Test Functions Research Articles

On the Cauchy problem for a weakly coupled system of semi-linear σ-evolution equations with double dissipation

In this paper, we would like to consider the Cauchy problem for a multi-component weakly coupled system of semi-linear σ-evolution equations with double dissipation for any σ≥1. The first main purpose is to obtain the global (in time) existence of small data solutions in the supercritical condition by assuming additional L1 regularity for the initial data and using multi-loss of decay wisely. For the second main one, we are interested in establishing the blow-up results together with sharp estimates for lifespan of solutions in the subcritical case. The proof is based on a contradiction argument with the help of modified test functions to derive the upper bound estimates. Finally, we succeed in catching the lower bound estimate by constructing Sobolev spaces with the time-dependent weighted functions of polynomial type in their corresponding norms.

Surrogate-model-based low-carbon optimization method for tolerance allocation of mechanical components under bidirectional constraints

The low-carbon optimization of tolerance allocation involves reducing production costs and carbon emissions, while ensuring dimensional precision, making it a crucial pathway to achieving low-carbon manufacturing. However, the complex mapping mechanism between tolerance, cost, and carbon emissions makes it challenging to construct effective mechanistic models. This complexity arises from both the forward constraints of multiple-coupled design features of components and backward constraints on the differentiated processing conditions of an enterprise. Therefore, a low-carbon optimization method for tolerance allocation based on surrogate models is proposed. Firstly, the RReliefF algorithm is utilized to analyze the influence of design features and enterprise processing condition factors on the low-carbon performance of tolerance allocation, identifying key influencing factors. Secondly, a convolutional neural network (CNN)-based surrogate model is established to predict the low-carbon performance of tolerance allocation. Specifically, datasets of tolerance, manufacturing costs, and carbon emissions under different design feature constraints are constructed. To improve the training efficiency and accuracy of the prediction model, the heterogeneous data of design features are processed using the one-hot encoding technique. Subsequently, the mapping relationship between tolerance, cost, and carbon emissions is established based on the CNN. Finally, with the aim of minimizing costs and carbon emissions, a low-carbon optimization method for tolerance allocation is established based on the surrogate model and the product size chain. The convolutional neural network-Harris Hawk optimization algorithm (CNN-HHO) is utilized to generate tolerance allocation schemes that minimize both cost and carbon emissions while satisfying dimensional precision. Through a series of multi-peak test functions and practical case studies of the overrunning clutch, the results indicate that the proposed CNN-HHO algorithm demonstrates exceptional accuracy and stability in the validation on the test functions. Furthermore, the optimized overrunning clutch solution achieves approximately 2.61% cost reduction and 2.63% decrease in carbon emissions, providing further support for the effectiveness of the proposed method.

Association of depression in multiple sclerosis with fatigue, sleep disturbances, disability, and health-related quality of life: Outcomes of a cross-sectional study

IntroductionDepression affect individuals with multiple sclerosis (MS) more frequently compared with the general population. It can worsen the symptoms of MS, influence disability progression, and significantly reduce the quality of life (QoL). MethodWe investigated the prevalence of depressive symptoms in a cohort of 200 patients with MS (76% women) and their association with sleep patterns, fatigue, QoL, demographics, and other clinical characteristics in real-world settings. The study was conducted through clinical evaluations and questionnaires related to depression: Beck Depression Inventory (BDI) and Hamilton Depression Rating Scale (HDRS); fatigue: Modified Fatigue Impact Scale; sleep quality: Pittsburgh Sleep Quality Index and Epworth Sleepiness Scale; and QoL: Multiple Sclerosis Quality of Life-54 (MSQOL-54). ResultsAccording to the BDI and HDRS, the prevalence of depressive symptoms was 40.5 and 28.27%, respectively. Patients with depressive symptoms exhibited higher disability scores, longer ambulation times, worse cognitive function in the Symbol Digit Modalities Test, and poorer sleep quality. They also had significantly higher fatigue and daytime somnolence scores, as well as lower scores on the MSQOL-54: physical (40.55 vs. 62.3; P<.001) and mental (44.49 vs. 71.89; P<.001) health composites. We demonstrated the correlation between depression and fatigue, as well as their negative impact on QoL in patients with MS. ConclusionThis study underscores the prevalence and impact of depression in MS, emphasizing the importance of routine screening and active management of psychiatric comorbidities in individuals with MS. These findings contribute valuable insights into the complex interplay between mental health, disease variables, and QoL in MS.

Absolute coronary blood flow across different endotypes of ANOCA.

Intracoronary continuous thermodilution is a novel technique to quantify absolute true coronary flow and microvascular resistance. However, few data are available in patients with angina with non-obstructive coronary arteries (ANOCA). This study aimed to investigate the diagnostic potential of hyperaemic absolute coronary flow (Qmax) and absolute microvascular resistance (Rμ,hyper) among different ANOCA endotypes, and to determine the correlation between continuous - and bolus - thermodilution indexes. A total of 222 patients were scheduled for clinically indicated coronary function testing (CFT), of whom 120 patients were included in this analysis. These patients underwent CFT including acetylcholine (ACh) provocation testing and microvascular function assessment using both bolus and continuous thermodilution. CFT was negative (CFT-) in 32 (26.7%) patients. Endothelium-dependent dysfunction (ACh+) was present in 63 (52.5%) patients, and coronary microvascular dysfunction (CMD) identified at bolus thermodilution (CMD+) was present in 62 (51.7%) patients. Patients with a positive CFT (CFT+) showed significantly lower Qmax and higher Rμ,hyper values as compared to CFT-. Qmax was significantly lower in CMD+ versus CMD- patients (0.174 vs 0.222 L/min; p=0.04) but did not differ in patients with or without a positive ACh test (0.198 vs 0.219 L/min; p=0.86). The prevalence of a CFT+ is high in a selected ANOCA population. In our study, Qmax and Rμ,hyper were associated with a positive CFT. Qmax was associated with the presence of microvascular dysfunction but not with a positive acetylcholine test. The novel continuous thermodilution method can provide further insights into ANOCA endotypes.

Adapting the population size in CMA-ES using nearest-better clustering method for multimodal optimization

The covariance matrix adaptation evolution strategy (CMA-ES) is one of the advanced algorithms for solving continuous single-objective optimization. In this algorithm, the population size is an important parameter which represents the number of candidate points generated in each iteration. A larger population size allows for better exploration of the search space and is typically required for handling multimodal functions, while a smaller population size facilitates quicker convergence. Adapting the population size in this algorithm raises a question about how to increase/decrease/keep it in an efficient way to solve specific problems. In this paper, we propose a novel approach for this purpose based on the information of niches observed during the evolution process. Firstly, the nearest-better clustering (NBC) technique is employed to detect the number of niches in each iteration, then the information will be used to adapt the population size accordingly. Additionally, a quasi-Newton method, which serves as a local search, can be incorporated into the algorithm in order to speed it up. We evaluate the effectiveness of our method through numerical simulations on multimodal test functions, the black-box optimization benchmarking (BBOB) noiseless testbed, and the CEC 2014 and CEC 2017 benchmark testing suites.

UAV path planning based on improved dung beetle algorithm with multiple strategy integration

This research presents a multi-strategy augmented dung beetle algorithm (CDBO) for UAV path planning in intricate 3D environments. Its main objective is to address the path planning challenge by formulating an integrated cost function model and environment representation that aligns the optimisation task with the navigation prerequisites and safety constraints of the UAV. Firstly, the algorithm initialises the particle population based on the Lévy flight principle to improve the species diversity and adequately search the solution space. Subsequently, an exponentially decreasing inertia weighting strategy is introduced to improve the convergence speed of the algorithm. In addition, the algorithm uses an adaptive [Formula: see text]-distribution with perturbed variation of the updated positions so that the algorithm avoids falling into a local optimum. Finally, to enhance the robustness of the system, the algorithm incorporates an elite retention strategy based on the Pareto principle. In this study, rigorous tests using 12 CEC2022 test functions and Wilcoxon rank sum test are conducted as benchmarks for the performance of the algorithm. The results show that the enhanced dung beetle algorithm outperforms the traditional algorithm, highlighting its efficiency and robustness. In addition, the efficacy of the enhanced dung beetle algorithm was validated in a variety of complex 3D environments, affirming its ability to generate optimal paths. This study further highlights the importance of effective algorithms in UAV path planning, addressing the key issue of optimising flight operations in intricate spatial scenarios.

How to combine different types of prefabricated components in a building to reduce construction costs and carbon emissions?

In the context of industrialized construction and carbon emission reduction globally, prefabrication has gained considerable attention. However, most studies cared the carbon emissions and construction costs from the perspective of a whole prefabricated building rather than the prefabricated components. It makes it difficult to understand the role of prefabricated components play and make improvements from the prefabricated components level. To fill this gap, this study proposes a model to optimize the selection and combination of prefabricated components in a building project to simultaneously reduce the construction costs and carbon emissions. Six common component types were considered: shear wall, beam, floor slab, stair, balcony, and air-conditioning slab. Their costs and carbon emissions were quantified when adopting prefabrication and cast-in-situ technologies. To obtain the optimal solution, we developed an improved multi-objective mayfly algorithm (IMOMA), which incorporates enhanced circle chaos mapping and a global best guiding strategy to generate Pareto solution sets. The performance of IMOMA was evaluated using the Zitzler-Deb-Thiele series test functions, demonstrating its advantages in convergence, diversity, and comprehensive performance through metrics such as generation distance, diversity metric Δ, and inverse generational distance. A case study validated the effectiveness of this proposed method, demonstrating an average reduction of 9.05% in total construction costs and 8.04% in carbon emissions when compared to the initial scheme. Further study revealed that different prefabrication rates correspond to different optimal components combination schemes, with different trends in the costs and carbon emission curves as the prefabrication rate increases. Additionally, carbon trading policies influence the components combination, with construction costs reduced by 10.88% at a carbon trading price of 42.80 CNY/t CO2eq. This study provides valuable guidance for general contractors to design optimal component combinations and for governments to promote the sustainable development of prefabricated construction.

Analysis and evaluation of the effectiveness of program codes for particle swarm and ant colony methods for lower semi-continuous functions

In this paper, a comparative analysis of two stochastic methods of global optimization is carried out: the Particle Swarm Optimization method and the Ant Colony Optimization method. The analysis and evaluation of efficiency were carried out using parameters such as the number of calls to the objective function, the rate of convergence, resources, computational efficiency, sensitivity to parameters, and resistance to initial conditions. The article presents the program codes of these methods in the Python environment, designed to calculate the global extremum of semi-continuous functions from below. Well- known test functions were used to construct (by gluing) semi-continuous functions at different values of input parameters.

Contextuality of cognitive control deficits in alcohol dependence — pro et contra

Cognitive impairment, including cognitive control, mediates the negative social consequences of alcohol-related behavior, but few studies have examined these processes in the Russian speaking population using modern and standardized assessment methods. Thus, the aim of the study was to examine the features of cognitive control (inhibition of automatic response) and the general level of cognitive functioning in a Russianspeaking sample of alcohol-dependent individuals (AD) using quantitative assessment methods. Materials and Methods. 111 individuals diagnosed with alcohol dependence (F10.30) and 27 healthy participants were examined by using the Brief Assessment of Cognitive Functioning in Affective Disorders Battery (BAC-A) and additional tests of cognitive control (Stroop test with incongruent stimuli, Stroop test with alcohol-associated stimuli). The statistical methods were U-Mann-Whitney test, Spearman correlation coefficient, two-stage least squares regression. Results. In the AD group the indices of cognitive functioning were significantly lower in all parameters except for the subtests of verbal memory and digit sequence (p&lt;0,05). The model of the relationship between the parameters of general cognitive functioning and cognitive control reveals that the index of incongruence to alcohol-related stimuli was a significant predictor of sampe affiliation. Discussion. The obtained results may indicate the presence of impairments of speed of mental processes, planning , verbal fluency and response inhibition function in the group of individuals with AD. In the studied group, the automatic response inhibition function mediates the general cognitive functioning only within the relevant contextual stimuli.

A Retrospective Herb-Drug Interaction Study of Oryeong-san (Wuling-san) Co-administration in Type 2 Diabetes Patients Receiving Hypoglycemic Treatment

Objectives: This study investigated the effects of Korean medicine Oryeong-san (五苓散) on blood glucose levels and evaluated its safety in patients with type 2 diabetes.Methods: A total of 87 patients aged 19 years and older, hospitalized for at least three days at the Kyung Hee University Korean Medical Hospital from January 1, 2021, to December 31, 2023 and continuously consumed Oryeong-san for a minimum of three days, were included. Their clinical characteristics and laboratory tests were reviewed retrospectively. The effects of Oryeong-san on fasting (FBS) and 2-hour postprandial (PP2) blood glucose were assessed by comparing the averages of measurements taken before and after the treatment. To evaluate the safety of the herbal extract, liver function test and kidney function test results were compared, including aspartate aminotransferase (AST), alanine aminotransferase (ALT), blood urea nitrogen (BUN), creatinine (Cr), and estimated glomerular filtration rate (eGFR).Results: The average duration of Oryeong-san consumption was 17.71±26.82 days. Although the FBS decreased and the PP2 slightly increased, these changes were not statistically significant (p&gt;0.05). Safety assessments showed that the average levels of AST decreased, while the level of ALT increased, without statistical significance. The BUN levels also significantly decreased, while Cr and eGFR levels remained stable.Conclusion: This study indicates that Oryeong-san is safe for use in type 2 diabetes patients without significant impact on blood glucose and that it has a positive safety profile.

Short-term Traffic Flow Prediction Based on KELM Optimized By Improved Slime Mould Algorithm

Traffic flow prediction plays a crucial role in improving transportation efficiency and enhancing Intelligent Transportation Systems (ITS). However, the temporal, spatial, and nonlinear nature of traffic flow data presents challenges for accurate short-term prediction. We propose a short-term traffic flow prediction model based on Kernel Extreme Learning Machine (KELM) optimized by the improved Slime Mould Algorithm (SMA). KELM is an improved version of Extreme Learning Machine (ELM) that incorporates kernel functions for improved generalization and stability. SMA is a meta-heuristic algorithm inspired by the behavior of slime mould in foraging, known for its strong global searching ability. For better performance, three strategies are introduced: the Good Point Set method for optimizing the initial population, the combination of Opposition Based Learning (OBL) and Differential Evolution (DE) to improve the slime mould generation mechanism, and the use of adaptive t distribution mutation to enhance convergence speed. After comparing the performance of these improved SMAs on twelve test functions, the ISMA improved by integrating three strategies as mentioned above is best. Then the ISMA is applied to search for the optimal parameters of KELM model. Finally, the optimized KELM with optimal parameters is applied to predict the short-term traffic flow on given traffic data set. Experimental results demonstrate that the proposed model, KELM optimized by ISMA namely ISMA-KELM, outperforms existing models such as Random Forest (RF), Least Squares Support Vector Machine (LSSVM), KELM optimized by Tuna Swarm Optimization Algorithm (TSO-KELM), and KELM optimized by SMA (SMA-KELM) in terms of traffic flow prediction accuracy. The proposed model ISMA-KELM provides a promising approach for addressing the challenges of traffic flow prediction, offering improved accuracy and efficiency in real-time traffic management systems.

Development of novel nanostructured biosensors for rapid detection of pathogens in clinical diagnostics

&lt;p class="MsoNormal" style="text-align: justify; text-justify: inter-ideograph; line-height: 120%; mso-pagination: none; layout-grid-mode: char; mso-layout-grid-align: none; margin: 12.0pt 0cm 6.0pt 0cm;"&gt;&lt;span lang="EN-US" style="font-size: 10.0pt; line-height: 120%; font-family: 'Times New Roman',serif;"&gt;The prompt and precise identification of microorganisms is crucial for successful clinical diagnostics and the prevention of infectious disease outbreaks. Traditional diagnostic methods often suffer from limitations such as extended processing durations, elevated expenses, and the necessity for specialized laboratory equipment. In this research, we propose the development of novel nanostructured biosensors that utilize the distinct characteristics of nanomaterials to improve the accuracy, specificity, and efficiency of identifying pathogens. These biosensors are created with the intention of offering point-of-care testing functionality, thus rendering them appropriate for utilization in a range of clinical settings. The integration of advanced nanotechnology with bioanalytical methods aims to create a reliable system for the real-time identification of bacterial, viral, and fungal pathogens. This review encompasses the design, fabrication, and testing of the biosensors, along with a comprehensive analysis of their performance in comparison to conventional diagnostic techniques. The results demonstrate the potential of nanostructured biosensors to revolutionize pathogen detection, offering significant improvements in efficiency and accuracy, which are essential for timely medical intervention and public health management.&lt;/span&gt;&lt;/p&gt;

Somersault Foraging and Elite Opposition-Based Learning Dung Beetle Optimization Algorithm

To tackle the shortcomings of the Dung Beetle Optimization (DBO) Algorithm, which include slow convergence speed, an imbalance between exploration and exploitation, and susceptibility to local optima, a Somersault Foraging and Elite Opposition-Based Learning Dung Beetle Optimization (SFEDBO) Algorithm is proposed. This algorithm utilizes an elite opposition-based learning strategy as the method for generating the initial population, resulting in a more diverse initial population. To address the imbalance between exploration and exploitation in the algorithm, an adaptive strategy is employed to dynamically adjust the number of dung beetles and eggs with each iteration of the population. Inspired by the Manta Ray Foraging Optimization (MRFO) algorithm, we utilize its somersault foraging strategy to perturb the position of the optimal individual, thereby enhancing the algorithm’s ability to escape from local optima. To verify the effectiveness of the proposed improvements, the SFEDBO algorithm is utilized to optimize 23 benchmark test functions. The results show that the SFEDBO algorithm achieves better solution accuracy and stability, outperforming the DBO algorithm in terms of optimization results on the test functions. Finally, the SFEDBO algorithm was applied to the practical application problems of pressure vessel design, tension/extension spring design, and 3D unmanned aerial vehicle (UAV) path planning, and better optimization results were obtained. The research shows that the SFEDBO algorithm proposed in this paper is applicable to actual optimization problems and has better performance.

A Combined Quasi-Newton-Type Method Using 4th-Order Directional Derivatives for Solving Degenerate Problems of Unconstrained Optimization

Introduction. Methods of unconstrained optimization play a significant role in machine learning [1–6]. When solving practical problems in machine learning, such as tuning nonlinear regression models, the extremum point of the chosen optimality criterion is often degenerate, which significantly complicates its search. Therefore, degenerate problems are the most challenging in optimization. Known numerical methods for solving the general unconstrained optimization problem, up to the second order, have very low convergence rates when solving degenerate problems [7, 8]. This is explained by the fact that for a significant improvement in convergence rate in this case, it is necessary to use higher-order derivatives in the method than the second order [10]. The purpose of the paper is to develop an efficient quasi-Newton method for solving degenerate unconstrained optimization problems, the idea of which (unlike regularization) involves dividing the entire space into the sum of two orthogonal subspaces. This idea was introduced in [23]. The space division at each iteration of the method is based on the spectral decomposition of the matrix approximating the Hessian of the objective function using the BFGS formula [3]. Each subspace exhibits its own behavior of the objective function, and therefore, an appropriate minimization method is applied on it. Results. A combined quasi-Newton method is presented for solving degenerate unconstrained optimization problems, based on orthogonal decomposition of the Hessian approximation matrix and division of the entire space into the sum of two orthogonal subspaces. On one subspace (the kernel of the Hessian approximation matrix), a method is applied where derivatives in the direction of the 4th order are computed, while on the orthogonal complement to it, a quasi-Newtonian method is applied. A separate one-dimensional search is applied on each of these subspaces to determine the step multiplier in the respective direction. The effectiveness of the presented combined method is confirmed by numerical experiments conducted on widely accepted test functions for unconstrained optimization problems. The proposed method allows obtaining fairly accurate solutions to test tasks in case of degeneracy of the minimum point with significantly lower computational costs for gradient calculations compared to optimization procedures of well-known mathematical packages. Conclusions. The idea of dividing the entire space into the sum of two (or possibly more) orthogonal subspaces when solving complex optimization problems is quite promising in terms of applying a combination of different numerical methods on separate subspaces. In the future, it is planned to conduct theoretical research on the convergence rate of the presented combined method in solving degenerate unconstrained optimization problems. Keywords: unconstrained optimization, quasi-Newton methods, degenerate minimum point, spectral matrix decomposition, Machine Learning.

Cannabigerol Reduces Acute and Chronic Hypernociception in Animals Exposed to Prenatal Hypoxia-Ischemia

Cannabigerol (CBG), a phytocannabinoid, has shown promise in pain management. Previous studies by our research group identified an increase in pain sensitivity as a consequence of prenatal hypoxia-ischemia (HI) in an animal model. This study aimed to investigate the efficacy of CBG in acute and chronic hyperalgesia induced by prenatal HI. A pharmacological screening was first conducted using hot plate and open-field tests to evaluate the antinociceptive and locomotor activities of animals administered with a 50 mg/kg oral dose of cannabis extract with a high CBG content. Prenatal HI was induced in pregnant rats, and the offspring were used to evaluate the acute antinociceptive effect of CBG in the formalin-induced peripheral pain model, while chronic antinociceptive effects were observed through spinal nerve ligation (SNL) surgery, a model used to induce neuropathic pain. Our results show that CBG exhibited an antinociceptive effect in the hot plate test without affecting the animals’ motor function in the open-field test. CBG significantly reduced formalin-induced reactivity in HI offspring during both the neurogenic and inflammatory phases. CBG treatment alleviated thermal and mechanical hypernociception induced by SNL. Biomolecular analysis revealed CBG’s ability to modulate expression, particularly reducing TNFα and Nav1.7 in HI male and female rats, respectively. These results highlight CBG as a potential antinociceptive agent in acute and chronic pain models, suggesting it as a promising therapeutic option without inducing motor impairment. Further research is needed to fully elucidate its mechanisms and clinical applications in pain management.

A Reinforced Whale Optimization Algorithm for Solving Mathematical Optimization Problems.

The whale optimization algorithm has several advantages, such as simple operation, few control parameters, and a strong ability to jump out of the local optimum, and has been used to solve various practical optimization problems. In order to improve its convergence speed and solution quality, a reinforced whale optimization algorithm (RWOA) was designed. Firstly, an opposition-based learning strategy is used to generate other optima based on the best optimal solution found during the algorithm's iteration, which can increase the diversity of the optimal solution and accelerate the convergence speed. Secondly, a dynamic adaptive coefficient is introduced in the two stages of prey and bubble net, which can balance exploration and exploitation. Finally, a kind of individual information-reinforced mechanism is utilized during the encircling prey stage to improve the solution quality. The performance of the RWOA is validated using 23 benchmark test functions, 29 CEC-2017 test functions, and 12 CEC-2022 test functions. Experiment results demonstrate that the RWOA exhibits better convergence accuracy and algorithm stability than the WOA on 20 benchmark test functions, 21 CEC-2017 test functions, and 8 CEC-2022 test functions, separately. Wilcoxon's rank sum test shows that there are significant statistical differences between the RWOA and other algorithms.

MSBWO: A Multi-Strategies Improved Beluga Whale Optimization Algorithm for Feature Selection.

Feature selection (FS) is a classic and challenging optimization task in most machine learning and data mining projects. Recently, researchers have attempted to develop more effective methods by using metaheuristic methods in FS. To increase population diversity and further improve the effectiveness of the beluga whale optimization (BWO) algorithm, in this paper, we propose a multi-strategies improved BWO (MSBWO), which incorporates improved circle mapping and dynamic opposition-based learning (ICMDOBL) population initialization as well as elite pool (EP), step-adaptive Lévy flight and spiral updating position (SLFSUP), and golden sine algorithm (Gold-SA) strategies. Among them, ICMDOBL contributes to increasing the diversity during the search process and reducing the risk of falling into local optima. The EP technique also enhances the algorithm's ability to escape from local optima. The SLFSUP, which is distinguished from the original BWO, aims to increase the rigor and accuracy of the development of local spaces. Gold-SA is introduced to improve the quality of the solutions. The hybrid performance of MSBWO was evaluated comprehensively on IEEE CEC2005 test functions, including a qualitative analysis and comparisons with other conventional methods as well as state-of-the-art (SOTA) metaheuristic approaches that were introduced in 2024. The results demonstrate that MSBWO is superior to other algorithms in terms of accuracy and maintains a better balance between exploration and exploitation. Moreover, according to the proposed continuous MSBWO, the binary MSBWO variant (BMSBWO) and other binary optimizers obtained by the mapping function were evaluated on ten UCI datasets with a random forest (RF) classifier. Consequently, BMSBWO has proven very competitive in terms of classification precision and feature reduction.

Meshfree Variational-Physics-Informed Neural Networks (MF-VPINN): An Adaptive Training Strategy

In this paper, we introduce a Meshfree Variational-Physics-Informed Neural Network. It is a Variational-Physics-Informed Neural Network that does not require the generation of the triangulation of the entire domain and that can be trained with an adaptive set of test functions. In order to generate the test space, we exploit an a posteriori error indicator and add test functions only where the error is higher. Four training strategies are proposed and compared. Numerical results show that the accuracy is higher than the one of a Variational-Physics-Informed Neural Network trained with the same number of test functions but defined on a quasi-uniform mesh.

Multiple elite strategy enhanced RIME algorithm for 3D UAV path planning

With the wave of artificial intelligence sweeping the world in recent years, UAVs is widely used in various fields. UAV path planning has attracted much attention from scientists as an essential part of UAV work. In order to design an efficient and reasonable 3D UAV path planning program, recent researchers have invented and improved many algorithms. This paper proposes an elite RIME algorithm for 3D UAV path planning. First, we propose an elite reverse learning population selection strategy based on piecewise mapping to enhance the population diversity of the algorithm for better exploration. Second, this paper proposes a stochastic factor-controlled elite pool exploration strategy so that the algorithm is difficult to enter the local optimum and can better explore the global optimum. Then, this paper proposes a hard frost puncture exploitation strategy based on the sine–cosine function so that the algorithm can find the global optimum faster during the exploitation process. Meanwhile, in order to test the performance of the algorithm proposed in this paper, we compare it with 13 other intelligent optimization algorithms that are classical and popular nowadays on 52 test functions in three test sets, CEC2017, CEC2020, and CEC2022, and obtain competitive results. Finally, we applied it to the 3D UAV path planning problem in three different terrain scenarios, and the ELRIME algorithm achieved good results in all of them. Especially in the 7-peak model, the ELRIME algorithm improves the performance of the RIME algorithm by a factor of two. In the 9-peak model, the average value aspect also reduce the cost by 91 compared to the RIME algorithm, and more importantly, it has the smallest fluctuation in 30 runs, which is among the most stable of all the compared algorithms. In the 12-peak model, its stability is also significantly enhanced, and in terms of worst-case cost, it improves the cost by 340 compared to RIME.

Parameter tuning for active disturbance rejection control of fixed-wing UAV based on improved bald eagle search algorithm

PurposeThis paper aims to develop a method for tuning the parameters of the active disturbance rejection controller (ADRC) for fixed-wing unmanned aerial vehicles (UAVs). The bald eagle search (BES) algorithm has been improved, and a cost function has been designed to enhance the optimization efficiency of ADRC parameters.Design/methodology/approachA six-degree-of-freedom nonlinear model for a fixed-wing UAV has been developed, and its attitude controller has been formulated using the active disturbance rejection control method. The parameters of the disturbance rejection controller have been fine-tuned using the collaborative mutual promotion bald eagle search (CMP-BES) algorithm. The pitch and roll controllers for the UAV have been individually optimized to obtain the most effective controller parameters.FindingsInspired by the salp swarm algorithm (SSA), the interaction among individual eagles has been incorporated into the CMP-BES algorithm, thereby enhancing the algorithm's exploration capability. The efficient and accurate optimization ability of the proposed algorithm has been demonstrated through comparative experiments with genetic algorithm, particle swarm optimization, Harris hawks optimization HHO, BES and modified bald eagle search algorithms. The algorithm's capability to solve complex optimization problems has been further proven by testing on the CEC2017 test function suite. A transitional function for fitness calculation has been introduced to accelerate the ability of the algorithm to find the optimal parameters for the ADRC controller. The tuned ADRC controller has been compared with the classical proportional-integral-derivative (PID) controller, with gust disturbances introduced to the UAV body axis. The results have shown that the tuned ADRC controller has faster response times and stronger disturbance rejection capabilities than the PID controller.Practical implicationsThe proposed CMP-BES algorithm, combined with a fitness function composed of transition functions, can be used to optimize the ADRC controller parameters for fixed-wing UAVs more quickly and effectively. The tuned ADRC controller has exhibited excellent robustness and disturbance rejection capabilities.Originality/valueThe CMP-BES algorithm and transitional function have been proposed for the parameter optimization of the active disturbance rejection controller for fixed-wing UAVs.