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.

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.

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.

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.

BACKGROUND: Accumulating evidence has demonstrated that long non-coding RNAs (lncRNAs) are closely associated with human diseases, and it is useful for the diagnosis and treatment of diseases to get the relationships between lncRNAs and diseases. Due to the high costs and time complexity of traditional bio-experiments, in recent years, more and more computational methods have been proposed by researchers to infer potential lncRNA-disease associations. However, there exist all kinds of limitations in these state-of-the-art prediction methods as well. RESULTS: In this manuscript, a novel computational model named FVTLDA is proposed to infer potential lncRNA-disease associations. In FVTLDA, its major novelty lies in the integration of direct and indirect features related to lncRNA-disease associations such as the feature vectors of lncRNA-disease pairs and their corresponding association probability fractions, which guarantees that FVTLDA can be utilized to predict diseases without known related-lncRNAs and lncRNAs without known related-diseases. Moreover, FVTLDA neither relies solely on known lncRNA-disease nor requires any negative samples, which guarantee that it can infer potential lncRNA-disease associations more equitably and effectively than traditional state-of-the-art prediction methods. Additionally, to avoid the limitations of single model prediction techniques, we combine FVTLDA with the Multiple Linear Regression (MLR) and the Artificial Neural Network (ANN) for data analysis respectively. Simulation experiment results show that FVTLDA with MLR can achieve reliable AUCs of 0.8909, 0.8936 and 0.8970 in 5-Fold Cross Validation (fivefold CV), 10-Fold Cross Validation (tenfold CV) and Leave-One-Out Cross Validation (LOOCV), separately, while FVTLDA with ANN can achieve reliable AUCs of 0.8766, 0.8830 and 0.8807 in fivefold CV, tenfold CV, and LOOCV respectively. Furthermore, in case studies of gastric cancer, leukemia and lung cancer, experiment results show that there are 8, 8 and 8 out of top 10 candidate lncRNAs predicted by FVTLDA with MLR, and 8, 7 and 8 out of top 10 candidate lncRNAs predicted by FVTLDA with ANN, having been verified by recent literature. Comparing with the representative prediction model of KATZLDA, comparison results illustrate that FVTLDA with MLR and FVTLDA with ANN can achieve the average case study contrast scores of 0.8429 and 0.8515 respectively, which are both notably higher than the average case study contrast score of 0.6375 achieved by KATZLDA. CONCLUSION: The simulation results show that FVTLDA has good prediction performance, which is a good supplement to future bioinformatics research.

Environmental contaminations such as fine particulate matter (PM2.5) and ultraviolet (UV) are expanding public health concerns globally. Existing centralized monitoring stations, however, are unable to properly estimate human exposure due to the low resolution spatiotemporal data. Wireless Sensor Network (WSN) uses real-time capable instrumentation could not only provide fine-grained readings of multiple environmental factors, but also create real-time mapping of the contaminants. In this paper we present a WSN system which is capable of sensing multiple environmental factors, collecting data from multiple dispersed sensor nodes and displaying the aggregated data in real-time. Each individual sensor node is capable of probing multiple factors, including temperature, humidity, atmospheric pressure, PM2.5, UV radiation, and geographical location. Sensor data are transmitted to a server, which then be stored into a database through Wi-Fi networks. Each sensor node is portable enough to be carried for personal use, enabling broad potential application of our system.