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Solving nonlinear equation systems (NESs) is one of the most important tasks in numerical computing. The NESs usually have multiple roots, and quickly locating their roots in a single algorithm run with a limited number of iterations has always been the algorithm improvement direction. In order to further enhance the efficiency of the existing methods, a density clustering-based differential evolution algorithm (DCDE) for the NESs problem solving is proposed in this paper. Firstly, density-based spatial clustering of applications with noise (DBSCAN) is used to divide the population into clusters and noises, which provides a better direction for population evolution. Secondly, a cluster evaluation factor is proposed, which not only divides the clusters into excellent clusters and non-excellent clusters, but also prevents the migration of excellent clusters and maintain the diversity of populations. Then, a migration strategy and individual generation mechanism are proposed to guide non-excellent clusters to migrate to promising regions. Finally, combined with an archive technique, the individuals which satisfy the solution requirements are archived and randomly initialized to further improve population diversity. To verify the effectiveness of the proposed algorithm, comparative experimental results of the propsoed DCDE with other state-of-the-art algorithms for thirty NESs problems solving show that the proposed DCDE is the most effective algorithm to locate more roots in a single run. [ABSTRACT FROM AUTHOR]

Clustering, as an essential technique in unsupervised learning, plays a pivotal role in the fields of data mining and machine learning. However, the classic K -means clustering algorithm has intrinsic drawbacks such as sensitivity to initial cluster centers, susceptibility to a local optimal solution, and challenges in handling data uncertainty. To address these problems, this paper proposes an artificial hummingbird algorithm (AHA)-based three-way K -means clustering algorithm, called AHA-3WKM. First, AHA is introduced to address the problems of sensitivity to initial cluster centers and local optima. Second, a fitness function of AHA is specifically constructed to find the best initial clustering centers so that the hummingbirds can search for high-quality food sources, i.e., the global optimum cluster centers. Third, a three-way clustering approach is utilized to capture information about data uncertainty. In this way, the results of clustering are divided into three distinct regions based on the relationship between objects and clusters. The experimental results demonstrate that AHA-3WKM has good performance, and enhances the stability and the accuracy of clustering results. • AHA is introduced to address the problems of the sensitivity to initial cluster centers and the proneness to local optima. Hummingbirds are treated as data points, which dynamically update their strategies and effectively find the optimal cluster centers during multiple iterations. • A fitness function is designed based on the clustering principle of "birds of a feather flock together", with the aim of simplifying calculations, which enhances the specificity and practicality of K-means algorithm. • An AHA-based three-way K-means clustering algorithm (i.e., AHA-3WKM) is proposed. The clustering process is initialized with cluster centers optimized by AHA, and the results are represented in three regions, which can capture the uncertainty within the datasets. [ABSTRACT FROM AUTHOR]

• An improved gaining-sharing knowledge-based algorithm named MSGSK is proposed. • A parameter adjustment strategy is developed to adjust relative parameters of MSGSK. • A backtracking differential mutation strategy is designed to enrich the population diversity. • A strategy selection mechanism is presented to integrate the former two strategies. • MSGSK extracts more accurate parameters for five PV models. The determination of photovoltaic (PV) model parameters has essential theoretical and practical significance for the performance evaluation, power monitoring, and power generation efficiency calculation of PV systems. In this paper, a multi-strategy gaining-sharing knowledge-based algorithm (MSGSK) is developed to determine these parameters. In our previous work, it has been demonstrated that gaining-sharing knowledge-based algorithm (GSK) is well suited for solving the concerned problem. To enhance its performance, a parameter adjustment strategy is developed to adjust the knowledge rate and knowledge ratio of GSK. Besides, a backtracking differential mutation strategy by combining the mutation scheme of differential evolution and the updating scheme of backtracking search optimization algorithm is developed to enrich the population diversity. Furthermore, a strategy selection mechanism is introduced to integrate the former two strategies to balance exploration and exploitation in different stages of the evolutionary process. The suggested MSGSK algorithm is applied to five PV cases (SDM, DDM, Photowatt-PW201, STM6-40/36, and STP6-120/36). From the experimental data, it can be observed that MSGSK extracts the PV model parameters more precisely than the basic GSK. Furthermore, it exhibits faster convergence speed and higher accuracy compared to other advanced algorithms found in the literature. [ABSTRACT FROM AUTHOR]

In the realm of practical problem-solving, multi-objective optimisation problems with redundant variables and indefinite objective functions (MOPRVIF) are becoming increasingly prevalent. MOPRVIF involve determining the optimal decision variables that optimise multiple objectives, leveraging the relational data of a set of variables and multiple objectives. For these problems, this paper focuses on the following two issues: one is the demand for a unified computational model to solve this problem; the other is how to improve the algorithm's deep intelligent search capability. In this regard, this paper designs a dual data-driven multi-objective optimisation method. The method used consisted of four parts: elimination of redundant variables (ERV), objective function construction (OFC), selection evolution operator (SEO), and multi-objective evolutionary algorithm (MOEA). MOEA was the main focus of the method. ERV is data preparation and variable selection according to multiple objectives. OFC involves constructing the relationship model between variables and objectives, and a high-accuracy model is important for guaranteeing reliable results. Furthermore, SEO can adjust the evolution operator during a deep search. This is an important guarantee for deep, intelligent search. MOEA combined OFC and SEO to form the final solution algorithm—Dual Data Driven Multi-Objective Evolutionary Algorithm (DDMOEA). DDMOEA was explored using two different disciplinary problems of drug compound optimisation and wild blueberry cultivation and benchmarks were selected. The first two problem domains are distinct. The first problem is more complex than the second; however, both encompass redundant variables and indefinite objective functions. Benchmarks are utilised independently to gauge the profound intelligent search capability. The experiments affirm that the dual data-driven optimization approach proposed in this paper is effective, practical, and scalable. • Provide a unified solution for optimisation problems with redundant variables and indefinite objective functions. • Propose a data-driven multi-objective optimisation algorithm. • Designing an adaptive optimiser to enhance the algorithm's depth search capability. [ABSTRACT FROM AUTHOR]

In this paper, a new differential evolution (DE) algorithm is presented for solving global optimization problems by guiding the individuals adaptively to explore different decision regions and setting the control parameters properly for individuals. To consolidate algorithm efficiency and preserve population diversity, we first introduce a proration-based mutation strategy. This strategy dynamically selects promising individuals from population as guiders and proportionately allocates the individuals following them based on their fitness values and unsuccessful updates. Besides, we design a multi-segment mixed parameter setting to provide suitable parameters for individuals, considering feedback information from the population, individual requirements, and parameters' interaction. Additionally, we devise an adaptive population maintaining mechanism to refresh the population by replacing individuals with higher unsuccessful updates and removing those with poor fitness values. Unlike previous DE versions, our new algorithm dynamically and appropriately explores promising areas, refines parameter suitability, and accelerates convergence by updating and removing unpromising individuals. This enhances the algorithm search efficiency and achieves a good balance between exploration and exploitation. Finally, we evaluate the proposed algorithm's performance by comparing it with 17 typical or state-of-the-art algorithms on IEEE CEC2014 and CEC2017 test suites. Experimental results indicate that the proposed algorithm is a more promising optimizer. [ABSTRACT FROM AUTHOR]

Large-volume and high-dimensional big datasets are being generated quickly. They are expected to provide data-driven solutions for various pressing challenges such as cybersecurity, credit card fraud, network intrusion detection, etc. The visual assessment of clustering tendency (VAT) family of algorithms provides an excellent tool for assessing clustering tendency and subsequent clustering of these novel datasets to extract groups and anomalies to better understand the data generation phenomenon. However, VAT and improved VAT (iVAT) algorithms are plagued with O (n 2) time and space complexity as they use Prim's algorithm for building Euclidean minimum spanning tree (EMST) of the data points, leaving it inapplicable to large datasets. This paper develops three novel time- and memory-scalable algorithms for fast computation of VAT EMST by reducing the search space of the following possible EMST edge and using an efficient data structure, the k-d tree. Next, we develop a novel approach to compute iVAT reordered dissimilarity image (RDI) in a novel memory-preserving manner using the EMST edge lengths calculated previously without having to compute memory intensive n × n VAT RDI. We experimented on several synthetic and real-life datasets to showcase that the proposed approaches can help quickly assess their clustering tendency in a memory-saving manner. We also demonstrate the applicability of the proposed methods for the anomaly detection task in large volumes of high-dimensional data. [ABSTRACT FROM AUTHOR]

As one of the main research tasks in software testing, automated test case generation based on path coverage (ATCG-PC) aims to achieve maximum path coverage with a minimized set of test cases. In ATCG-PC, the correlation among the dimensions of test cases is widely utilized in academia to minimize the search efforts of the search-based algorithm. Nevertheless, the information related to target path selection is not utilized, which leads to blind decision-making by the search-based algorithm during the target path selection. Therefore, this paper proposes an enhanced scatter search strategy by using opposition-based learning. An arithmetic optimization algorithm is also proposed to solve ATCG-PC based on the enhanced scatter search strategy, namely, ESSENT. The ESSENT algorithm selects the path with the lowest path entropy among the uncovered paths as the target path, and generates new test cases that cover the target path by modifying the dimensions of the existing test cases. The performance of the ESSENT algorithm is evaluated on six iFogSim subprograms and six Stanford coreNLP subprograms. Experiment results show that the ESSENT algorithm achieves a higher convergence rate than other state-of-the-art algorithms. Furthermore, it enables maximum path coverage with fewer test cases. [ABSTRACT FROM AUTHOR]

The joint order batching and picker routing problem (JOBPRP) is a combinatorial optimization problem that occurs during in the order-picking operation of warehouse management. It consists of simultaneous assignment of customer orders to batches and routing of picking operations in the batches such that the total travel distance is minimized. In this paper, we develop a memetic algorithm with fuzzy-based population control (MA-FPC) to solve the JOBPRP. MA-FPC takes advantage of the hierarchical nature of the problem to design a batch exchange crossover (BEX) operator and a two-level local improvement procedure. BEX transfers complete batches from parent solutions to offsprings. Local improvement systematically employs a combined heuristic and exact routing approach to solve the picker routing problem. Furthermore, fuzzy-based population control is used to dynamically regulate population diversity during the search, which removes individuals from or adds individuals to the population. In numerical experiments, MA-FPC significantly outperforms state-of-the-art point-based and population-based algorithms developed for the order batching problem and JOBPRP with respect to solution quality in reasonable running times. Our algorithm improves the previous best-known solutions for 57 of the 64 benchmark instances. [ABSTRACT FROM AUTHOR]