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Algorithms
Special Issues
Numerical Optimization and Algorithms: 3rd Edition
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Numerical Optimization and Algorithms: 3rd Edition

A special issue of Algorithms (ISSN 1999-4893). This special issue belongs to the section "Algorithms for Multidisciplinary Applications".

Deadline for manuscript submissions: 30 April 2025 | Viewed by 4493

Special Issue Editors

Prof. Dr. Dunhui Xiao

E-Mail Website
Guest Editor
School of Mathematical Sciences, Tongji University, Shanghai 200092, China
Interests: AI; machine learning; model reduction; finite element analysis
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Shuai Li

E-Mail Website
Guest Editor
Faculty of Information Technology and Electrical Engineering, University of Oulu, 90570 Oulu, Finland
Interests: robotic manipulation; autonomous manufacturing; multi-robot coordination; intelligent control and optimization
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Numerical algorithms and optimization are widely used in fields of science and engineering such as physics, environment, mechanics, biology, data science, economics, and finance for problems which are complex, highly nonlinear, and difficult to predict. Over the last decade, computational problems have become popular due to improved computer performance, computing methods, and the rapid development of data science technology. However, these developments have also raised various issues and challenges, including high nonlinearity, the curse of dimensionality, uncertainty, and complexity, which urgently need to be addressed by developing new numerical algorithms such as graph theory, optimization algorithms, algebra, uncertainty, data science or analysis, new differential equation-solving algorithms and methods, probability, and statistic algorithms and methods.

This Special Issue deals with various numerical algorithms in the science and engineering fields.

Prof. Dr. Dunhui Xiao
Prof. Dr. Shuai Li
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Algorithms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • graph theory
  • optimization
  • algebra
  • uncertainty
  • data science
  • differential equations
  • probability and statistics
  • numerical algorithms

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Related Special Issue

Published Papers (7 papers)

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Research

18 pages, 479 KiB  
Article
Computational Aspects of L0 Linking in the Rasch Model
by Alexander Robitzsch
Algorithms 2025, 18(4), 213; https://doi.org/10.3390/a18040213 - 9 Apr 2025
Viewed by 218
Abstract
The L0 linking approach replaces the L2 loss function in mean–mean linking under the Rasch model with the L0 loss function. Using the L0 loss function offers the advantage of potential robustness against fixed differential item functioning effects. However, [...] Read more.
The L0 linking approach replaces the L2 loss function in mean–mean linking under the Rasch model with the L0 loss function. Using the L0 loss function offers the advantage of potential robustness against fixed differential item functioning effects. However, its nondifferentiability necessitates differentiable approximations to ensure feasible and computationally stable estimation. This article examines alternative specifications of two approximations, each controlled by a tuning parameter ε that determines the approximation error. Results demonstrate that the optimal ε value minimizing the RMSE of the linking parameter estimate depends on the magnitude of DIF effects, the number of items, and the sample size. A data-driven selection of ε outperformed a fixed ε across all conditions in both a numerical illustration and a simulation study. Full article
(This article belongs to the Special Issue Numerical Optimization and Algorithms: 3rd Edition)
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45 pages, 10045 KiB  
Article
An Automated Framework for Streamlined CFD-Based Design and Optimization of Fixed-Wing UAV Wings
by Chris Pliakos, Giorgos Efrem, Dimitrios Terzis and Pericles Panagiotou
Algorithms 2025, 18(4), 186; https://doi.org/10.3390/a18040186 - 24 Mar 2025
Viewed by 508
Abstract
The increasing complexity of the UAV aerodynamic design, imposed by novel configurations and requirements, has highlighted the need for efficient tools for high-fidelity simulation, especially for optimization purposes. The current work presents an automated CFD framework, tailored for fixed-wing UAVs, designed to streamline [...] Read more.
The increasing complexity of the UAV aerodynamic design, imposed by novel configurations and requirements, has highlighted the need for efficient tools for high-fidelity simulation, especially for optimization purposes. The current work presents an automated CFD framework, tailored for fixed-wing UAVs, designed to streamline the geometry generation of wings, mesh creation, and simulation execution into a Python-based pipeline. The framework employs a parameterized meshing module capable of handling a broad range of wing geometries within an extensive design space, thereby reducing manual effort and achieving pre-processing times in the order of five minutes. Incorporating GPU-enabled solvers and high-performance computing environments allows for rapid and scalable aerodynamic evaluations. An automated methodology for assessing the CFD results is presented, addressing the discretization and iterative errors, as well as grid resolution, especially near wall surfaces. Comparisons with the results produced by a specialized mechanical engineer with over five years of experience in aircraft-related CFD indicate high accuracy, with deviations below 3% for key aerodynamic metrics. A large-scale deployment further demonstrates consistency across diverse wing samples. A Bayesian Optimization case study then illustrates the framework’s utility, identifying a wing design with an 8% improvement in the lift-to-drag ratio, while maintaining an average y+ value below 1 along the surface. Overall, the proposed approach streamlines fixed-wing UAV design processes and supports advanced aerodynamic optimization and data generation. Full article
(This article belongs to the Special Issue Numerical Optimization and Algorithms: 3rd Edition)
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28 pages, 2644 KiB  
Article
The Euler-Type Universal Numerical Integrator (E-TUNI) with Backward Integration
by Paulo M. Tasinaffo, Gildárcio S. Gonçalves, Johnny C. Marques, Luiz A. V. Dias and Adilson M. da Cunha
Algorithms 2025, 18(3), 153; https://doi.org/10.3390/a18030153 - 8 Mar 2025
Viewed by 357
Abstract
The Euler-Type Universal Numerical Integrator (E-TUNI) is a discrete numerical structure that couples a first-order Euler-type numerical integrator with some feed-forward neural network architecture. Thus, E-TUNI can be used to model non-linear dynamic systems when the real-world plant’s analytical model is unknown. From [...] Read more.
The Euler-Type Universal Numerical Integrator (E-TUNI) is a discrete numerical structure that couples a first-order Euler-type numerical integrator with some feed-forward neural network architecture. Thus, E-TUNI can be used to model non-linear dynamic systems when the real-world plant’s analytical model is unknown. From the discrete solution provided by E-TUNI, the integration process can be either forward or backward. Thus, in this article, we intend to use E-TUNI in a backward integration framework to model autonomous non-linear dynamic systems. Three case studies, including the dynamics of the non-linear inverted pendulum, were developed to verify the computational and numerical validation of the proposed model. Full article
(This article belongs to the Special Issue Numerical Optimization and Algorithms: 3rd Edition)
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6 pages, 686 KiB  
Communication
Means and Issues for Adjusting Principal Component Analysis Results
by Tomokazu Konishi
Algorithms 2025, 18(3), 129; https://doi.org/10.3390/a18030129 - 25 Feb 2025
Viewed by 350
Abstract
Background: Principal component analysis (PCA) is a method that identifies common directions within multivariate data and presents the data in as few dimensions as possible. One of the advantages of PCA is its objectivity, as the same results can be obtained regardless of [...] Read more.
Background: Principal component analysis (PCA) is a method that identifies common directions within multivariate data and presents the data in as few dimensions as possible. One of the advantages of PCA is its objectivity, as the same results can be obtained regardless of who performs the analysis. However, PCA is not a robust method and is sensitive to noise. Consequently, the directions identified by PCA may deviate slightly. If we can teach PCA to account for this deviation and correct it, the results should become more comprehensible. Methods: The top two PCA results were rotated using a rotation unitary matrix. Results: These contributions were determined and compared with the original. At smaller rotations, the change in contribution was also small and the effect on independence was not severe. The rotation made the data considerably more comprehensible. Conclusions: The methods for achieving this and an issue with this are presented. However, care should be taken not to detract from the superior objectivity of PCA. Full article
(This article belongs to the Special Issue Numerical Optimization and Algorithms: 3rd Edition)
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13 pages, 375 KiB  
Article
Algorithms for Calculating Generalized Trigonometric Functions
by Ivanna Dronyuk
Algorithms 2025, 18(2), 60; https://doi.org/10.3390/a18020060 - 23 Jan 2025
Viewed by 728
Abstract
In this paper, algorithms for calculating different types of generalized trigonometric and hyperbolic functions are developed and presented. The main attention is focused on the Ateb-functions, which are the inverse functions to incomplete Beta-functions. The Ateb-functions can generalize every kind [...] Read more.
In this paper, algorithms for calculating different types of generalized trigonometric and hyperbolic functions are developed and presented. The main attention is focused on the Ateb-functions, which are the inverse functions to incomplete Beta-functions. The Ateb-functions can generalize every kind of implementation where trigonometric and hyperbolic functions are used. They have been successfully applied to vibration motion modeling, data protection, signal processing, and others. In this paper, the Fourier transform’s generalization for periodic Ateb-functions in the form of Ateb-transform is determined. Continuous and discrete Ateb-transforms are constructed. Algorithms for their calculation are created. Also, Ateb-transforms with one and two parameters are considered, and algorithms for their realization are built. The quantum calculus generalization for hyperbolic Ateb-functions is constructed. Directions for future research are highlighted. Full article
(This article belongs to the Special Issue Numerical Optimization and Algorithms: 3rd Edition)
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19 pages, 2939 KiB  
Article
An Efficient and Accurate Adaptive Time-Stepping Method for the Landau–Lifshitz Equation
by Hyundong Kim, Soobin Kwak, Moumni Mohammed, Seungyoon Kang, Seokjun Ham and Junseok Kim
Algorithms 2025, 18(1), 1; https://doi.org/10.3390/a18010001 - 26 Dec 2024
Cited by 1 | Viewed by 860
Abstract
This article presents an efficient and accurate adaptive time-stepping finite difference method (FDM) for solving the Landau–Lifshitz (LL) equation, which is an important mathematical model in understanding magnetic materials and processes. Our proposed algorithm strategically selects an adaptive time step, ensuring that the [...] Read more.
This article presents an efficient and accurate adaptive time-stepping finite difference method (FDM) for solving the Landau–Lifshitz (LL) equation, which is an important mathematical model in understanding magnetic materials and processes. Our proposed algorithm strategically selects an adaptive time step, ensuring that the maximum displacement falls within a predefined tolerance threshold. Furthermore, this adaptive approach allows the utilization of larger time steps near equilibrium states and results in faster computations. For example, we introduce a numerical test where the adaptive time step decreases from 3.05×10−7 to 3.52×10−9. If a uniform time step is applied, around a 100 times smaller time step must be applied at unnecessary cases. To demonstrate the high performance of our proposed algorithm, we conduct several characteristic benchmark tests. The computational results confirm that the proposed algorithm is efficient and accurate. Overall, our adaptive time-stepping FDM offers a promising solution for accurately and efficiently solving the LL equation and contributes to advancements in the understanding and analysis of magnetic phenomena. Full article
(This article belongs to the Special Issue Numerical Optimization and Algorithms: 3rd Edition)
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31 pages, 9187 KiB  
Article
Optimized Analytical–Numerical Procedure for Ultrasonic Sludge Treatment for Agricultural Use
by Filippo Laganà, Salvatore A. Pullano, Giovanni Angiulli and Mario Versaci
Algorithms 2024, 17(12), 592; https://doi.org/10.3390/a17120592 - 21 Dec 2024
Cited by 2 | Viewed by 1062
Abstract
This paper presents an integrated approach based on physical–mathematical models and numerical simulations to optimize sludge treatment using ultrasound. The main objective is to improve the efficiency of the purification system by reducing the weight and moisture of the purification sludge, therefore ensuring [...] Read more.
This paper presents an integrated approach based on physical–mathematical models and numerical simulations to optimize sludge treatment using ultrasound. The main objective is to improve the efficiency of the purification system by reducing the weight and moisture of the purification sludge, therefore ensuring regulatory compliance and environmental sustainability. A coupled temperature–humidity model, formulated by partial differential equations, describes materials’ thermal and water evolution during treatment. The numerical resolution, implemented by the finite element method (FEM), allows the simulation of the system behavior and the optimization of the operating parameters. Experimental results confirm that ultrasonic treatment reduces the moisture content of sludge by up to 20% and improves its stability, making it suitable for agricultural applications or further treatment. Functional controls of sonication and the reduction of water content in the sludge correlate with the obtained results. Ultrasound treatment has been shown to decrease the specific weight of the sludge sample both in pretreatment and treatment, therefore improving stabilization. In various experimental conditions, the weight of the sludge is reduced by a maximum of about 50%. Processed sludge transforms waste into a resource for the agricultural sector. Treatment processes have been optimized with low-energy operating principles. Additionally, besides utilizing energy-harvesting technology, plant operating processes have been optimized, accounting for approximately 55% of the consumption due to the aeration of active sludge. In addition, an extended analysis of ultrasonic wave propagation is proposed. Full article
(This article belongs to the Special Issue Numerical Optimization and Algorithms: 3rd Edition)
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