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Algorithms
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Numerical Optimization and Algorithms
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Numerical Optimization and Algorithms

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

Deadline for manuscript submissions: closed (31 December 2023) | Viewed by 6604

Special Issue Editors

Prof. Dr. Dunhui Xiao

E-Mail Website
Guest Editor
School of Mathematical Sciences, Tongji University, Shanghai 201804, 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, 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, finance, and so on. These problems are complex, highly nonlinear, and difficult to predict. Over the last decade, computational problems have become popular and have gained much attention due to the improved computer performance, computing methods, and the rapid development of data science technology. However, these developments have also raised various issues and challenges, such as high non-linearity, the curse of dimensionality, uncertainty, complexity, and so on. Therefore, these challenges urgently need to be addressed by developing new numerical algorithms such as graph theory, optimization algorithms, algebra, uncertainty, data science or analysis, new differential equations solving algorithms and methods, probability, and statistics algorithms and methods.

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

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

Related Special Issue

Published Papers (5 papers)

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Research

41 pages, 9086 KiB  
Article
Generator of Fuzzy Implications
by Athina Daniilidou, Avrilia Konguetsof, Georgios Souliotis and Basil Papadopoulos
Algorithms 2023, 16(12), 569; https://doi.org/10.3390/a16120569 - 15 Dec 2023
Cited by 1 | Viewed by 1376
Abstract
In this research paper, a generator of fuzzy methods based on theorems and axioms of fuzzy logic is derived, analyzed and applied. The family presented generates fuzzy implications according to the value of a selected parameter. The obtained fuzzy implications should satisfy a [...] Read more.
In this research paper, a generator of fuzzy methods based on theorems and axioms of fuzzy logic is derived, analyzed and applied. The family presented generates fuzzy implications according to the value of a selected parameter. The obtained fuzzy implications should satisfy a number of axioms, and the conditions of satisfying the maximum number of axioms are denoted. New theorems are stated and proven based on the rule that the fuzzy function of fuzzy implication, which is strong, leads to fuzzy negation. In this work, the data taken were fuzzified for the application of the new formulae. The fuzzification of the data was undertaken using four kinds of membership degree functions. The new fuzzy functions were compared based on the results obtained after a number of repetitions. The new proposed methodology presents a new family of fuzzy implications, and also an algorithm is shown that produces fuzzy implications so as to be able to select the optimal method of the generator according to the value of a free parameter. Full article
(This article belongs to the Special Issue Numerical Optimization and Algorithms)
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21 pages, 516 KiB  
Article
Time-Dependent Unavailability Exploration of Interconnected Urban Power Grid and Communication Network
by Matej Vrtal, Radek Fujdiak, Jan Benedikt, Pavel Praks, Radim Bris, Michal Ptacek and Petr Toman
Algorithms 2023, 16(12), 561; https://doi.org/10.3390/a16120561 - 10 Dec 2023
Viewed by 1436
Abstract
This paper presents a time-dependent reliability analysis created for a critical energy infrastructure use case, which consists of an interconnected urban power grid and a communication network. By utilizing expert knowledge from the energy and communication sectors and integrating the renewal theory of [...] Read more.
This paper presents a time-dependent reliability analysis created for a critical energy infrastructure use case, which consists of an interconnected urban power grid and a communication network. By utilizing expert knowledge from the energy and communication sectors and integrating the renewal theory of multi-component systems, a representative reliability model of this interconnected energy infrastructure, based on real network located in the Czech Republic, is established. This model assumes reparable and non-reparable components and captures the topology of the interconnected infrastructure and reliability characteristics of both the power grid and the communication network. Moreover, a time-dependent reliability assessment of the interconnected system is provided. One of the significant outputs of this research is the identification of the critical components of the interconnected network and their interdependencies by the directed acyclic graph. Numerical results indicate that the original design has an unacceptable large unavailability. Thus, to improve the reliability of the interconnected system, a slightly modified design, in which only a limited number of components in the system are modified to keep the additional costs of the improved design limited, is proposed. Consequently, numerical results indicate reducing the unavailability of the improved interconnected system in comparison with the initial reliability design. The proposed unavailability exploration strategy is general and can bring a valuable reliability improvement in the power and communication sectors. Full article
(This article belongs to the Special Issue Numerical Optimization and Algorithms)
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22 pages, 719 KiB  
Article
Computing the Matrix Logarithm with the Romberg Integration Method
by Javier Ibáñez, José M. Alonso, Emilio Defez, Pedro Alonso-Jordá and Jorge Sastre
Algorithms 2023, 16(9), 434; https://doi.org/10.3390/a16090434 - 09 Sep 2023
Viewed by 1057
Abstract
The matrix logarithm function has applicability in many engineering and science fields. Improvements in its calculation, from the point of view of both accuracy and/or execution time, have a direct impact on these disciplines. This paper describes a new numerical algorithm devoted to [...] Read more.
The matrix logarithm function has applicability in many engineering and science fields. Improvements in its calculation, from the point of view of both accuracy and/or execution time, have a direct impact on these disciplines. This paper describes a new numerical algorithm devoted to matrix logarithm computation and using the Romberg integration method, together with the inverse scaling and squaring technique. This novel method was implemented and compared with three different state-of-the-art codes, all based on Padé approximation. The experimental results, under a heterogeneous matrix test battery, showed that the new method was numerically stable, with an elapsed time midway among the other codes, and it generally offered a higher accuracy. Full article
(This article belongs to the Special Issue Numerical Optimization and Algorithms)
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14 pages, 423 KiB  
Article
Neural-Network-Assisted Finite Difference Discretization for Numerical Solution of Partial Differential Equations
by Ferenc Izsák and Rudolf Izsák
Algorithms 2023, 16(9), 410; https://doi.org/10.3390/a16090410 - 28 Aug 2023
Viewed by 941
Abstract
A neural-network-assisted numerical method is proposed for the solution of Laplace and Poisson problems. Finite differences are applied to approximate the spatial Laplacian operator on nonuniform grids. For this, a neural network is trained to compute the corresponding coefficients for general quadrilateral meshes. [...] Read more.
A neural-network-assisted numerical method is proposed for the solution of Laplace and Poisson problems. Finite differences are applied to approximate the spatial Laplacian operator on nonuniform grids. For this, a neural network is trained to compute the corresponding coefficients for general quadrilateral meshes. Depending on the position of a given grid point x0 and its neighbors, we face with a nonlinear optimization problem to obtain the finite difference coefficients in x0. This computing step is executed with an artificial neural network. In this way, for any geometric setup of the neighboring grid points, we immediately obtain the corresponding coefficients. The construction of an appropriate training data set is also discussed, which is based on the solution of overdetermined linear systems. The method was experimentally validated on a number of numerical tests. As expected, it delivers a fast and reliable algorithm for solving Poisson problems. Full article
(This article belongs to the Special Issue Numerical Optimization and Algorithms)
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20 pages, 1283 KiB  
Article
Systematic Analysis and Design of Control Systems Based on Lyapunov’s Direct Method
by Rick Voßwinkel and Klaus Röbenack
Algorithms 2023, 16(8), 389; https://doi.org/10.3390/a16080389 - 14 Aug 2023
Viewed by 956
Abstract
This paper deals with systematic approaches for the analysis of stability properties and controller design for nonlinear dynamical systems. Numerical methods based on sum-of-squares decomposition or algebraic methods based on quantifier elimination are used. Starting from Lyapunov’s direct method, these methods can be [...] Read more.
This paper deals with systematic approaches for the analysis of stability properties and controller design for nonlinear dynamical systems. Numerical methods based on sum-of-squares decomposition or algebraic methods based on quantifier elimination are used. Starting from Lyapunov’s direct method, these methods can be used to derive conditions for the automatic verification of Lyapunov functions as well as for the structural determination of control laws. This contribution describes methods for the automatic verification of (control) Lyapunov functions as well as for the constructive determination of control laws. Full article
(This article belongs to the Special Issue Numerical Optimization and Algorithms)
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