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Axioms
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Differential Equations and Genetic Algorithms
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Differential Equations and Genetic Algorithms

A special issue of Axioms (ISSN 2075-1680).

Deadline for manuscript submissions: closed (31 January 2023) | Viewed by 9443

Special Issue Editor

Dr. Ioannis G. Tsoulos

E-Mail Website
Guest Editor
Department of Informatics and Telecommunications, University of Ioannina, 45110 Ioannina, Greece
Interests: global optimization; neural networks; genetic algorithms; genetic programming
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

It is my pleasure to invite you to submit your valuable work to this Special Issue on “Differential Equations and Genetic Algorithm” to the MDPI journal Axioms.

The aim of this Special Issue is to present recent advances and new machine-learning methods to model and solve differential equations. This Special Issue aims to highlight recent advances in solving differential equations using genetic algorithms and other evolutionary algorithms. Topics include but are not limited to:

  • Stochastic differential equations and machine learning methods;
  • The usage of neural networks to solve differential equations;
  • Deep learning and differential equations;
  • Time-delay differential equations and machine-learning methods;
  • The application of differential equations to robotics;
  • Software specialized to solve differential equations using evolutionary techniques;
  • Parallel techniques to solve differential equations;
  • The usage of grammatical-evolution-based methods to solve and model differential equations.

Dr. Ioannis G. Tsoulos
Guest Editor

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. Axioms 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 2400 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.

Published Papers (6 papers)

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Research

19 pages, 5180 KiB  
Article
Generalized Type 2 Fuzzy Differential Evolution Applied to a Sugeno Controller
by Patricia Ochoa, Cinthia Peraza, Oscar Castillo and Patricia Melin
Axioms 2023, 12(2), 156; https://doi.org/10.3390/axioms12020156 - 02 Feb 2023
Cited by 2 | Viewed by 1096
Abstract
The papers using fuzzy logic have generated continuous improvements for applications, and an example of this is the use of generalized type 2 fuzzy systems in real-world problems. The key idea of this paper is to present a generalized type 2 fuzzy system [...] Read more.
The papers using fuzzy logic have generated continuous improvements for applications, and an example of this is the use of generalized type 2 fuzzy systems in real-world problems. The key idea of this paper is to present a generalized type 2 fuzzy system for augmenting differential evolution with dynamic parameter variation in order to enhance its performance and convergence. A generalized type 2 Sugeno controller was implemented with the aim of enhancing the trajectory of a robot, and an analysis of the execution time and the errors obtained by ITAE, IAE, ITSE, ISEV, RMSE, and MSE is presented. In addition, a comparison with different levels of disturbance applied to the controller was performed with the goal of demonstrating the efficiency of a type 2 fuzzy system. Full article
(This article belongs to the Special Issue Differential Equations and Genetic Algorithms)
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9 pages, 258 KiB  
Article
On Entire Function Solutions to Fermat Delay-Differential Equations
by Xue-Ying Zhang, Ze-Kun Xu and Wei-Ran Lü
Axioms 2022, 11(10), 554; https://doi.org/10.3390/axioms11100554 - 14 Oct 2022
Viewed by 1208
Abstract
This paper concerns the existence and precise expression form of entire solutions to a certain type of delay-differential equation. The significance of our results lie in that we generalize and supplement the related results obtained recently. Full article
(This article belongs to the Special Issue Differential Equations and Genetic Algorithms)
14 pages, 3493 KiB  
Article
Regularization Cuckoo Search Algorithm for Multi-Parameter Optimization of the Multi-Laminated Controlled Release System
by Xinming Zhang, Yi Li and Youhua Fan
Axioms 2022, 11(10), 500; https://doi.org/10.3390/axioms11100500 - 24 Sep 2022
Cited by 2 | Viewed by 1079
Abstract
The multi-laminated controlled release system has been widely used in the modern pharmaceutical industry because of its simple structure and safety, which can control the drug release behavior by regulating its internal parameters. To achieve three desired drug release behaviors of constant rate, [...] Read more.
The multi-laminated controlled release system has been widely used in the modern pharmaceutical industry because of its simple structure and safety, which can control the drug release behavior by regulating its internal parameters. To achieve three desired drug release behaviors of constant rate, linear reduction, and nonlinearity, which can be controlled by the optimization of the controllable parameters in the controlled release system, such as initial concentration and diffusion coefficient, a new regularization cuckoo search algorithm based on the cuckoo search algorithm and Tikhonov regularization method is proposed. The numerical examples confirm the stability, effectiveness, and feasibility of the proposed method. The effect of the number of model layers on the optimization results is also analyzed. Full article
(This article belongs to the Special Issue Differential Equations and Genetic Algorithms)
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15 pages, 452 KiB  
Article
All Traveling Wave Exact Solutions of the Kawahara Equation Using the Complex Method
by Feng Ye, Jian Tian, Xiaoting Zhang, Chunling Jiang, Tong Ouyang and Yongyi Gu
Axioms 2022, 11(7), 330; https://doi.org/10.3390/axioms11070330 - 07 Jul 2022
Cited by 3 | Viewed by 1258
Abstract
In this article, we prove that the ⟨p,q⟩ condition holds, first by using the Fuchs index of the complex Kawahara equation, and then proving that all meromorphic solutions of complex Kawahara equations belong to the class W. Moreover, [...] Read more.
In this article, we prove that the ⟨p,q⟩ condition holds, first by using the Fuchs index of the complex Kawahara equation, and then proving that all meromorphic solutions of complex Kawahara equations belong to the class W. Moreover, the complex method is employed to get all meromorphic solutions of complex Kawahara equation and all traveling wave exact solutions of Kawahara equation. Our results reveal that all rational solutions ur(x+νt) and simply periodic solutions us,1(x+νt) of Kawahara equation are solitary wave solutions, while simply periodic solutions us,2(x+νt) are not real-valued. Finally, computer simulations are given to demonstrate the main results of this paper. At the same time, we believe that this method is a very effective and powerful method of looking for exact solutions to the mathematical physics equations, and the search process is simpler than other methods. Full article
(This article belongs to the Special Issue Differential Equations and Genetic Algorithms)
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21 pages, 402 KiB  
Article
RbfDeSolver: A Software Tool to Approximate Differential Equations Using Radial Basis Functions
by Ioannis G. Tsoulos, Alexandros Tzallas and Evangelos Karvounis
Axioms 2022, 11(6), 294; https://doi.org/10.3390/axioms11060294 - 16 Jun 2022
Viewed by 1627
Abstract
A new method for solving differential equations is presented in this work. The solution of the differential equations is done by adapting an artificial neural network, RBF, to the function under study. The adaptation of the parameters of the network is done with [...] Read more.
A new method for solving differential equations is presented in this work. The solution of the differential equations is done by adapting an artificial neural network, RBF, to the function under study. The adaptation of the parameters of the network is done with a hybrid genetic algorithm. In addition, this text presents in detail the software developed for the above method in ANSI C++. The user can code the underlying differential equation either in C++ or in Fortran format. The method was applied to a wide range of test functions of different types and the results are presented and analyzed in detail. Full article
(This article belongs to the Special Issue Differential Equations and Genetic Algorithms)
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14 pages, 8145 KiB  
Article
Pipeline Corrosion Prediction Using the Grey Model and Artificial Bee Colony Algorithm
by Shiguo Li, Hualong Du, Qiuyu Cui, Pengfei Liu, Xin Ma and He Wang
Axioms 2022, 11(6), 289; https://doi.org/10.3390/axioms11060289 - 14 Jun 2022
Viewed by 1302
Abstract
Pipeline corrosion prediction (PCP) is an important technology for pipeline maintenance and management. How to accurately predict pipeline corrosion is a challenging task. To address the drawback of the poor prediction accuracy of the grey model (GM(1,1)), this paper proposes a method named [...] Read more.
Pipeline corrosion prediction (PCP) is an important technology for pipeline maintenance and management. How to accurately predict pipeline corrosion is a challenging task. To address the drawback of the poor prediction accuracy of the grey model (GM(1,1)), this paper proposes a method named ETGM(1,1)-RABC. The proposed method consists of two parts. First, the exponentially transformed grey model (ETGM(1,1)) is an improvement of the GM(1,1), in which exponential transformation (ET) is used to preprocess the raw data. Next, dynamic coefficients, instead of background fixed coefficients, are optimized by the reformative artificial bee colony (RABC) algorithm, which is a variation of the artificial bee colony (ABC) algorithm. Experiments are performed on actual pipe corrosion data, and four different methods are included in the comparative study, including GM(1,1), ETGM(1,1), and three ETGM(1,1)-ABC variants. The results show that the proposed method proves to be superior for the PCP in terms of Taylor diagram and absolute error. Full article
(This article belongs to the Special Issue Differential Equations and Genetic Algorithms)
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