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Axioms
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Advances in Mathematical Optimization Algorithms and Its Applications
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Advances in Mathematical Optimization Algorithms and Its Applications

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: 30 September 2025 | Viewed by 11369

Special Issue Editor

Dr. Fevrier Valdez

E-Mail Website
Guest Editor
Tijuana Institute of Technology, TecNM, Tijuana 22379, Mexico
Interests: optimization algorithms; swarm intelligence; bio-inspired algorithms; fuzzy logic; neural networks
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Mathematical optimization algorithms based on collective intelligence and its applications are a recent tool for solving complex optimization in computational intelligence.

Several algorithms have recently been developed in this area, such as particle swarm optimization, bat algorithm, ant colony optimization, bee colony, dolphin algorithm, wolf search, flower pollination algorithm, firefly, mayfly, ant colony, cuckoo search, termite colony, and cat swarm. However, determining how to design efficient methods and how to use these algorithms for real problems is still an open issue—in particular, in fuzzy logic systems, where if-then rules are used to represent the knowledge of the problems, mathematical optimization algorithms can be implemented for parameter adaptation in control systems. Also, neural networks have received some interest. However, in recent years, several mathematical models have been developed to optimize the architectures of the neural networks. In addition, new emerging neural models have recently been proposed. In all these models, a common problem is determining how to obtain an optimal topology, which can be handled by mathematical optimization algorithms.

This Special Issue invites researchers to report their latest research work on the development of new improved mathematical optimization algorithms, or new applications of existing methods in the design of topologies of neural models, parameter adaptation  in control systems and path planning of robots, etc., with ultimate goal of exploring future research directions.

Potential themes include but are not limited to the following:

  • Theoretical methods for understanding the behavior of mathematical optimization algorithms;
  • Statistical approaches for understanding the behavior of mathematical optimization algorithms;
  • Optimization of neuro-fuzzy models;
  • Optimization of mathematical fuzzy logic models;
  • Optimization of emergent neural models with nature-inspired algorithms;
  • Mathematical fuzzy logic and intelligent and automatic control;
  • Mathematical bio-inspired algorithms.

Dr. Fevrier Valdez
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.

Keywords

  • optimization algorithms
  • swarm intelligence
  • bio-inspired algorithms
  • fuzzy logic
  • neural networks
  • collective intelligence
  • mathematical algorithms

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Published Papers (7 papers)

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Research

13 pages, 278 KiB  
Article
Korpelevich Method for Solving Bilevel Variational Inequalities on Riemannian Manifolds
by Jiagen Liao and Zhongping Wan
Axioms 2025, 14(2), 78; https://doi.org/10.3390/axioms14020078 - 22 Jan 2025
Viewed by 535
Abstract
The bilevel variational inequality on Riemannian manifolds refers to a mathematical problem involving the interaction between two levels of optimization, where one level is constrained by the other level. In this context, we present a variant of Korpelevich’s method specifically designed for solving [...] Read more.
The bilevel variational inequality on Riemannian manifolds refers to a mathematical problem involving the interaction between two levels of optimization, where one level is constrained by the other level. In this context, we present a variant of Korpelevich’s method specifically designed for solving bilevel variational inequalities on Riemannian manifolds with nonnegative sectional curvature and pseudomonotone vector fields. This variant aims to find a solution that satisfies certain conditions. Through our proposed algorithm, we are able to generate iteration sequences that converge to a solution, given mild conditions. Finally, we provide an example to demonstrate the effectiveness of our algorithm. Full article
(This article belongs to the Special Issue Advances in Mathematical Optimization Algorithms and Its Applications)
15 pages, 418 KiB  
Article
Using Artificial Neural Networks to Solve the Gross–Pitaevskii Equation
by Ioannis G. Tsoulos, Vasileios N. Stavrou and Dimitrios Tsalikakis
Axioms 2024, 13(10), 711; https://doi.org/10.3390/axioms13100711 - 15 Oct 2024
Viewed by 960
Abstract
The current work proposes the incorporation of an artificial neural network to solve the Gross–Pitaevskii equation (GPE) efficiently, using a few realistic external potentials. With the assistance of neural networks, a model is formed that is capable of solving this equation. The adaptation [...] Read more.
The current work proposes the incorporation of an artificial neural network to solve the Gross–Pitaevskii equation (GPE) efficiently, using a few realistic external potentials. With the assistance of neural networks, a model is formed that is capable of solving this equation. The adaptation of the parameters for the constructed model is performed using some evolutionary techniques, such as genetic algorithms and particle swarm optimization. The proposed model is used to solve the GPE for the linear case (γ=0) and the nonlinear case (γ≠0), where γ is the nonlinearity parameter in GPE. The results are close to the reported results regarding the behavior and the amplitudes of the wavefunctions. Full article
(This article belongs to the Special Issue Advances in Mathematical Optimization Algorithms and Its Applications)
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17 pages, 2201 KiB  
Article
Dementia Classification Approach Based on Non-Singleton General Type-2 Fuzzy Reasoning
by Claudia I. Gonzalez
Axioms 2024, 13(10), 672; https://doi.org/10.3390/axioms13100672 - 28 Sep 2024
Viewed by 1081
Abstract
Dementia is the most critical neurodegenerative disease that gradually destroys memory and other cognitive functions. Therefore, early detection is essential, and to build an effective detection model, it is required to understand its type, symptoms, stages and causes, and diagnosis methodologies. This paper [...] Read more.
Dementia is the most critical neurodegenerative disease that gradually destroys memory and other cognitive functions. Therefore, early detection is essential, and to build an effective detection model, it is required to understand its type, symptoms, stages and causes, and diagnosis methodologies. This paper presents a novel approach to classify dementia based on a data set with some relevant patient features. The classification methodology employs non-singleton general type-2 fuzzy sets, non-singleton interval type-2 fuzzy sets, and non-singleton type 1 fuzzy sets. These advanced fuzzy sets are compared with traditional singleton fuzzy sets to evaluate their performance. The Takagi–Sugeno–Kang TSK inference method is used to handle fuzzy reasoning. In the process, the parameters of the membership functions (MFs) and rules are obtained using ANFIS, and non-singleton MFs are optimized with PSO. The results demonstrate that non-singleton general type-2 fuzzy sets improve classification accuracy compared to singleton fuzzy sets, demonstrating their ability to model the uncertainties inherent in the diagnosis of dementia. This improvement suggests that non-singleton fuzzy systems offer a more robust framework for developing effective diagnostic tools in the medical domain. Accurate classification of dementia is of utmost importance to improve patient care and advance medical research. Full article
(This article belongs to the Special Issue Advances in Mathematical Optimization Algorithms and Its Applications)
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31 pages, 13721 KiB  
Article
An Enhanced Fuzzy Hybrid of Fireworks and Grey Wolf Metaheuristic Algorithms
by Juan Barraza, Luis Rodríguez, Oscar Castillo, Patricia Melin and Fevrier Valdez
Axioms 2024, 13(7), 424; https://doi.org/10.3390/axioms13070424 - 24 Jun 2024
Viewed by 1132
Abstract
This research work envisages addressing fuzzy adjustment of parameters into a hybrid optimization algorithm for solving mathematical benchmark function problems. The problem of benchmark mathematical functions consists of finding the minimal values. In this study, we considered function optimization. We are presenting an [...] Read more.
This research work envisages addressing fuzzy adjustment of parameters into a hybrid optimization algorithm for solving mathematical benchmark function problems. The problem of benchmark mathematical functions consists of finding the minimal values. In this study, we considered function optimization. We are presenting an enhanced Fuzzy Hybrid Algorithm, which is called Enhanced Fuzzy Hybrid Fireworks and Grey Wolf Metaheuristic Algorithm, and denoted as EF-FWA-GWO. The fuzzy adjustment of parameters is achieved using Fuzzy Inference Systems. For this work, we implemented two variants of the Fuzzy Systems. The first variant utilizes Triangular membership functions, and the second variant employs Gaussian membership functions. Both variants are of a Mamdani Fuzzy Inference Type. The proposed method was applied to 22 mathematical benchmark functions, divided into two parts: the first part consists of 13 functions that can be classified as unimodal and multimodal, and the second part consists of the 9 fixed-dimension multimodal benchmark functions. The proposed method presents better performance with 60 and 90 dimensions, averaging 51% and 58% improvement in the benchmark functions, respectively. And then, a statistical comparison between the conventional hybrid algorithm and the Fuzzy Enhanced Hybrid Algorithm is presented to complement the conclusions of this research. Finally, we also applied the Fuzzy Hybrid Algorithm in a control problem to test its performance in designing a Fuzzy controller for a mobile robot. Full article
(This article belongs to the Special Issue Advances in Mathematical Optimization Algorithms and Its Applications)
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42 pages, 10325 KiB  
Article
Multi-Strategy-Improved Growth Optimizer and Its Applications
by Rongxiang Xie, Liya Yu, Shaobo Li, Fengbin Wu, Tao Zhang and Panliang Yuan
Axioms 2024, 13(6), 361; https://doi.org/10.3390/axioms13060361 - 28 May 2024
Cited by 1 | Viewed by 1129
Abstract
The growth optimizer (GO) is a novel metaheuristic algorithm designed to tackle complex optimization problems. Despite its advantages of simplicity and high efficiency, GO often encounters localized stagnation when dealing with discretized, high-dimensional, and multi-constraint problems. To address these issues, this paper proposes [...] Read more.
The growth optimizer (GO) is a novel metaheuristic algorithm designed to tackle complex optimization problems. Despite its advantages of simplicity and high efficiency, GO often encounters localized stagnation when dealing with discretized, high-dimensional, and multi-constraint problems. To address these issues, this paper proposes an enhanced version of GO called CODGBGO. This algorithm incorporates three strategies to enhance its performance. Firstly, the Circle-OBL initialization strategy is employed to enhance the quality of the initial population. Secondly, an exploration strategy is implemented to improve population diversity and the algorithm’s ability to escape local optimum traps. Finally, the exploitation strategy is utilized to enhance the convergence speed and accuracy of the algorithm. To validate the performance of CODGBGO, it is applied to solve the CEC2017, CEC2020, 18 feature selection problems, and 4 real engineering optimization problems. The experiments demonstrate that the novel CODGBGO algorithm effectively addresses the challenges posed by complex optimization problems, offering a promising approach. Full article
(This article belongs to the Special Issue Advances in Mathematical Optimization Algorithms and Its Applications)
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19 pages, 7083 KiB  
Article
An Interval Type-2 Fuzzy Logic Approach for Dynamic Parameter Adaptation in a Whale Optimization Algorithm Applied to Mathematical Functions
by Leticia Amador-Angulo and Oscar Castillo
Axioms 2024, 13(1), 33; https://doi.org/10.3390/axioms13010033 - 31 Dec 2023
Cited by 2 | Viewed by 2297
Abstract
In this paper, an improved whale optimization algorithm (WOA) based on the utilization of an interval type-2 fuzzy logic system (IT2FLS) is presented. The main idea is to present a proposal for adjusting the values of the r→1 and [...] Read more.
In this paper, an improved whale optimization algorithm (WOA) based on the utilization of an interval type-2 fuzzy logic system (IT2FLS) is presented. The main idea is to present a proposal for adjusting the values of the r→1 and r→2 parameters in the WOA using an IT2FLS to achieve excellent results in the execution of the WOA. The original WOA has already proven itself as an algorithm with excellent results; therefore, a wide variety of improvements have been made to it. Herein, the main purpose is to provide a hybridization of the WOA algorithm employing fuzzy logic to find the appropriate values of the r→1 and r→2 parameters that can optimize the mathematical functions used in this study, thereby providing an improvement to the original WOA algorithm. The performance of the fuzzy WOA using IT2FLS (FWOA-IT2FLS) shows good results in the case study of the benchmark function optimization. An important comparative with other metaheuristics is also presented. A statistical test and the comparative with other bio-inspired algorithms, namely, the original WOA with type-1 FLS (FWOA-T1FLS) are analyzed. The performance index used is the average of the minimum errors in each proposed method. Full article
(This article belongs to the Special Issue Advances in Mathematical Optimization Algorithms and Its Applications)
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22 pages, 7897 KiB  
Article
Interval Type-3 Fuzzy Inference System Design for Medical Classification Using Genetic Algorithms
by Patricia Melin, Daniela Sánchez and Oscar Castillo
Axioms 2024, 13(1), 5; https://doi.org/10.3390/axioms13010005 - 20 Dec 2023
Cited by 6 | Viewed by 2740
Abstract
An essential aspect of healthcare is receiving an appropriate and opportune disease diagnosis. In recent years, there has been enormous progress in combining artificial intelligence to help professionals perform these tasks. The design of interval Type-3 fuzzy inference systems (IT3FIS) for medical classification [...] Read more.
An essential aspect of healthcare is receiving an appropriate and opportune disease diagnosis. In recent years, there has been enormous progress in combining artificial intelligence to help professionals perform these tasks. The design of interval Type-3 fuzzy inference systems (IT3FIS) for medical classification is proposed in this work. This work proposed a genetic algorithm (GA) for the IT3FIS design where the fuzzy inputs correspond to attributes relational to a particular disease. This optimization allows us to find some main fuzzy inference systems (FIS) parameters, such as membership function (MF) parameters and the fuzzy if-then rules. As a comparison against the proposed method, the results achieved in this work are compared with Type-1 fuzzy inference systems (T1FIS), Interval Type-2 fuzzy inference systems (IT2FIS), and General Type-2 fuzzy inference systems (GT2FIS) using medical datasets such as Haberman’s Survival, Cryotherapy, Immunotherapy, PIMA Indian Diabetes, Indian Liver, and Breast Cancer Coimbra dataset, which achieved 75.30, 87.13, 82.04, 77.76, 71.86, and 71.06, respectively. Also, cross-validation tests were performed. Instances established as design sets are used to design the fuzzy inference systems, the optimization technique seeks to reduce the classification error using this set, and finally, the testing set allows the validation of the real performance of the FIS. Full article
(This article belongs to the Special Issue Advances in Mathematical Optimization Algorithms and Its Applications)
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