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hyperparameter optimization of orthogonal functions in the numerical solution of differential equations

MATHEMATICAL METHODS IN THE APPLIED SCIENCES 2025年第1期48卷 605-625页

作者： Aghaei, Alireza Afzal Parand, Kourosh Shahid Beheshti Univ Fac Math Sci Dept Comp & Data Sci Tehran Iran Shahid Beheshti Univ Inst Cognit & Brain Sci Dept Cognit Modeling Tehran Iran

Numerical methods for solving differential equations often rely on the expansion of the approximate solution using basis functions. The choice of an appropriate basis function plays a crucial role in enhancing the accuracy of the solution. In this study, our aim is to develop algorithms that can identify an optimal basis function for any given differential equation. To achieve this, we explore fractional rational Jacobi functions as a versatile basis, incorporating hyperparameters related to rational mappings, Jacobi polynomial parameters, and fractional components. Our research develops hyperparameter optimization algorithms, including parallel grid search, parallel random search, Bayesian optimization, and parallel genetic algorithms. To evaluate the impact of each hyperparameter on the accuracy of the solution, we analyze two benchmark problems on a semi-infinite domain: Volterra's population model and Kidder's equation. We achieve improved convergence and accuracy by judiciously constraining the ranges of the hyperparameters through a combination of random search and genetic algorithms. Notably, our findings demonstrate that the genetic algorithm consistently outperforms other approaches, yielding superior hyperparameter values that significantly enhance the quality of the solution, surpassing state-of-the-art results.

关键词： hyperparameter optimization Jacobi polynomials machine learning nonlinear differential equations

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hyperparameter optimization in Generative Adversarial Networks (GANs) Using Gaussian AHP

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IEEE ACCESS 2025年 13卷 770-788页

作者： Rodrigues, Thiago Serafim Pinheiro, Placido Rogerio Univ Fortaleza Grad Program Appl Informat BR-60811905 Fortaleza Brazil

This study explores optimizing hyperparameters in Generative Adversarial Networks (GANs) using the Gaussian Analytical Hierarchy Process (Gaussian AHP). By integrating machine learning techniques and multi-criteria decision methods, the aim is to enhance the performance and efficiency of GAN models. It trains GAN models using the Fashion MNIST dataset. It applies Gaussian AHP to optimize hyperparameters based on multiple performance criteria, such as the quality of generated images, training stability, and training time. Iterative experiments validate the methodology by automatically adjusting hyperparameters based on the obtained scores, thereby maximizing the model's efficiency and quality. Results indicate significant improvements in image generation quality and computational efficiency. The study highlights the effectiveness of combining Gaussian AHP with GANs for systematic hyperparameter optimization, providing insights into achieving higher performance in image generation tasks. Future research could extend this approach to other neural network architectures and diverse datasets, further demonstrating the versatility of this optimization technique. This method's potential applications extend across various domains, including data augmentation and anomaly detection, indicating its broad applicability and impact.

关键词： Training hyperparameter optimization Generative adversarial networks optimization Computational modeling Bayes methods Scalability Analytic hierarchy process Load modeling Iterative methods hyperparameter optimization gaussian analytical hierarchy process multicriteria decision-making machine learning

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hyperparameter optimization of apple leaf dataset for the disease recognition based on the YOLOv8

JOURNAL OF AGRICULTURE AND FOOD RESEARCH

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JOURNAL OF AGRICULTURE AND FOOD RESEARCH 2025年 21卷

作者： Lee, Yong-Suk Patil, Maheshkumar Prakash Kim, Jeong Gyu Seo, Yong Bae Ahn, Dong-Hyun Kim, Gun-Do Pukyong Natl Univ Inst Food Sci Dept Food Sci & Technol Busan 48513 South Korea Pukyong Natl Univ Ind Univ Cooperat Fdn Busan 48513 South Korea Pukyong Natl Univ Dept Microbiol Busan 48513 South Korea

Apple leaf diseases have a major influence on apple productivity and quality, demanding a precise and efficient recognition system. Using the YOLOv8 family of object detection models, we created a disease recognition model for the apple leaf dataset in this study. The developed model was fine-tuned extensively by hyperparameter optimization to identify the best variant for practical deployment. Firstly, fine-tuning with different YOLOv8 series was conducted on an apple leaf dataset including various types of images. Among them, the YOLOv8s demonstrated the best balance with a fitness of 0.97171, a precision of 0.97082, a recall of 0.96837, a mAP@0.5 of 0.98016, and an image processing speed of 1.58 ms. Further hyperparameter optimization was conducted using the One-Factor-At-a-Time (OFAT) and Random Search (RS) methods. In this case, the optimal settings determined as per the OFAT method were a batch size of 48, a learning rate of 0.01, a weight decay of 0.0005, a momentum of 0.963, and 200 epochs. These settings were adopted as the baseline for RS. RS then searched for 50 additional configurations;the best configuration, C34 (batch size of 48, learning rate of 0.0137, momentum of 0.9433, and weight decay of 0.0009), achieved a fitness score of 0.97688, a precision of 0.97797, a recall of 0.97295, and a mAP@0.5 of 0.98257. The correlation analysis showed that learning rate and momentum significantly impacted the performance of the models. Overall, the C34 model demonstrates high accuracy, rapid processing speed, and robustness suitable for training real-time, large-scale apple leaf disease recognition.

关键词： Apple leaf disease YOLOv8 hyperparameter optimization One-factor-at-a-time Random search

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Penalty hyperparameter optimization with diversity measure for nonnegative low-rank approximation

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APPLIED NUMERICAL MATHEMATICS 2025年 208卷 189-204页

作者： Del Buono, Nicoletta Esposito, Flavia Selicato, Laura Zdunek, Rafal Univ Bari Aldo Moro Dept Math Via Orabona 4 I-70125 Bari Italy Natl Res Council IRSA CNR Water Res Inst Vle Francesco Blasio 5 I-70132 Bari Italy Wroclaw Univ Sci & Technol Fac Elect Photon & Microsyst 27 Wybrzeze Wyspianskiego St PL-50370 Wroclaw Poland

Learning tasks are often based on penalized optimization problems in which a sparse solution is desired. This can lead to more interpretative results by identifying a smaller subset of important features or components and reducing the dimensionality of the data representation, as well. In this study, we propose a new method to solve a constrained Frobenius norm-based nonnegative low- rank approximation, and the tuning of the associated penalty hyperparameter, simultaneously. The penalty term added is a particular diversity measure that is more effective for sparseness purposes than other classical norm-based penalties (i.e., 81 or 8 2,1 norms). As it is well known, setting the hyperparameters of an algorithm is not an easy task. Our work drew on developing an optimization method and the corresponding algorithm that simultaneously solves the sparsity-constrained nonnegative approximation problem and optimizes its associated penalty hyperparameters. We test the proposed method by numerical experiments and show its promising results on several synthetic and real datasets.

关键词： hyperparameter optimization Penalty coefficient Sparseness Low-rank approximation

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Patient-Specific hyperparameter optimization of a Deep Learning-Based Tumor Autocontouring Algorithm on 2D Liver, Prostate, and Lung Cine MR Images: A Pilot Study

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ALGORITHMS 2025年第4期18卷 233-233页

作者： Han, Gawon Wachowicz, Keith Usmani, Nawaid Yee, Don Wong, Jordan Elangovan, Arun Yun, Jihyun Fallone, B. Gino Univ Alberta Dept Oncol Med Phys Div 11560 Univ Ave Edmonton AB T6G 1Z2 Canada Cross Canc Inst Dept Med Phys 11560 Univ Ave Edmonton AB T6G 1Z2 Canada Cross Canc Inst Dept Radiat Oncol 11560 Univ Ave Edmonton AB T6G 1Z2 Canada Univ Alberta Dept Oncol Radiat Oncol Div 11560 Univ Ave Edmonton AB T6G 1Z2 Canada British Columbia Canc Victoria Radiat Oncol 2410 Lee Ave Victoria BC V8R 6V5 Canada Univ Calgary Tom Baker Canc Ctr Dept Oncol Radiat Oncol 1331 29th St NW Calgary AB T2N 4N2 Canada

Linear accelerator-magnetic resonance (linac-MR) hybrid systems allow for real-time magnetic resonance imaging (MRI)-guided radiotherapy for more accurate dose delivery to the tumor and improved sparing of the adjacent healthy tissues. However, for real-time tumor detection, it is unfeasible for a human expert to manually contour (gold standard) the tumor at the fast imaging rate of a linac-MR. This study aims to develop a neural network-based tumor autocontouring algorithm with patient-specific hyperparameter optimization (HPO) and to validate its contouring accuracy using in vivo MR images of cancer patients. Two-dimensional (2D) intrafractional MR images were acquired at 4 frames/s using 3 tesla (T) MRI from 11 liver, 24 prostate, and 12 lung cancer patients. A U-Net architecture was applied for tumor autocontouring and was further enhanced by implementing HPO using the Covariance Matrix Adaptation Evolution Strategy. Six hyperparameters were optimized for each patient, for which intrafractional images and experts' manual contours were input into the algorithm to find the optimal set of hyperparameters. For evaluation, Dice's coefficient (DC), centroid displacement (CD), and Hausdorff distance (HD) were computed between the manual contours and autocontours. The performance of the algorithm was benchmarked against two standardized autosegmentation methods: non-optimized U-Net and nnU-Net. For the proposed algorithm, the mean (standard deviation) DC, CD, and HD of the 47 patients were 0.92 (0.04), 1.35 (1.03), and 3.63 (2.17) mm, respectively. Compared to the two benchmarking autosegmentation methods, the proposed algorithm achieved the best overall performance in terms of contouring accuracy and speed. This work presents the first tumor autocontouring algorithm applicable to the intrafractional MR images of liver and prostate cancer patients for real-time tumor-tracked radiotherapy. The proposed algorithm performs patient-specific HPO, enabling accurate tumor deli

关键词： autocontouring intrafractional motion management tumor tracking linac-MR hybrid MRI guidance radiotherapy hyperparameter optimization

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Surrogate-based automated hyperparameter optimization for expensive automotive crashworthiness optimization

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STRUCTURAL AND MULTIDISCIPLINARY optimization 2025年第4期68卷 1-19页

作者： Long, Fu Xing van Stein, Niki Frenzel, Moritz Krause, Peter Gitterle, Markus Back, Thomas BMW Grp Knorrstr 147 D-80788 Munich Germany Leiden Univ LIACS Niels Bohrweg 1 NL-2333 Leiden Netherlands Altair Engn GmbH Calwer Str 7 D-71034 Boblingen Germany Divis Intelligent Solut GmbH Joseph von Fraunhofer Str 20 D-44227 Dortmund Germany Munich Univ Appl Sci Dachauer Str 98b D-80335 Munich Germany

In the automotive industry, solving crashworthiness optimization problems efficiently is crucial to minimize time and cost investment on expensive function evaluations, e.g., using simulation runs. Nonetheless, automotive crashworthiness optimization is time-consuming and challenging even with domain knowledge, due to the fact that crash problems are typically high-dimensional, nonlinear, and discontinuous. In this work, we propose an automated hyperparameter optimization (HPO) approach for expensive black-box optimization (BBO) problems that can assist practitioners to solve automotive crash problems efficiently using optimally configured optimization algorithms. Precisely, the landscape characteristics of BBO problems, e.g., quantified using exploratory landscape analysis (ELA), are analyzed to identify cheap-to-evaluate representative functions that belong to the same optimization problem class. Based on these representative functions, algorithm configurations can be optimally fine-tuned at a relatively low computational cost. Using three optimization algorithms, consisting of modular covariance matrix adaptation evolutionary strategy (CMA-ES), modular differential evolution (DE), and Bayesian optimization (BO), we evaluate the potential of our approach based on the black-box optimization benchmarking (BBOB) suite and an automotive side crash problem. Since the optimal configurations identified using our approach can perform well on most of the BBOB functions, we believe that our approach can generalize well to BBO problems with similar optimization complexity. For the automotive side crash problem, the BO configuration fine-tuned using our approach can outperform the default BO configuration as well as the conventional response surface method (RSM), in terms of the best-found-solution and convergence speed. Furthermore, better solutions can be identified using the proposed approach compared to successive RSM (SRSM), when dealing with complex crash functions and

关键词： Black-box optimization hyperparameter optimization Representative functions Bayesian optimization Exploratory landscape analysis Automotive crashworthiness

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Accelerating hyperparameter optimization with a secretary

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NEUROCOMPUTING 2025年 625卷

作者： Munoz, Victor Ballester, Carmen Copaci, Dorin Moreno, Luis Blanco, Dolores Univ Carlos III Madrid Syst Engn & Automat Dept Avda Univ 30 Leganes 28911 Madrid Spain

hyperparameter optimization (HPO) is a vital step in machine learning (ML) for enhancing model performance. However, the vast and complex nature of the search space makes HPO both challenging and resource- intensive. Automatic HPO methods have demonstrated their ability to efficiently explore high-dimensional hyperparameter spaces and identify optimal solutions, but training and evaluating the model for each set of hyperparameters is still computationally expensive. To further reduce the computational cost, we propose a novel strategy that wraps the HPO process and terminates it based on the sequence of hyperparameters evaluated. The algorithm is inspired by the classic secretary problem, with two additional variations to better adjust to the HPO process. We evaluated the algorithm using popular HPO samplers, including Random Search (RS), Tree-structured Parzen Estimator (TPE), Bayesian optimization with Gaussian Processes (BOGP), Genetic Algorithms (GA), and Particle Swarm optimization (PSO). Results indicate that the proposed algorithm accelerates the HPO process by an average of 34%, with only a minimal trade-off in solution quality of 8%. The algorithm is straightforward to implement, compatible with any HPO setup, and particularly effective in the early stages of optimization. This makes it a valuable tool for practitioners aiming to quickly identify promising hyperparameters or reducing the search space, significantly cutting down the time and computational resources required.

关键词： hyperparameter optimization Secretary problem Machine learning

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Multi-objective hyperparameter optimization of artificial neural network in emulating building energy simulation

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ENERGY AND BUILDINGS 2025年 337卷

作者： Ibrahim, Mahdi Harkouss, Fatima Biwole, Pascal Fardoun, Farouk Ouldboukhitine, Salah-Eddine Univ Clermont Auvergne Inst Pascal CNRS SIGMA Clermont F-63000 Clermont Ferrand France Al Maaref Univ Fac Engn Beirut Lebanon PSL Res Univ Ctr Proc MINES Paris PERSEE CS 10207 F-06904 Sophia Antipolis France Calif State Polytech Univ Sch Engn Arcata CA 95521 USA Lebanese Univ Fac Engn Beirut Lebanon

Artificial Neural Networks (ANNs) play a significant role in emulating Building Energy Simulation (BES), forecasting building energy consumption, and optimizing energy retrofit measures. Determining the appropriate architecture for an ANN that can manage multiple predictions simultaneously is a complex task that requires extensive experimentation and validation to achieve optimal performance. To address this challenge, a novel methodology referred to as Multi-Objective hyperparameter optimization of ANN (MOHO-ANN) is introduced. This approach involves aligning ANN prediction results with data to achieve optimal performance by tuning the ANN's hyperparameters. The methodology consists of calibrating the BES model, creating data using a model sampling step for ANN training, and formulating multi-objective optimization using hyperparameter tuning to obtain the set of optimal ANN architectures. Lastly, a Multi-Criteria Decision-Making (MCDM) step is employed to select the optimal ANN. This method is applied to retrofit an existing building by incorporating weather data, passive, and renewable retrofit measures. The ANN is used to predict hourly energy consumption, energy generation, and thermal comfort in the retrofit scenario. 1.75 million hourly data points have been used to train, validate, and test the ANN model. The results underscore the practicality of MOHO-ANN procedure in achieving predictions, demonstrating a coefficient of determination (R2) exceeding 0.98. Further research directions should consider employing the optimal architectural model to perform retrofit optimization by incorporating climate change.

关键词： Artificial Neural Network Machine learning hyperparameter optimization Building energy simulation Multi criteria decision making Multi-objective optimization

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A Novel hyperparameter optimization Approach for Supervised Classification: Phase Prediction of Multi-Principal Element Alloys

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COGNITIVE COMPUTATION 2025年第1期17卷 1-14页

作者： Fatimi, Syed Hassan Wang, Zidong Chang, Isaac T. H. Liu, Weibo Liu, Xiaohui Brunel Univ London Dept Comp Sci Uxbridge UB8 3PH Middlesex England Brunel Univ London Brunel Ctr Adv Solidificat Technol BCAST Uxbridge UB8 3PH Middlesex England

In this paper, a hyperparameter optimization approach is proposed for the phase prediction of multi-principal element alloys (MPEAs) through the introduction of two novel hyperparameters: outlier detection and feature subset selection. To gain a deeper understanding of the connection between alloy phases and their elemental properties, an artificial neural network is employed, with hyperparameter optimization performed using a genetic algorithm to select the optimum hyperparameters. The two novel hyperparameters, outlier detection and feature subset selection, are introduced within the optimization framework, along with new crossover and mutation operators for handling single and multi-valued genes simultaneously. Ablation studies are conducted, illustrating an improvement in prediction accuracy with the inclusion of these new hyperparameters. A comparison with five existing algorithms in multi-class classification is made, demonstrating an improvement in the performance of phase prediction, thereby providing a better perception of the alloy phase space for high-throughput MPEA design.

关键词： hyperparameter optimization Outlier detection Feature selection Artificial neural networks Genetic algorithm Multi-principal element alloys

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Least Squares Support Vector Machines With Variable Selection and hyperparameter optimization for Complex Structures Reliability Assessment

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QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL 2025年第4期41卷 1461-1470页

作者： Dong, Xiaowei Zhang, Hao Li, Zhenao Zhu, Chunyan Yi, Shujuan Chen, Changhai Heilongjiang Bayi Agr Univ Sch Engn Daqing Heilongjiang Peoples R China Minist Agr & Rural Affairs Inspect & Test Ctr Agr Prod & Processed Prod Qual Daqing Heilongjiang Peoples R China Heilongjiang Bayi Agr Univ Coll Elect & Informat Daqing Heilongjiang Peoples R China Harbin Acad Agr Sci Harbin Heilongjiang Peoples R China

For effectively estimating the reliability of complex structures, a least squares support vector machine with variable selection and hyperparameter optimization (SVMSO, short for) is proposed based on local linear embedding with Pearson coefficient and location density with particle swarm optimization (LDPSO) algorithm. In this proposed method, the local linear embedding with Pearson coefficient is used to select the variables that have a strong correlation with output responses, which are embedded in relatively low-dimensional space to avoid the negative influence of high-dimensional input parameters. The optimal hyperparameters of least squares support vector machines (LSSVM) are obtained by applying the LDPSO to improve the accuracy of LSSVM affected by the hyperparameters. Taking civil aircraft turbine blisk as a study case, the effectiveness and applicability of SVMSO are verified in aspects of modeling quality and simulation characteristics, by comparing direct simulation, support vector machine, and LSSVM. The case results and conclusions represent that the proposed method has good precision and efficiency under a high-dimensional data scale, and is suitable for reliability analysis of complex structures.

关键词： hyperparameter optimization least squares support vector machines reliability analysis turbine blisk variable selection

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