Test Functions Research Articles

Silent cerebral microvascular disease and longitudinal risk of cognitive decline in atrial fibrillation

Abstract Background A relationship between silent stroke and cognitive disorder has recently been suggested in patients with nonvalvular atrial fibrillation (NVAF). This research is an exploratory research study to investigate the occurrence of asymptomatic cerebrovascular disorders with NVAF. Methods The SKAF (Silent cerebral microvascular disease and longitudinal risK of cognitive decline in Atrial Fibrillation) study is a prospective, investigator-initiated, multicenter, observational study of Japanese patients with NVAF aged 60 years or older. We had planned to enroll two hundred NVAF patients with no history of symptomatic stroke or dementia, and an anticoagulant therapy with edoxaban is being performed or an anticoagulant therapy is not being performed, and one hundred patients with sinus rhythm, for comparison. We collected patient characteristics, clinical course, the data of head MRI test and cognitive function test (Montreal Cognitive Assessment (MoCA)) at the baseline and the 24 months follow-up. The primary endpoint was the composite of silent ischemic stroke and micro-bleeding over a 24-month follow-up period. The secondary endpoint was cognitive decline over a 24-month follow-up period. Results The study was started in October 2016, with a planned 2-year recruitment period. As of January 31, 2018, a total of 326 patients were enrolled. Of those, 99 patients with sinus rhythm (SR group) and 214 patients with NVAF (NVAF group) were analyzed (male, 193 (62%) patients; age, 72.2±6.5 years). 156 of 195 (80%) patients with NVAF received the anticoagulant therapy with edoxaban. There was no significant difference of the primary composite for the endpoints between two groups (17.4% versus 17.4%; p=1.00). The incidences of silent ischemic stroke and micro-bleeding in SR and NVAF groups over a 24-month follow-up period were 9.3% and 10.8% (p= 0.833), and 8.1% and 9.2% (p=1.00), respectively. The NVAF group exhibited a significantly larger decline in cognition changes in MoCA score than SR group (-0.830 versus 0,000; p=0.0131). Notably, NVAF was found to be associated with cognitive decline. Conclusion The SKAF registry provided an equivalent risk of silent cerebral microvascular disease in patients with SR and NVAF. Clinically, NVAF had an impact on cognitive decline.

Phase-Angle-Encoded Snake Optimization Algorithm for K-Means Clustering

The rapid development of metaheuristic algorithms proves their advantages in optimization. Data clustering, as an optimization problem, faces challenges for high accuracy. The K-means algorithm is traditaaional but has low clustering accuracy. In this paper, the phase-angle-encoded snake optimization algorithm (θ-SO), based on mapping strategy, is proposed for data clustering. The disadvantages of traditional snake optimization include slow convergence speed and poor optimization accuracy. The improved θ-SO uses phase angles for boundary setting and enables efficient adjustments in the phase angle vector to accelerate convergence, while employing a Gaussian distribution strategy to enhance optimization accuracy. The optimization performance of θ-SO is evaluated by CEC2013 datasets and compared with other metaheuristic algorithms. Additionally, its clustering optimization capabilities are tested on Iris, Wine, Seeds, and CMC datasets, using the classification error rate and sum of intra-cluster distances. Experimental results show θ-SO surpasses other algorithms on over 2/3 of CEC2013 test functions, hitting a 90% high-performance mark across all clustering optimization tasks. The method proposed in this paper effectively addresses the issues of data clustering difficulty and low clustering accuracy.

Spherical Shepard-Bernoulli operator

AbstractWe consider the problem of interpolating large sets of scattered data on the sphere using Shepard-Bernoulli operators constructed based on two types of basis functions. We study the interpolation properties and the approximation errors of the methods proposed here. We evaluate the efficiency using several test functions and the practical applicability through two real-data problems.

Galerkin approximation of Burgers-Huxley equation with fractional order arising in reaction mechanism and diffusion transport

Abstract Burgers-Huxley model depicts a prototype model of the interaction of convection effect, reaction mechanisms and diffusion transport, used to study the liquid crystal and nerve fibers. This study introduces Galerkin approximation for time-fractional Burgers-Huxley equation (TFBHE) . The Caputo derivative is used to evaluate the temporal part using the $L_1$ formula. The Galerkin approach employs cubic B-spline as a shape and test function, resulting in a symmetric matrix that is easily convergent. In addition, the three-point quadrature rule is implemented to evaluate the integration of complex function . The Von Neumann analysis is used to discuss stability of the scheme. The performance and robustness of the technique is measured using various error norms. The results are compared with the exact solution, demonstrating effectiveness of the proposed method.

Dynamic step opposition-based learning sparrow search algorithm for UAV path planning

In this paper, aiming at the problems of large randomness, low convergence accuracy, and easy falling into local optimum in the application of sparrow search algorithm to UAV three-dimensional path planning, a dynamic step opposition-based learning sparrow search algorithm is proposed. The algorithm first uses a good point set in the population initialization phase to improve the quality of the initial solution; secondly, the piecewise dynamic step size is used to optimize the update formula of the discoverer, and the extensive search is carried out in the early stage of the iteration. In the later stage, the known area is mined as much as possible to improve the search accuracy and convergence speed of the algorithm. Then, the crazy operator is integrated to optimize the predator update formula and improve the local search ability. Finally, t-distribution opposition-based learning is used to prevent the algorithm from falling into the local optimum. In this paper, the effectiveness of the improved algorithm is verified by six test functions and applied to the three-dimensional path planning of UAVs. The experimental results show that the proposed algorithm has a faster convergence speed than the traditional algorithm, and the planned path is shorter.

The evaluation of a novel single-lead biopotential device for home sleep testing.

This paper reports on the clinical evaluation of the sleep staging performance of a novel single-lead biopotential device. 133 patients suspected of obstructive sleep apnea were included in a multi-site cohort. All patients underwent polysomnography and received the study device, a single-lead biopotential measurement device attached to the forehead. Clinical endpoint parameters were selected to evaluate the device's ability to determine sleep stages. Finally, the device's performance was compared to the clinical study results of comparable devices. Concurrent PSG and study device data were successfully acquired for 106 of the 133 included patients. The results of this study demonstrated significant similarity in overall sleep staging performance (5-stage Cohen's Kappa of 0.70) to the best-performing reduced-lead biopotential device to which it was compared (5-stage Cohen's Kappa of 0.73). Contrary to the comparator devices, the study device reported a higher Cohen's Kappa for REM (0.78) compared to N3 (0.61), which can be explained by its particular measuring electrode placement (diagonally across the lateral cross-section of the eye). This placement was optimized to ensure the polarity of rapid eye movements could be adequately captured, enhancing the capacity to discriminate between N3 and REM sleep when using only a single-lead setup. The results of this study demonstrate the feasibility of incorporating a single-lead biopotential extension in a reduced-channel home sleep apnea testing setup. Such incorporation could narrow the gap in the functionality of reduced-channel home sleep testing and in-lab polysomnography without compromising the patient's ease of use and comfort.

Graph neural processes for molecules: an evaluation on docking scores and strategies to improve generalization

Neural processes (NPs) are models for meta-learning which output uncertainty estimates. So far, most studies of NPs have focused on low-dimensional datasets of highly-correlated tasks. While these homogeneous datasets are useful for benchmarking, they may not be representative of realistic transfer learning. In particular, applications in scientific research may prove especially challenging due to the potential novelty of meta-testing tasks. Molecular property prediction is one such research area that is characterized by sparse datasets of many functions on a shared molecular space. In this paper, we study the application of graph NPs to molecular property prediction with DOCKSTRING, a diverse dataset of docking scores. Graph NPs show competitive performance in few-shot learning tasks relative to supervised learning baselines common in chemoinformatics, as well as alternative techniques for transfer learning and meta-learning. In order to increase meta-generalization to divergent test functions, we propose fine-tuning strategies that adapt the parameters of NPs. We find that adaptation can substantially increase NPs' regression performance while maintaining good calibration of uncertainty estimates. Finally, we present a Bayesian optimization experiment which showcases the potential advantages of NPs over Gaussian processes in iterative screening. Overall, our results suggest that NPs on molecular graphs hold great potential for molecular property prediction in the low-data setting.Scientific contributionNeural processes are a family of meta-learning algorithms which deal with data scarcity by transferring information across tasks and making probabilistic predictions. We evaluate their performance on regression and optimization molecular tasks using docking scores, finding them to outperform classical single-task and transfer-learning models. We examine the issue of generalization to divergent test tasks, which is a general concern of meta-learning algorithms in science, and propose strategies to alleviate it.

Approximation by Schurer Type λ-Bernstein–Bézier Basis Function Enhanced by Shifted Knots Properties

In this article, a novel Schurer form of λ-Bernstein operators augmented by Bézier basis functions is presented by utilizing the features of shifted knots. The shifted knots form of Bernstein operators and the Schurer form of the Bézier basis function are used in this article, then, new operators, the Schurer type λ-Bernstein shifted knots operators are constructed in terms of the Bézier basis function. First, the test functions are calculated and the central moments for these operators are obtained. Then, Korovkin’s type approximation properties are studied by the use of a modulus of continuity of orders one and two. Finally, the convergence theorems for these new operators are obtained by using Peetre’s K-functional and Lipschitz continuous functions. In the end, some direct approximation theorems are also obtained.

A multi-strategy improved sparrow search algorithm for indoor AGV path planning

To address the problems of weak search ability, easily falling into local optimal solutions and poor path quality of sparrow search algorithm in AGV path planning, a multi-strategy improved sparrow search algorithm (MISSA) is proposed in this paper. MISSA improves the global search ability by improving the discoverer position update operator and introducing the sine cosine algorithm; adopts the adaptive number of vigilantes and adaptive adjustment step size to improve the convergence speed; introduces the Levy flight variation strategy to reduce the probability of falling into any local optimal solution; optimizes the boundary handling mechanism to prevent the loss of population diversity at a later stage; finally, uses the large-scale neighborhood search strategy and path smoothing mechanism for path optimization to further improve the path quality. The superiority-seeking ability of MISSA was verified by 12 standard test functions, and then 30 simulation experiments were conducted in grid maps with two specifications of 20×20 and 30×30. The experimental results showed that, by using MISSA, the path length was reduced by 44.1% and 63.1%, the number of turns was reduced by 68.4% and 78.4%, and the risk degree was reduced by 61.3% and 77.2%, which verifies the superiority of MISSA in path planning. Finally, MISSA was ported to the QBot2e mobile robot for physical verification to prove its feasibility in practical applications.

An Innovative Enhanced JAYA Algorithm for the Optimization of Continuous and Discrete Problems

Metaheuristic algorithms have gained popularity in the past decade due to their remarkable ability to address various optimization challenges. Among these, the JAYA algorithm has emerged as a recent contender that demonstrates strong performance across different optimization problems, largely attributed to its simplicity. However, real-world problems have become increasingly complex in today’s era, creating a demand for more robust and effective solutions to tackle these intricate challenges and achieve outstanding results. This article proposes an enhanced JAYA (EJAYA) method that addresses its inherent shortcomings, resulting in improved convergence and search capabilities when dealing with diverse problems. The current study evaluates the performance of the proposed optimization methods on both continuous and discontinuous problems. Initially, EJAYA is applied to solve 20 prominent test functions and is validated by comparison with other contemporary algorithms in the literature, including moth–flame optimization, particle swarm optimization, the dragonfly algorithm, and the sine–cosine algorithm. The effectiveness of the proposed approach in discrete scenarios is tested using feature selection and compared to existing optimization strategies. Evaluations across various scenarios demonstrate that the proposed enhancements significantly improve the JAYA algorithm’s performance, facilitating escape from local minima, achieving faster convergence, and expanding the search capabilities.

Path Planning of an Unmanned Aerial Vehicle Based on a Multi-Strategy Improved Pelican Optimization Algorithm.

The UAV path planning algorithm has many applications in urban environments, where an effective algorithm can enhance the efficiency of UAV tasks. The main concept of UAV path planning is to find the optimal flight path while avoiding collisions. This paper transforms the path planning problem into a multi-constraint optimization problem by considering three costs: path length, turning angle, and collision avoidance. A multi-strategy improved POA algorithm (IPOA) is proposed to address this. Specifically, by incorporating the iterative chaotic mapping method with refracted reverse learning strategy, nonlinear inertia weight factors, the Levy flight mechanism, and adaptive t-distribution variation, the convergence accuracy and speed of the POA algorithm are enhanced. In the CEC2022 test functions, IPOA outperformed other algorithms in 69.4% of cases. In the real map simulation experiment, compared to POA, the path length, turning angle, distance to obstacles, and flight time improved by 8.44%, 5.82%, 4.07%, and 9.36%, respectively. Similarly, compared to MPOA, the improvements were 4.09%, 0.76%, 1.85%, and 4.21%, respectively.

Experimental study on the cyclic performance of innovative self-centering three-dimensional isolation bearing

To improve vertical seismic isolation and seismic resilience in isolation bearings, this paper introduces an innovative three-dimensional isolation bearing combining a disc-spring system (DSS), a high-damping rubber bearing (HDR), and a horizontal spring system (HSS). The DSS is designed with low vertical stiffness to enhance vertical isolation, while the HSS provides self-centering force to improve the seismic resilience of the HDR. This study first presents a comprehensive theoretical analysis of the horizontal and vertical stiffness composition. The vertical performance of this three-dimensional isolation bearing is attributed to the DSS, while the HSS and HDR jointly contribute to its horizontal performance. Seven specimens were designed and subjected to shear-compression cyclic tests to assess the horizontal and vertical cyclic performance. Experimental parameters included loading amplitude, loading frequency, vertical pre-load, and DSS combinations for vertical tests, and axial compression force, loading frequency, shear strain, and HSS function in horizontal tests. The cyclic performance parameters for the three-dimensional isolation bearing, including equivalent damping ratio, equivalent stiffness, and energy dissipation, was evaluated. In general, the proposed three-dimensional isolation bearing exhibits stable cyclic performance and advantageous seismic resilience, warranting its promotion to practical engineering applications.

Application of spiral enhanced whale optimization algorithm in solving optimization problems

The Whale Optimization Algorithm (WOA) is regarded as a classic metaheuristic algorithm, yet it suffers from limited population diversity, imbalance between exploitation and exploration, and low solution accuracy. In this paper, we propose the Spiral-Enhanced Whale Optimization Algorithm (SEWOA), which incorporates a nonlinear time-varying self-adaptive perturbation strategy and an Archimedean spiral structure into the original WOA. The Archimedean spiral structure enhances the diversity of the solution space, aiding the algorithm in escaping local optima. The nonlinear time-varying self-adaptive optimization dynamic perturbation strategy improves the algorithm’s local search capability and enhances solution accuracy. The effectiveness of the proposed algorithm is validated from multiple perspectives using CEC2014 test functions, CEC2017 test functions, and 23 benchmark test functions. The experimental results demonstrate that the enhanced Whale Optimization Algorithm significantly improves population diversity, balances global and local search, and enhances solution accuracy. Additionally, SEWOA exhibits excellent performance in solving three engineering design problems, showcasing its value and wide range of potential applications.

Application of improved Jellyfish search algorithm for 9-parameters cell extraction and GMPPT in PV systems

Optimization algorithms are essential tools used to address real-world problems through minimization or maximization processes. In the context of photovoltaic (PV) systems, various optimization algorithms have been employed to extract solar cell parameters using minimization techniques, and to identify the maximum power point (MPP) using maximization approaches. However, under partial shading conditions or during rapidly changing irradiance, many of these algorithms tend to get trapped in local minima, failing to locate the global maximum power point (GMPPT). This shortcoming leads to significant energy losses from PV cells. Similarly, the extraction of solar cell parameters is often compromised by the random search behavior and inadequate exploration and exploitation capabilities of many existing algorithms. The Jellyfish Search Optimization (JSO) algorithm is a recent, parameter-free method developed to tackle a wide range of optimization problems. Despite its innovative design, JSO is prone to premature convergence and exhibits a longer convergence time. To address these limitations, this paper proposes a modified version of the JSO algorithm, which integrates the state-of-the-art features of JSO with the Lévy flight characteristic from the cuckoo search algorithm. This combination aims to achieve a better balance between exploration and exploitation. To validate the effectiveness of the proposed Improved Jellyfish Search Optimization (IJSO) algorithm in PV systems, extensive experiments were conducted. These experiments included benchmarking with complex test functions, extracting cell parameters using various solar cell models, and maximizing energy output from PV systems under different environmental conditions. The results demonstrate that the proposed IJSO algorithm effectively enhances parameter extraction and global maximum power point tracking, making it a promising solution for optimizing energy extraction from PV cells in dynamic conditions.

Multi-group sparrow search algorithm based on K-means clustering

In order to improve the defects of the Sparrow Search Algorithm (SSA) in single-species search, which causes redundancy in its speed of collection and easily ignores high-quality solutions and falls into local optimality, a K-means Multigroup Sparrow Search Algorithm (KSSA) based on K-means clustering was proposed. Firstly, the multi-population mechanism is introduced into SSA to weaken the collection ability of a single population and reduce the probability of falling into the local optimum. Secondly, the K-means algorithm is used to divide the sub-populations to increase the differences between the sub-populations, and at the same time, the individuals in the sub-populations focus on searching in a small range, thereby improving the efficiency of the initial search. Then, the weighted centroid communication strategy is used to improve the quality of communication between populations, reduce the interference of the own population, and reduce the risk of all sub-populations falling into the local optimum due to a sub-population falling into the local optimum. Finally, dynamic reverse learning is introduced into the vigilant to enhance its anti-predator behavior and improve the defects of slower collection speed and insufficient collection accuracy caused by the increase in the number of sub-populations. The test function simulation experiment shows that KSSA has better optimization performance than SSA and other algorithms.

Relational Strict Almost Contractions Employing Test Functions and an Application to Nonlinear Integral Equations

Relational Strict Almost Contractions Employing Test Functions and an Application to Nonlinear Integral Equations

Nonexistence of the compressible Euler equations with space-dependent damping in high dimensions

Abstract Compressible Euler equations with space-dependent damping in high dimensions R n ( n = 2 , 3 ) {{\bf{R}}}^{n}\hspace{0.33em}\hspace{0.33em}\left(n=2,3) are considered in this article. Assuming that the small initial velocity and small perturbation of the initial density have compact support, we establish finite-time blow-up results for the Euler system, by combining energy estimate and new test functions constructed by the solutions of the following linear elliptic partial differential equations system: − G 1 ( x ) + ∇ ⋅ G 2 → ( x ) = 0 , − G 2 → ( x ) + ∇ G 1 ( x ) = μ G 2 → ( x ) ( 1 + ∣ x ∣ ) λ . \left\{\begin{array}{l}-{G}_{1}\left(x)+\nabla \cdot \overrightarrow{{G}_{2}}\left(x)=0,\\ -\overrightarrow{{G}_{2}}\left(x)+\nabla {G}_{1}\left(x)=\frac{\mu \overrightarrow{{G}_{2}}\left(x)}{{(1+| x| )}^{\lambda }}.\end{array}\right. This result generalizes the one in the literature from 1 − D 1-D to high dimension R n ( n = 2 , 3 ) {{\bf{R}}}^{n}\hspace{0.33em}\hspace{0.33em}\left(n=2,3) .

Improved Bald Eagle Search Optimization Algorithm for the Inverse Kinematics of Robotic Manipulators.

The inverse kinematics of robotic manipulators involves determining an appropriate joint configuration to achieve a specified end-effector position. This problem is challenging because the inverse kinematics of manipulators are highly nonlinear and complexly coupled. To address this challenge, the bald eagle search optimization algorithm is introduced. This algorithm combines the advantages of evolutionary and swarm techniques, making it more effective at solving nonlinear problems and improving search efficiency. Due to the tendency of the algorithm to fall into local optima, the Lévy flight strategy is introduced to enhance its performance. This strategy adopts a heavy-tailed distribution to generate long-distance jumps, thereby preventing the algorithm from becoming trapped in local optima and enhancing its global search efficiency. The experiments first evaluated the accuracy and robustness of the proposed algorithm based on the inverse kinematics problem of manipulators, achieving a solution accuracy of up to 10-18 m. Subsequently, the proposed algorithm was compared with other algorithms using the CEC2017 test functions. The results showed that the improved algorithm significantly outperformed the original in accuracy, convergence speed, and stability. Specifically, it achieved over 70% improvement in both standard deviation and mean for several test functions, demonstrating the effectiveness of the Lévy flight strategy in enhancing global search capabilities. Furthermore, the practicality of the proposed algorithm was verified through two real engineering optimization problems.

A hybrid algorithm based on Bayesian optimization and Interior Point OPTimizer for optimal operation of energy conversion systems

Optimization methods are essential to improve the operation of energy conversion systems including energy storage equipment and fluctuating renewable energy. Modern systems consist of many components, operating in a wide range of conditions and governed by nonlinear balance equations. Consequently, identifying their optimal operation (e.g. minimizing operational costs) requires solving challenging optimization problems, with the global optimum often hidden behind many local ones. In this work, we propose a hybrid method that advantageously combines Bayesian optimization (BO) and Interior Point OPTimizer (IPOPT). The BO is a global approach exploiting Gaussian process regression to build a surrogate model of the cost function to be optimized, while IPOPT is a local approach using quasi-Newton updates. The proposed BO-IPOPT combination allows leveraging the parameter space exploration of the BO with the quasi-Newton convergence of IPOPT once solution candidates are in the neighborhood of an optimum. Using a challenging constrained test function, we test BO-IPOPT in accuracy and computational efficiency. Finally, we showcase the proposed method in the optimal operation of a renewable steam generation system. The results show that BO-IPOPT combines high accuracy and computational efficiency, achieving up to 50% better objective function values at the same CPU time than other state-of-the-art methods.

Gorilla algorithm based on double random perturbation and its engineering application

Aiming at the problems of artificial gorilla troop optimization algorithm, such as easy to fall into local optimum, slow convergence speed and low optimization accuracy, an artificial gorilla troop optimization algorithm based on double random perturbation strategy is proposed. Firstly, the Halton sequence is introduced to initialize the population to increase the diversity of the population; secondly, a multi-dimensional random number strategy is used in the algorithm optimization stage and an adaptive position search mechanism is proposed in the exploration stage to improve the convergence speed of the algorithm; thirdly, a double random perturbation strategy is proposed to solve the group effect of gorillas and enhance the ability of the algorithm to jump out of the local optimum; finally, a dimension-by-dimensional update strategy is adopted to update individual positions, which improves the convergence accuracy of the algorithm. Through the comparison of the optimization results of 10 benchmark test functions and the Wilcoxon rank sum test, it can be seen that the improved algorithm has greatly improved the optimization accuracy and convergence speed. In addition, through the experimental comparative analysis of an engineering optimization problem, the superiority of the proposed algorithm in dealing with real engineering problems is further verified.