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.

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.

Feature selection plays a significant role in data mining and machine learning. It is challenging to determine how many features are necessary to form an optimal feature subset. To address this challenge, an innovative visual 2D feature selection framework is introduced, in which the feature discernibility and independence are defined to evaluate its capability for classification and its relevance to other features, respectively. All features are represented in 2D space with discernibility as$x$-axis and independence as$y$-axis. The features located in the upper right corner represent high discernibility and high independence, so comprise the optimal feature subset. This leads to the formation of a family of feature selection algorithms. Three such algorithms are proposed in this paper referred to as FSDIE, FSDIR, and FSDIS (Feature Selection based on the Discernibility and the Independence, respectively, of Exponent, Reciprocal, and anti-Similarity). To speed-up these three algorithms, a clustering based feature preselection first eliminates some unrelated and redundant features. Extensive experiments on UCI datasets, face datasets and gene expression datasets demonstrate that these three 2D feature selection algorithms are superior to the state-of-the-art methods indicating the power of our 2D feature selection framework.

BACKGROUND: Portal vein system thrombosis (PVST) is potentially fatal for patients if the diagnosis is not timely or the treatment is not proper. There hasn't been any available technique to detect clinic risk factors to predict PVST after splenectomy in cirrhotic patients. The aim of this study is to detect the clinic risk factors of PVST for splenectomy and cardia devascularization patients for liver cirrhosis and portal hypertension, and build an efficient predictive model to PVST via the detected risk factors, by introducing the machine learning method. We collected 92 clinic indexes of splenectomy plus cardia devascularization patients for cirrhosis and portal hypertension, and proposed a novel algorithm named as RFA-PVST (Risk Factor Analysis for PVST) to detect clinic risk indexes of PVST, then built a SVM (support vector machine) predictive model via the detected risk factors. The accuracy, sensitivity, specificity, precision, F-measure, FPR (false positive rate), FNR (false negative rate), FDR (false discovery rate), AUC (area under ROC curve) and MCC (Matthews correlation coefficient) were adopted to value the predictive power of the detected risk factors. The proposed RFA-PVST algorithm was compared to mRMR, SVM-RFE, Relief, S-weight and LLEScore. The statistic test was done to verify the significance of our RFA-PVST. RESULTS: Anticoagulant therapy and antiplatelet aggregation therapy are the top-2 risk clinic factors to PVST, followed by D-D (D dimer), CHOL (Cholesterol) and Ca (calcium). The SVM (support vector machine) model built on the clinic indexes including anticoagulant therapy, antiplatelet aggregation therapy, RBC (Red blood cell), D-D, CHOL, Ca, TT (thrombin time) and Weight factors has got pretty good predictive capability to PVST. It has got the highest PVST predictive accuracy of 0.89, and the best sensitivity, specificity, precision, F-measure, FNR, FPR, FDR and MCC of 1, 0.75, 0.85, 0.92, 0, 0.25, 0.15 and 0.8 respectively, and the comparable good AUC value of 0.84. The statistic test results demonstrate that there is a strong significant difference between our RFA-PVST and the compared algorithms, including mRMR, SVM-RFE, Relief, S-weight and LLEScore, that is to say, the risk indicators detected by our RFA-PVST are statistically significant. CONCLUSIONS: The proposed novel RFA-PVST algorithm can detect the clinic risk factors of PVST effectively and easily. Its most contribution is that it can display all the clinic factors in a 2-dimensional space with independence and discernibility as y-axis and x-axis, respectively. Those clinic indexes in top-right corner of the 2-dimensional space are detected automatically as risk indicators. The predictive SVM model is powerful with the detected clinic risk factors of PVST. Our study can help medical doctors to make proper treatments or early diagnoses to PVST patients. This study brings the new idea to the study of clinic treatment for other diseases as well.

The weighted sum of objective functions is one of the simplest fitness functions widely applied in evolutionary algorithms (EAs) for multiobjective programming. However, EAs with this fitness function cannot find uniformly distributed solutions on the entire Pareto front for nonconvex and complex multiobjective programming. In this paper, a novel EA based on adaptive multiple fitness functions and adaptive objective space division is proposed to overcome this shortcoming. The objective space is divided into multiple regions of about the same size by uniform design, and one fitness function is defined on each region by the weighted sum of objective functions to search for the nondominated solutions in this region. Once a region contains fewer nondominated solutions, it is divided into several sub-regions and one additional fitness function is defined on each sub-region. The search will be carried out simultaneously in these sub-regions, and it is hopeful to find more nondominated solutions in such a region. As a result, the nondominated solutions in each region are changed adaptively, and eventually are uniformly distributed on the entire Pareto front. Moreover, the complexity of the proposed algorithm is analyzed. The proposed algorithm is applied to solve 13 test problems and its performance is compared with that of 10 widely used algorithms. The results show that the proposed algorithm can effectively handle nonconvex and complex problems, generate widely spread and uniformly distributed solutions on the entire Pareto front, and outperform those compared algorithms.

The problem of divisible load scheduling in network based heterogeneous distributed systems is addressed in this paper, where a general platform is considered, and the communication is in non-blocking message receiving mode, moreover, the communication speeds, computation speeds, start-up overheads and workload size are arbitrary. To solve the problem efficiently, we set up an optimization model which can effectively tackle the following three issues: (1) how many and which processors are required in computation; (2) in which order the load fractions are distributed to processors; (3) how much the load fraction should be distributed to each processor. For this model, a novel genetic algorithm is proposed, and the convergence of the proposed algorithm to a globally optimal solution with probability one is proved. Finally, the experiments on several examples indicate the efficiency and effectiveness of the proposed algorithm.