first attention-derived NAS benchmark for the text classification task.

Automatic heart sound diagnosis plays an important role in the early detection of cardiovascular diseases. Phonocardiogram (PCG) signals are often used in this field f or its low cost and non-invasive advantages. In this paper, we design a new time and time-frequency features integrated CNN (TTFI-CNN) model for heart sound signals detection. In the model, a 1D CNN and a BiLSTM are combined into 1D CRNN module to extract temporal features from the original PCG signal, and a 2D CNN module is applied to capture high-level features from time-frequency domain MFCCs inputs. The outputs of the two modules are recalibrated by attention mechanism to selectively emphasize informative features and suppress less useful ones. To verify the proposed TTFI-CNN model, it is applied to two public datasets with different classification t asks (binary and multiclassification). The TTFI-CNN model has achieved 97.15% accuracy, 97.13% sensitivity, and 97.17% specificity on physionet/cinc database, and obtained 3.31 and 2.61 precision scores on the PASCAL database A and B, respectively. Compared with the previous state-of-the-art methods, the TTFI-CNN performs best on all the above metrics. https://github.com/XxxNnnSssWww/TTFI-CNN.

MOTIVATION: Mislabeled samples often appear in gene expression profile because of the similarity of different sub-type of disease and the subjective misdiagnosis. The mislabeled samples deteriorate supervised learning procedures. The LOOE-sensitivity algorithm is an approach for mislabeled sample detection for microarray based on data perturbation. However, the failure of measuring the perturbing effect makes the LOOE-sensitivity algorithm a poor performance. The purpose of this article is to design a novel detection method for mislabeled samples of microarray, which could take advantage of the measuring effect of data perturbations. RESULTS: To measure the effect of data perturbation, we define an index named perturbing influence value (PIV), based on the support vector machine (SVM) regression model. The Column Algorithm (CAPIV), Row Algorithm (RAPIV) and progressive Row Algorithm (PRAPIV) based on the PIV value are proposed to detect the mislabeled samples. Experimental results obtained by using six artificial datasets and five microarray datasets demonstrate that all proposed methods in this article are superior to LOOE-sensitivity. Moreover, compared with the simple SVM and CL-stability, the PRAPIV algorithm shows an increase in precision and high recall. AVAILABILITY: The program and source code (in JAVA) are publicly available at http://ccst.jlu.edu.cn/CSBG/PIVS/index.htm