Data clustering is one of the most influential branches of machine learning and data analysis, and Gaussian Mixture Models (GMMs) are frequently adopted in data clustering due to their ease of implementation. However, there are certain limitations to this approach that need to be acknowledged. GMMs need to determine the cluster numbers manually, and they may fail to extract the information within the dataset during initialization. To address these issues, a new clustering algorithm called PFA-GMM has been proposed. PFA-GMM is based on GMMs and the Pathfinder algorithm (PFA), and it aims to overcome the shortcomings of GMMs. The algorithm automatically determines the optimal number of clusters based on the dataset. Subsequently, PFA-GMM considers the clustering problem as a global optimization problem for getting trapped in local convergence during initialization. Finally, we conducted a comparative study of our proposed clustering algorithm against other well-known clustering algorithms using both synthetic and real-world datasets. The results of our experiments indicate that PFA-GMM outperformed the competing approaches.

The vehicle routing problem with time windows (VRPTW) is a classical optimization problem. There have been many related studies in recent years. At present, many studies have generally analyzed this problem on the two-dimensional plane, and few studies have explored it on spherical surfaces. In order to carry out research related to the distribution of goods by unmanned vehicles and unmanned aerial vehicles, this study carries out research based on the situation of a three-dimensional sphere and proposes a three-dimensional spherical VRPTW model. All of the customer nodes in this problem were mapped to the three-dimensional sphere. The chimp optimization algorithm is an excellent intelligent optimization algorithm proposed recently, which has been successfully applied to solve various practical problems and has achieved good results. The chimp optimization algorithm (ChOA) is characterized by its excellent ability to balance exploration and exploitation in the optimization process so that the algorithm can search the solution space adaptively, which is closely related to its outstanding adaptive factors. However, the performance of the chimp optimization algorithm in solving discrete optimization problems still needs to be improved. Firstly, the convergence speed of the algorithm is fast at first, but it becomes slower and slower as the number of iterations increases. Therefore, this paper introduces the multiple-population strategy, genetic operators, and local search methods into the algorithm to improve its overall exploration ability and convergence speed so that the algorithm can quickly find solutions with higher accuracy. Secondly, the algorithm is not suitable for discrete problems. In conclusion, this paper proposes an improved chimp optimization algorithm (MG-ChOA) and applies it to solve the spherical VRPTW model. Finally, this paper analyzes the performance of this algorithm in a multi-dimensional way by comparing it with many excellent algorithms available at present. The experimental result shows that the proposed algorithm is effective and superior in solving the discrete problem of spherical VRPTW, and its performance is superior to that of other algorithms.

Due to the traditional use of manual methods for the parameter adjustment of a nonlinear beta transform, which is inefficient and unstable, an adaptive image enhancement algorithm based on a variable step size fruit fly optimization algorithm and a nonlinear beta transform is proposed. Utilizing the intelligent optimization characteristics of the fruit fly algorithm, we automatically optimize the adjustment parameters of a nonlinear beta transform to achieve better image enhancement effects. Firstly, the dynamic step size mechanism is introduced into the fruit fly optimization algorithm (FOA) to obtain a variable step size fruit fly optimization algorithm (VFOA). Then, with the adjustment parameters of the nonlinear beta transform as the optimization object, and the gray variance of the image as the fitness function, an adaptive image enhancement algorithm (VFOA-Beta) is obtained by combining the improved fruit fly optimization algorithm with the nonlinear beta function. Finally, nine sets of photos were used to test the VFOA-Beta algorithm, while seven other algorithms were used for comparative experiments. The test results show that the VFOA-Beta algorithm can significantly enhance images and achieve better visual effects, which has a certain practical application value.

Traditional optimization methods rely on parameter selection and a require high mathematical performance of the objective function. Thus, swarm intelligence optimization algorithms have attracted extensive attention as modern optimization methods in recent years, achieving remarkable results in the fields of machine learning, engineering optimization, process control, and elsewhere. Swarm intelligence optimization algorithms are a form of computing technology built upon the laws of biological group behavior, they are simple, fast, and place low requirements upon the objective functions. The traditional swarm intelligence algorithm offers new ideas for solving certain practical problems, however, it suffers from shortcomings in several experiments. In recent years, numerous scholars have proposed new swarm intelligence optimization algorithms, this paper selects several of the more typical swarm intelligence algorithms proposed in recent years at home and abroad, including the Whale Optimization Algorithm, Moth-Flame Optimization Algorithm, Fireworks Algorithm, Dragonfly Algorithm, Crow Search Algorithm, Butterfly Optimization Algorithm, and Pigeons Algorithm. Furthermore, the experimental performances of these algorithms are compared with respect to their convergence speed, accuracy, and stability, using 18 standard test functions, and the relative improvement methods are compared and analyzed. Finally, the characteristics of the swarm intelligence optimization algorithm are summarized, and its future development potential is discussed.

Clustering is an unsupervised learning method. Density Peak Clustering (DPC), a density-based algorithm, intuitively determines the number of clusters and identifies clusters of arbitrary shapes. However, it cannot function effectively without the correct parameter, referred to as the cutoff distance (d_c). The traditional DPC algorithm exhibits noticeable shortcomings in the initial setting of d_c when confronted with different datasets, necessitating manual readjustment. To solve this defect, we propose a new algorithm where we integrate DPC with the Black Widow Optimization Algorithm (BWOA), named Black Widow Density Peaks Clustering (BWDPC), to automatically optimize d_c for maximizing accuracy, achieving automatic determination of d_c. In the experiment, BWDPC is used to compare with three other algorithms on six synthetic data and six University of California Irvine (UCI) datasets. The results demonstrate that the proposed BWDPC algorithm more accurately identifies density peak points (cluster centers). Moreover, BWDPC achieves superior clustering results. Therefore, BWDPC represents an effective improvement over DPC.

Estimates from the international basketball federation suggest that globally, at least 450 million individuals are engaged in basketball sports. This paper an enhanced dwarf mongoose optimization algorithm with encircling foraging strategy (EDMOA) for comparative analysis basketball shooting percentage is proposed. Initially, it identifies shooting parameters-such as shooting distance, shooting velocity, shooting height, and angle-for general shooting scenarios, analyzing these parameters to provide scientifically sound shooting recommendations. Subsequently, it investigates the parameters affecting three-pointers and free throws, outlining feasible shooting strategies. It compares and analyzes the differences between three-pointer and free-throw shooting techniques while assessing the impact of distance on shooting outcomes. Finally, the study investigates shooting for tall players and short players, identifying distinct shooting parameters for both types of athletes and analyzing the differences in shooting approaches. The experimental results show that within reasonable ranges of other parameters, shooting three-pointer yields 87.09% increase in shooting accuracy compared to shooting two-pointers, while maintaining a shooting angle of approximately 52° results in an 86.30% increase in shooting accuracy. Leveraging the EDMOA, this paper addresses the above-mentioned issues. The EDMOA improves upon the limitations of the dwarf mongoose optimization algorithm (DMOA), which suffers from slow convergence and susceptibility to local optima, by introducing encircling foraging strategies and a survival-of-the-fittest population mindset. The outcomes of this study offer reference points for basketball coaches in designing training regimes for athletes. This research aims to provide scientifically grounded guidance for basketball player training, ultimately enhancing shooting percentage.