Abstract The vehicle routing problem with time windows (VRPTW) has gained much attention recently due to its wide application in operations research and logistics. VRPTW has been proven to be an NP-hard problem whose optimal solution is computationally costly. Scholars have proposed many methods, such as exact algorithms, heuristics, and metaheuristics, to find near-optimal solutions for the VRPTW. Exact algorithms are limited to small-scale problems, while heuristic algorithms and metaheuristics often converge to locally optimal solutions, despite their applicability to larger-scale problems. This paper proposes a novel membrane-inspired evolutionary algorithm framework (MEAF) consisting of isolated evolutionary rules, communication output rules, communication input rules, fusion-exchange information operation, and membrane dissolution rules. By leveraging the advantages of multiple metaheuristics algorithms and avoiding the pitfalls of local optima, MEAF offers a promising solution to address complex problems. The effectiveness of the proposed MEAF is verified by applying three classical metaheuristics, namely Genetic Algorithm (GA), Ant Colony System (ACS), and Particle Swarm Algorithm (PSO), to solve the VRPTW problem. The experiments are run on 56 instances of Solomon with 100 client benchmarks. The evaluation of the experimental results combined with the mean and standard deviation values show that the algorithm performs better in 54 out of 56 instances, demonstrating the effectiveness and stability of the proposed algorithm.

Feature selection, as one of the essential dimensionality reduction techniques, hasbecome one popular yet challenging area in the field, such as data mining andmachine learning. Unlike feature extraction (such as principle component analysis andnon-negative matrix factorization), preserving the entire information but losing thefeature relevance. Data processing in feature selection will lose information, leading tothe need to develop lightweight, efficient, and practical methods that preserve the datainformation as much as possible while performing dimensional reduction. In this paper,we propose a rankability-based feature selection method. The rankability concept wasproposed in 2019, similar to the entropy concept, and has not been studied widely yet.The proposed method is lightweight in terms of complexity, which requires no iterativeoptimization or auxiliary estimator tools.We experimented with sixteen datasets and compared our results with four otheralgorithms. The results show that our rankability-based feature selection methodoutperforms the fuzzy entropy-based method on five datasets in eight, and the averageaccuracy increased by 0.1482, 0.1078, and 0.1157, respectively. Then, in the varieddimension-reducing experiments, the proposed method shows superiority on fourdatasets out of eight and is competitive with others on two datasets out of eight.

Gaussian processes (GPs) have attracted considerable attention in assisting evolutionary algorithms (EAs) to solve computationally expensive optimization problems (EOPs) because they can directly provide information about the uncertainty of their predictions. However, the computational complexity of GPs grows cubically as the amount of data increases, which severely limits their computational efficiency in high-dimensional expensive multiobjective optimization problems (EMOPs). To address this limitation, we propose a surrogate-assisted evolutionary algorithm (SAEA) that integrates multilayer perceptron (MLP) grouping with sparse GPs, referred to as MLPSGP-SAEA. First, the MLP grouping selects a subspace from the original space by evaluating the impact of each decision variable on the objective functions. Then, for each objective function, a sparse GP model is employed, and the locations of pseudo-input points are optimized to enhance computational efficiency while improving model accuracy. Moreover, an adaptive sparse and diverse (ASD) infill criterion is proposed, based on the characteristics of the sparse GP model predictive distribution, to better balance exploration and exploitation. Finally, extensive experiments are conducted on four benchmark suites and an aerodynamic design optimization problem. The experimental results demonstrate that MLPSGP-SAEA exhibits significant competitive advantages over the state-of-the-art SAEAs.

Despite notable progress in domain adaptation for classification, regression-based domain adaptation remains challenging, particularly in terms of handling complex data structures, ensuring cross-domain generalization, and maintaining the precision and mathematical rigor required to validate model effectiveness. Unlike classification tasks, which are more resilient to variations in feature scaling, regression tasks are notably more sensitive, making their performance more vulnerable in domain adaptation scenarios. In this paper, we propose a generalized regularization technique grounded in the Grassmannian manifold to address the feature alignment problem. This approach leverages the underlying manifold structure of the data while preserving mathematical bounds, thereby enhancing the precision and efficiency of problem-solving. To demonstrate the effectiveness of the proposed algorithm, we apply it to estimate multi-output parameters in two distinct domains: 1) the Arabidopsis thaliana plant dataset, collected from a high-throughput phenotyping platform at Palacký University, and 2) the publicly available dSprites shape recognition with six adaptation tasks. These tasks are critical to advance agricultural research and address generalization challenges in multi-output regression. Accurate predictions provide deeper insights into plant growth and health, thereby supporting more effective crop management strategies. We evaluate the effectiveness of our framework by comparing it with state-of-the-art regression alignment techniques that are independent of the underlying backbone and adaptable to transfer learning tasks. Experimental results show that our framework consistently outperforms existing methods,results description. The source code will be made publicly available upon acceptance at https://github.com/lingping-fuzzy.

Fetal examinations are a significant and challenging field of healthcare. Cardiotocography is the most commonly used method for monitoring fetal heart rate and uterine contractions. As a promising alternative to cardiotocography, fetal phonocardiography is beginning to emerge. It is an entirely non-invasive, passive, and low-cost method. However, it is tough to estimate the ideal form of the fetal sound signal in most cases due to the presence of disturbances. The disturbances originate from movements or rotations of the fetal body, making fetal heart sound processing difficult. This study presents an automatic method for segmenting the fetal heart sounds in a phonocardiographic signal that is loaded with different types of disturbances and analyzes which of these disturbances most affect segmentation accuracy. To provide a comprehensive investigation, we propose a hybrid classifier based on Transformer and eXtreme Gradient Boosting, short for XGBoost, to improve segmentation performance by decision-making integration. 2000 segments of data from the Research Resource for Complex Physiologic Signals, PhysioNet repository, and created synthetic data (873 recordings) were used for the experiment. In the S1 label, our proposed method ranks first among all compared algorithms in precision, recall, F1, and accuracy score, tying with Transformer in recall score. It achieves an accuracy increase of 5% and 1.3% compared to XGBoost and Transformer, respectively. Similarly, in the S2 label, there is a precision score increase of 5.8% and 3.7% compared to XGBoost and Transformer, respectively. In general, our proposed method shows effective and promising performance..

This study proposes a novel artificial protozoa optimizer (APO) that is inspired by protozoa in nature. The APO mimics the survival mechanisms of protozoa by simulating their foraging, dormancy, and reproductive behaviors. The APO was mathematically modeled and implemented to perform the optimization processes of metaheuristic algorithms. The performance of the APO was verified via experimental simulations and compared with 32 state-of-the-art algorithms. Wilcoxon signed-rank test was performed for pairwise comparisons of the proposed APO with the state-of-the-art algorithms, and Friedman test was used for multiple comparisons. First, the APO was tested using 12 functions of the 2022 IEEE Congress on Evolutionary Computation benchmark. Considering practicality, the proposed APO was used to solve five popular engineering design problems in a continuous space with constraints. Moreover, the APO was applied to solve a multilevel image segmentation task in a discrete space with constraints. The experiments confirmed that the APO could provide highly competitive results for optimization problems. The source codes of Artificial Protozoa Optimizer are publicly available at https://seyedalimirjalili.com/projects and https://ww2.mathworks.cn/matlabcentral/fileexchange/162656-artificial-protozoa-optimizer.

With the continuous development of the communication service industry, users pay more attention to the quality of network service. Previous studies on offloading problems, especially in the Cloud Radio Access Network (C-RAN) architecture with Mobile Edge Computing (MEC), are primarily focused on the economic perspective, with little consideration given to user-oriented satisfaction problems. To fill this gap, this article proposes a mathematical model for maximizing user satisfaction in the C-RAN architecture with multi-layer MEC. The problem is divided into two stages for solution. The first stage addresses the optimal connection problem between users and Remote Radio Heads (RRHs). The second stage then schedules user tasks reasonably based on the solution obtained in the first stage. The two-stage problems are all proved to be NP-Hard. Two efficient approximation algorithms, namely User-to-RRH Association Algorithm (URAA) and Maximum Satisfaction Algorithm (MSA), are proposed to solve the problems in different stages. This article proves and analyzes the theoretical performance of the two algorithms. Finally, the performance of the proposed algorithms is verified by simulation experiments. The experimental results demonstrate that the two proposed algorithms can achieve reasonable solutions to the problems, and the user satisfaction level can be maintained at a high level.

Transformer architectures have been applied to graph-specific data such as protein structure and shopper lists, and they perform accurately on graph/node classification and prediction tasks. Researchers have proved that the attention matrix in Transformers has low-rank properties, and the self-attention plays a scoring role in the aggregation function of the Transformers. However, it can not solve the issues such as heterophily and over-smoothing. The low-rank properties and the limitations of Transformers inspire this work to propose a Global Representation (GR) based attention mechanism to alleviate the two heterophily and over-smoothing issues. First, this GR-based model integrates geometric information of the nodes of interest that conveys the structural properties of the graph. Unlike a typical Transformer where a node feature forms a Key, we propose to use GR to construct the Key, which discovers the relation between the nodes and the structural representation of the graph. Next, we present various compositions of GR emanating from nodes of interest and α-hop neighbors. Then, we explore this attention property with an extensive experimental test to assess the performance and the possible direction of improvements for future works. Additionally, we provide mathematical proof showing the efficient feature update in our proposed method. Finally, we verify and validate the performance of the model on eight benchmark datasets that show the effectiveness of the proposed method.

Since the last three decades, numerous search strategies have been introduced within the framework of different evolutionary algorithms (EAs). Most of the popular search strategies operate on the hypercube (HC) search model, and search models based on other hypershapes, such as hyper-spherical (HS), are not investigated well yet. The recently developed spherical search (SS) algorithm utilizing the HS search model has been shown to perform very well for the bound-constrained and constrained optimization problems compared to several state-of-the-art algorithms. Nevertheless, the computational burdens for generating an HS locus are higher than that for an HC locus. We propose an efficient technique to construct an HS locus by approximating the orthogonal projection matrix to resolve this issue. As per our empirical experiments, this technique significantly improves the performance of the original SS with less computational effort. Moreover, to enhance SS's search capability, we put forth a self-adaptation technique for choosing the effective values of the control parameters dynamically during the optimization process. We validate the proposed algorithm's performance on a plethora of real-world and benchmark optimization problems with and without constraints. Experimental results suggest that the proposed algorithm remains better than or at least comparable to the best-known state-of-the-art algorithms on a wide spectrum of problems.

A wireless sensor network is a sensing system composed of a few or thousands of sensor nodes. These nodes, however, are powered by internal batteries, which cannot be recharged or replaced, and have a limited lifespan. Traditional two-tier networks with one sink node are thus vulnerable to communication gaps caused by nodes dying when their battery power is depleted. In such cases, some nodes are disconnected with the sink node because intermediary nodes on the transmission path are dead. Energy load balancing is a technique for extending the lifespan of node batteries, thus preventing communication gaps and extending the network lifespan. However, while energy conservation is important, strategies that make the best use of available energy are also important. To decrease transmission energy cost and prolong network lifespan, a three-tier wireless sensor network is proposed, in which the first level is the sink node and the third-level nodes communicate with the sink node via the service sites on the second level. Moreover, this study aims to minimize the number of service sites to decrease the construction cost. Statistical evaluation criteria are used as benchmarks to compare traditional methods and the proposed method in the simulations.