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Differential evolution algorithm is a very powerful and recently proposed evolutionary algorithm. Generally, only a mutation operator and predefined parameter values of differential evolution algorithm are utilized to solve various optimization problems, which limits the performance of the algorithm. In this paper, six commonly used mutation operators are divided into three categories according to their own features. A mutation pool is established based on the three categories. A parameter pool with three predefined values is designed. During evolution, three mutation operators are randomly chosen from the three categories, and three parameter values are also randomly selected from the parameter pool. The three groups of mutation operators and parameter values are employed to produce trial vectors. The proposed algorithm makes good use of different mutation operators. Three recently proposed differential evolution variants and three non-differential evolution algorithms are used to make comparisons on the 29 testing functions from CEC. The experimental results have demonstrated that the proposed algorithm is very competitive. The proposed algorithm is utilized to solve three real applications, and the results are superior. [ABSTRACT FROM AUTHOR]

Flow Direction Algorithm (FDA) has better searching performance than some traditional optimization algorithms. To give the basic Flow Direction Algorithm more effective searching ability and avoid multiple local minima under the searching space, and enable it to obtain better search results, an improved FDA based on the Lévy flight strategy and the self-renewable method (LSRFDA) was proposed in this paper. The Lévy flight strategy and the self-renewable approach were added to the basic Flow Direction Algorithm. Random parameters generated by the Lévy flight strategy can increase the algorithm's diversity of feasible solutions in a short calculation time and greatly enhance the operational efficiency of the algorithm. The self-renewable method lets the algorithm quickly obtain a better possible solution and jump to the local solution space. Then, this paper tested different mathematical testing functions, including low-dimensional and high-dimensional functions, and the test results were compared with those of different algorithms. This paper includes iterative figures, box plots, and search paths to show the different performances of the LSRFDA. Finally, this paper calculated different engineering optimization problems. The test results show that the proposed algorithm in this paper has better searching ability and quicker searching speed than the basic Flow Direction Algorithm. [ABSTRACT FROM AUTHOR]

This paper introduces a novel formulation of the clustering problem, namely, the minimum sum-of-squares clustering of infinitely tall data (MSSC-ITD), and presents HPClust, an innovative set of hybrid parallel approaches for its effective solution. By utilizing modern high-performance computing techniques, HPClust enhances key clustering metrics: effectiveness, computational efficiency, and scalability. In contrast to vanilla data parallelism, which only accelerates processing time through the MapReduce framework, our approach unlocks superior performance by leveraging the multi-strategy competitive–cooperative parallelism and intricate properties of the objective function landscape. Unlike other available algorithms that struggle to scale, our algorithm is inherently parallel in nature, improving solution quality through increased scalability and parallelism and outperforming even advanced algorithms designed for small- and medium-sized datasets. Our evaluation of HPClust, featuring four parallel strategies, demonstrates its superiority over traditional and cutting-edge methods by offering better performance in the key metrics. These results also show that parallel processing not only enhances the clustering efficiency, but the accuracy as well. Additionally, we explore the balance between computational efficiency and clustering quality, providing insights into optimal parallel strategies based on dataset specifics and resource availability. This research advances our understanding of parallelism in clustering algorithms, demonstrating that a judicious hybridization of advanced parallel approaches yields optimal results for MSSC-ITD. Experiments on the synthetic data further confirm HPClust's exceptional scalability and robustness to noise. [ABSTRACT FROM AUTHOR]

This paper introduces novel enhancements to the most recent versions of DIRECT-type algorithms, especially when dealing with solutions located at the hyper-rectangle vertices. The BIRECT algorithm encounters difficulties in efficiently sampling points at the boundaries of the feasible region, leading to potential slowdowns in convergence. This issue is particularly pronounced when the optimal solution resides near the boundary. Our research explores diverse approaches, with a primary focus on incorporating a grouping strategy for hyper-rectangles of similar sizes. This categorization into different classes, constrained by a predefined threshold, aims to enhance computational efficiency, particularly involving a substantial number of hyper-rectangles of varying sizes. To further improve the new algorithm's efficiency, we implemented a mechanism to prevent oversampling and mitigate redundancy in sampling at shared vertices within descendant sub-regions. Comparisons with several DIRECT-type algorithms highlight the promising nature of the proposed algorithms as a global optimization solution. Statistical analyses, including Friedman and Wilcoxon tests, demonstrated the effectiveness of the improvements introduced in this new algorithm. [ABSTRACT FROM AUTHOR]

This article considers a box-constrained global optimization problem for Lipschitz continuous functions with an unknown Lipschitz constant. The well-known derivative-free global search algorithm DIRECT (DIvide RECTangle) is a promising approach for such problems. Several studies have shown that recent two-step (global and local) Pareto selection-based algorithms are very efficient among all DIRECT-type approaches. However, despite its encouraging performance, it was also observed that the candidate selection procedure has two possible shortcomings. First, there is no limit on how small the size of selected candidates can be. Secondly, a balancing strategy between global and local candidate selection is missing. Therefore, it may waste function evaluations by over-exploring the current local minimum and delaying finding the global one. This paper reviews and employs different strategies in a two-step Pareto selection framework (1-DTC-GL) to overcome these limitations. A detailed experimental study has revealed that existing strategies do not always improve and sometimes even worsen results. Since 1-DTC-GL is a DIRECT-type algorithm, the results of this paper provide general guidance for all DIRECT-type algorithms on how to deal with excessive local refinement more efficiently. [ABSTRACT FROM AUTHOR]

Differential evolution (DE) is a simple, effective, and robust algorithm, which has demonstrated excellent performance in dealing with global optimization problems. However, different search strategies are designed for different fitness landscape conditions to find the optimal solution, and there is not a single strategy that can be suitable for all fitness landscapes. As a result, developing a strategy to adaptively steer population evolution based on fitness landscape is critical. Motivated by this fact, in this paper, a novel adaptive DE based on fitness landscape (FL-ADE) is proposed, which utilizes the local fitness landscape characteristics in each generation population to (1) adjust the population size adaptively; (2) generate DE/current-to-pcbest mutation strategy. The adaptive mechanism is based on local fitness landscape characteristics of the population and enables to decrease or increase the population size during the search. Due to the adaptive adjustment of population size for different fitness landscapes and evolutionary processes, computational resources can be rationally assigned at different evolutionary stages to satisfy diverse requirements of different fitness landscapes. Besides, the DE/current-to-pcbest mutation strategy, which randomly chooses one of the top p% individuals from the archive cbest of local optimal individuals to be the pcbest, is also an adaptive strategy based on fitness landscape characteristic. Using the individuals that are approximated as local optimums increases the algorithm's ability to explore complex multimodal functions and avoids stagnation due to the use of individuals with good fitness values. Experiments are conducted on CEC2014 benchmark test suit to demonstrate the performance of the proposed FL-ADE algorithm, and the results show that the proposed FL-ADE algorithm performs better than the other seven highly performing state-of-art DE variants, even the winner of the CEC2014 and CEC2017. In addition, the effectiveness of the adaptive population mechanism and DE/current-to-pcbest mutation strategy based on landscape fitness proposed in this paper are respectively verified. [ABSTRACT FROM AUTHOR]

This paper introduces an innovative extension of the DIRECT algorithm specifically designed to solve global optimization problems that involve Lipschitz continuous functions subject to linear constraints. Our approach builds upon recent advancements in DIRECT-type algorithms, incorporating novel techniques for partitioning and selecting potential optimal hyper-rectangles. A key contribution lies in applying a new mapping technique to eliminate the infeasible region efficiently. This allows calculations to be performed only within the feasible region defined by linear constraints. We perform extensive tests using a diverse set of benchmark problems to evaluate the effectiveness and performance of the proposed algorithm compared to existing DIRECT solvers. Statistical analyses using Friedman and Wilcoxon tests demonstrate the superiority of a new algorithm in solving such problems. [ABSTRACT FROM AUTHOR]

End-to-end obstacle avoidance path planning for intelligent vehicles has been a widely studied topic. To resolve the typical issues of the solving algorithms, which are weak global optimization ability, ease in falling into local optimization and slow convergence speed, an efficient optimization method is proposed in this paper, based on the whale optimization algorithm. We present an adaptive adjustment mechanism which can dynamically modify search behavior during the iteration process of the whale optimization algorithm. Meanwhile, in order to coordinate the global optimum and local optimum of the solving algorithm, we introduce a controllable variable which can be reset according to specific routing scenarios. The evolutionary strategy of differential variation is also applied in the algorithm presented to further update the location of search individuals. In numerical experiments, we compared the proposed algorithm with the following six well-known swarm intelligence optimization algorithms: Particle Swarm Optimization (PSO), Bat Algorithm (BA), Gray Wolf Optimization Algorithm (GWO), Dragonfly Algorithm (DA), Ant Lion Algorithm (ALO), and the traditional Whale Optimization Algorithm (WOA). Our method gave rise to better results for the typical twenty-three benchmark functions. In regard to path planning problems, we observed an average improvement of 18.95% in achieving optimal solutions and 77.86% in stability. Moreover, our method exhibited faster convergence compared to some existing approaches. [ABSTRACT FROM AUTHOR]

Feature selection (FS) is applied to reduce data dimensions while retaining much information. Many optimization methods have been applied to enhance the efficiency of FS algorithms. These approaches reduce the processing time and improve the accuracy of the learning models. In this paper, a developed method called MPAO based on the marine predators algorithm (MPA) and the "narrowed exploration" strategy of the Aquila optimizer (AO) is proposed to handle FS, global optimization, and engineering problems. This modification enhances the exploration behavior of the MPA to update and explore the search space. Therefore, the narrowed exploration of the AO increases the searchability of the MPA, thereby improving its ability to obtain optimal or near-optimal results, which effectively helps the original MPA overcome the local optima issues in the problem domain. The performance of the proposed MPAO method is evaluated on solving FS and global optimization problems using some evaluation criteria, including the maximum value (Max), minimum value (Min), and standard deviation (Std) of the fitness function. Furthermore, the results are compared to some meta-heuristic methods over four engineering problems. Experimental results confirm the efficiency of the proposed MPAO method in solving FS, global optimization, and engineering problems. [ABSTRACT FROM AUTHOR]

This paper contains two main parts, Part I and Part II, which discuss the local and global minimization problems, respectively. In Part I, a fresh conjugate gradient (CG) technique is suggested and then combined with a line-search technique to obtain a globally convergent algorithm. The finite difference approximations approach is used to compute the approximate values of the first derivative of the function f. The convergence analysis of the suggested method is established. The comparisons between the performance of the new CG method and the performance of four other CG methods demonstrate that the proposed CG method is promising and competitive for finding a local optimum point. In Part II, three formulas are designed by which a group of solutions are generated. This set of random formulas is hybridized with the globally convergent CG algorithm to obtain a hybrid stochastic conjugate gradient algorithm denoted by HSSZH. The HSSZH algorithm finds the approximate value of the global solution of a global optimization problem. Five combined stochastic conjugate gradient algorithms are constructed. The performance profiles are used to assess and compare the rendition of the family of hybrid stochastic conjugate gradient algorithms. The comparison results between our proposed HSSZH algorithm and four other hybrid stochastic conjugate gradient techniques demonstrate that the suggested HSSZH method is competitive with, and in all cases superior to, the four algorithms in terms of the efficiency, reliability and effectiveness to find the approximate solution of the global optimization problem that contains a non-convex function. [ABSTRACT FROM AUTHOR]

This paper proposes a multi-objective teaching–learning studying-based algorithm (MTLSBA) to handle different objective frameworks for solving the large-scale Combined Heat and Power Economic Environmental Dispatch (CHPEED) problem. It aims at minimizing the fuel costs and emissions by managing the power-only, CHP and heat-only units. TLSBA is a modified version of TLBA to increase its global optimization performance by merging a new studying strategy. Based on this integrated tactic, every participant gathers knowledge from someone else randomly to improve his position. The position is specified as the vector of the design variables, which are the power and heat outputs from the power-only, CHP and heat-only units. TLSBA has been upgraded to include an extra Pareto archiving to capture and sustain the non-dominated responses. The objective characteristic is dynamically adapted by systematically modifying the shape of the applicable objective model. Likewise, a decision-making approach based on the fuzzy concept is used to select the most suitable CHPEED solution for large-scale dispatching of combined electrical power and heat energies. The proposed MTLSBA is assigned to multiple testing of 5-unit, 7-unit and 96-unit systems. It is contrasted with other reported techniques in the literature. According to numerical data, the suggested MTLSBA outperforms the others in terms of effectiveness and robustness indices. For the 5-unit system, the proposed MTLSBA achieves improvement in the fuel costs of 0.6625% and 0.3677% and reduction in the emissions of 2.723% and 7.4669% compared to non-dominated sorting genetic algorithm (NSGA-II) and strength Pareto evolutionary algorithm (SPEA 2), respectively. For the 7-unit system, the proposed MTLSBA achieves improvement in the fuel costs of 2.927% and 3.041% and reduction in the emissions of 40.156% and 40.050% compared to NSGA-II and SPEA 2, respectively. [ABSTRACT FROM AUTHOR]

Many of the applied algorithms that have been developed for solving a system of logical equations or the Boolean satisfiability problem have solved the problem in the Boolean domain. However, other approaches have recently been developed and improved. One of these developments is the transformation of a system of logical equations to a real continuous domain. The essence of this development is that a system of logical equations is transformed into a system in a real domain and the solution is sought in a real continuous domain. A real continuous domain is a richer domain, as it involves many well-developed algorithms. In this paper, we have constructively transformed the solution of any system of logical equations with a unique solution into an optimization problem for a polylinear target function in a unit n -dimensional cube K n . The resulting polylinear target function in K n does not have a local minimum. We proved that only once by calculating the gradient of the polylinear target function at any interior point of the K n cube, we can determine the solution to the system of logical equations. [ABSTRACT FROM AUTHOR]

A neural network algorithm is a meta-heuristic algorithm inspired by an artificial neural network, which has a strong global search ability and can be used to solve global optimization problems. However, a neural network algorithm sometimes shows the disadvantage of slow convergence speed when solving some complex problems. In order to improve the convergence speed, this paper proposes the neural network algorithm with dropout using elite selection. In the neural network algorithm with dropout using elite selection, the neural network algorithm is viewed from the perspective of an evolutionary algorithm. In the crossover phase, the dropout strategy in the neural network is introduced: a certain proportion of the individuals who do not perform well are dropped and they do not participate in the crossover process to ensure the outstanding performance of the population. Additionally, in the selection stage, a certain proportion of the individuals of the previous generation with the best performance are retained and directly enter the next generation. In order to verify the effectiveness of the improved strategy, the neural network algorithm with dropout using elite selection is used on 18 well-known benchmark functions. The experimental results show that the introduced dropout strategy improves the optimization performance of the neural network algorithm. Moreover, the neural network algorithm with dropout using elite selection is compared with other meta-heuristic algorithms to illustrate it is a powerful algorithm in solving optimization problems. [ABSTRACT FROM AUTHOR]

The Harris Hawks optimization (HHO) is a population-based metaheuristic algorithm; however, it has low diversity and premature convergence in certain problems. This paper proposes an adaptive relative reflection HHO (ARHHO), which increases the diversity of standard HHO, alleviates the problem of stagnation of local optimal solutions, and improves the search accuracy of the algorithm. The main features of the algorithm define nonlinear escape energy and adaptive weights and combine adaptive relative reflection with the HHO algorithm. Furthermore, we prove the computational complexity of the ARHHO algorithm. Finally, the performance of our algorithm is evaluated by comparison with other well-known metaheuristic algorithms on 23 benchmark problems. Experimental results show that our algorithms performs better than the compared algorithms on most of the benchmark functions. [ABSTRACT FROM AUTHOR]

Federated Learning (FL) is a promising distributed machine learning framework that emphasizes privacy protection. However, inconsistencies between local optimization objectives and the global objective, commonly referred to as client drift, primarily arise due to non-independently and identically distributed (Non-IID) data, multiple local training steps, and partial client participation in training. The majority of current research tackling this challenge is mainly based on the empirical risk minimization (ERM) principle, while giving little consideration to the connection between the global loss landscape and generalization capability. This study proposes FedGAM, an innovative FL algorithm that incorporates Gradient Norm-Aware Minimization (GAM) to efficiently search for a local flat landscape. FedGAM specifically modifies the client model training objective to simultaneously minimize the loss value and first-order flatness, thereby seeking flat minima. To directly smooth the global flatness, we propose the more significant FedGAM-CV, which employs control variables to correct local updates, guiding each client to train models in a globally flat direction. Experiments on three datasets (CIFAR-10, MNIST, and FashionMNIST) demonstrate that our proposed algorithms outperform existing FL baselines, effectively finding flat minima and addressing the client drift problem. [ABSTRACT FROM AUTHOR]

The registration of point clouds in a three-dimensional space is an important task in many areas of computer vision, including robotics and autonomous driving. The purpose of registration is to find a rigid geometric transformation to align two point clouds. The registration problem can be affected by noise and partiality (two point clouds only have a partial overlap). The Iterative Closed Point (ICP) algorithm is a common method for solving the registration problem. Recently, artificial neural networks have begun to be used in the registration of point clouds. The drawback of ICP and other registration algorithms is the possible convergence to a local minimum. Thus, an important characteristic of a registration algorithm is the ability to avoid local minima. In this paper, we propose an ICP-type registration algorithm (λ -ICP) that uses a multiparameter functional (λ -functional). The proposed λ -ICP algorithm generalizes the NICP algorithm (normal ICP). The application of the λ -functional requires a consistent choice of the eigenvectors of the covariance matrix of two point clouds. The paper also proposes an algorithm for choosing the directions of eigenvectors. The performance of the proposed λ -ICP algorithm is compared with that of a standard point-to-point ICP and neural network Deep Closest Points (DCP). [ABSTRACT FROM AUTHOR]

Quadratically constrained quadratic programs (QCQP), which often appear in engineering practice and management science, and other fields, are investigated in this paper. By introducing appropriate auxiliary variables, QCQP can be transformed into its equivalent problem (EP) with non-linear equality constraints. After these equality constraints are relaxed, a series of linear relaxation subproblems with auxiliary variables and bound constraints are generated, which can determine the effective lower bound of the global optimal value of QCQP. To enhance the compactness of sub-rectangles and improve the ability to remove sub-rectangles, two rectangle-reduction strategies are employed. Besides, two ϵ -subproblem deletion rules are introduced to improve the convergence speed of the algorithm. Therefore, a relaxation and bound algorithm based on auxiliary variables are proposed to solve QCQP. Numerical experiments show that this algorithm is effective and feasible. [ABSTRACT FROM AUTHOR]

This paper proposes a new meta-heuristic called Jumping Spider Optimization Algorithm (JSOA), inspired by Arachnida Salticidae hunting habits. The proposed algorithm mimics the behavior of spiders in nature and mathematically models its hunting strategies: search, persecution, and jumping skills to get the prey. These strategies provide a fine balance between exploitation and exploration over the solution search space and solve global optimization problems. JSOA is tested with 20 well-known testbench mathematical problems taken from the literature. Further studies include the tuning of a Proportional-Integral-Derivative (PID) controller, the Selective harmonic elimination problem, and a few real-world single objective bound-constrained numerical optimization problems taken from CEC 2020. Additionally, the JSOA's performance is tested against several well-known bio-inspired algorithms taken from the literature. The statistical results show that the proposed algorithm outperforms recent literature algorithms and is capable to solve challenging real-world problems with unknown search space. [ABSTRACT FROM AUTHOR]

This paper introduces a novel population-based bio-inspired meta-heuristic optimization algorithm, called Blood Coagulation Algorithm (BCA). BCA derives inspiration from the process of blood coagulation in the human body. The underlying concepts and ideas behind the proposed algorithm are the cooperative behavior of thrombocytes and their intelligent strategy of clot formation. These behaviors are modeled and utilized to underscore intensification and diversification in a given search space. A comparison with various state-of-the-art meta-heuristic algorithms over a test suite of 23 renowned benchmark functions reflects the efficiency of BCA. An extensive investigation is conducted to analyze the performance, convergence behavior and computational complexity of BCA. The comparative study and statistical test analysis demonstrate that BCA offers very competitive and statistically significant results compared to other eminent meta-heuristic algorithms. Experimental results also show the consistent performance of BCA in high dimensional search spaces. Furthermore, we demonstrate the applicability of BCA on real-world applications by solving several real-life engineering problems. [ABSTRACT FROM AUTHOR]

Swarm intelligence techniques have been created to respond to theoretical and practical global optimization problems. This paper puts forward an enhanced version of the firefly algorithm that corrects the acknowledged drawbacks of the original method, by an explicit exploration mechanism and a chaotic local search strategy. The resulting augmented approach was theoretically tested on two sets of bound-constrained benchmark functions from the CEC suites and practically validated for automatically selecting the optimal dropout rate for the regularization of deep neural networks. Despite their successful applications in a wide spectrum of different fields, one important problem that deep learning algorithms face is overfitting. The traditional way of preventing overfitting is to apply regularization; the first option in this sense is the choice of an adequate value for the dropout parameter. In order to demonstrate its ability in finding an optimal dropout rate, the boosted version of the firefly algorithm has been validated for the deep learning subfield of convolutional neural networks, with respect to five standard benchmark datasets for image processing: MNIST, Fashion-MNIST, Semeion, USPS and CIFAR-10. The performance of the proposed approach in both types of experiments was compared with other recent state-of-the-art methods. To prove that there are significant improvements in results, statistical tests were conducted. Based on the experimental data, it can be concluded that the proposed algorithm clearly outperforms other approaches. [ABSTRACT FROM AUTHOR]

Harnessing solar energy efficiently via photovoltaic (PV) technology is pivotal for future sustainable energy. Accurate modeling of PV cells entails an optimization problem due to the multimodal and nonlinear characteristics of the cells. This study introduces the Multi-strategy Gradient-Based Algorithm (MAGBO) for the precise parameter estimation of solar PV systems. MAGBO incorporates a modified gradient search rule (MGSR) inspired by the quasi-Newton approach, a novel refresh operator (NRO) for improved solution quality, and a crossover mechanism balancing exploration and exploitation. Validated through CEC2021 test functions, MAGBO excelled in global optimization. To further validate and underscore the reliability of MAGBO, we utilized data from the PVM 752 GaAs thin-film cell and the STP6-40/36 module. The simulation parameters were discerned using 44 I-V pairs from the PVM 752 cell and diverse data from the STP6-40/36 module tested under different conditions. Consistency between simulated and observed I-V and P-V curves for the STM6-40/36 and PVM 752 models validated MAGBO's accuracy. In application, MAGBO attained an RMSE of 9.8 × 10−4 for double-diode and single-diode modules. For Photowatt-PWP, STM6-40/36, and PVM 752 models, RMSEs were 2.4 × 10−3, 1.7 × 10−3, and 1.7 × 10−3, respectively. Against prevalent methods, MAGBO exhibited unparalleled precision and reliability, advocating its superior utility for intricate PV data analysis. [ABSTRACT FROM AUTHOR]

Moth-flame optimization (MFO) is a prominent problem solver with a simple structure that is widely used to solve different optimization problems. However, MFO and its variants inherently suffer from poor population diversity, leading to premature convergence to local optima and losses in the quality of its solutions. To overcome these limitations, an enhanced moth-flame optimization algorithm named MFO-SFR was developed to solve global optimization problems. The MFO-SFR algorithm introduces an effective stagnation finding and replacing (SFR) strategy to effectively maintain population diversity throughout the optimization process. The SFR strategy can find stagnant solutions using a distance-based technique and replaces them with a selected solution from the archive constructed from the previous solutions. The effectiveness of the proposed MFO-SFR algorithm was extensively assessed in 30 and 50 dimensions using the CEC 2018 benchmark functions, which simulated unimodal, multimodal, hybrid, and composition problems. Then, the obtained results were compared with two sets of competitors. In the first comparative set, the MFO algorithm and its well-known variants, specifically LMFO, WCMFO, CMFO, ODSFMFO, SMFO, and WMFO, were considered. Five state-of-the-art metaheuristic algorithms, including PSO, KH, GWO, CSA, and HOA, were considered in the second comparative set. The results were then statistically analyzed through the Friedman test. Ultimately, the capacity of the proposed algorithm to solve mechanical engineering problems was evaluated with two problems from the latest CEC 2020 test-suite. The experimental results and statistical analysis confirmed that the proposed MFO-SFR algorithm was superior to the MFO variants and state-of-the-art metaheuristic algorithms for solving complex global optimization problems, with 91.38% effectiveness. [ABSTRACT FROM AUTHOR]