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Mathematics
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Analysis and Application of Optimization Algorithms
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Analysis and Application of Optimization Algorithms

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematics and Computer Science".

Deadline for manuscript submissions: 30 September 2024 | Viewed by 3308

Special Issue Editors

Dr. Youcef Gheraibia

E-Mail Website
Guest Editor
School of Computer Science and Informatics, De Montfort University, Leicester LE2 7DP, UK
Interests: data analysis; optimisation; machine learning; bio-inspired algorithm; algorithm analysis; computation; discrete optimization
Special Issues, Collections and Topics in MDPI journals
Dr. Jabir Alshehabi Al-Ani

E-Mail Website
Guest Editor
Department of Data Science, York St John University, Lord Mayor’s Walk, York YO31 7EX, UK
Interests: algorithm design; machine learning; statistics; data analysis; natural language processing; image processing; deep learning

Special Issue Information

Dear Colleagues,

We invite you to submit your research in the area of analysis of optimization and its applications to the Special Issue, “Analysis and Application of Optimization Algorithms”, in the journal Mathematics.

High-quality papers are solicited to address both theoretical and practical issues in the development of efficient solution methods and theoretical analysis of optimization problems.

Over the past decade, several optimization techniques have been proposed to solve a wide range of complex problems. This Special Issue serves as a forum for facilitating and enhancing information sharing among researchers, including the development of advanced optimization algorithms. Researchers are invited to submit their original and unpublished research work for the applications of optimization algorithms. Papers on optimization algorithm development and analysis are welcome, as well as papers on the application of optimization algorithms.

Dr. Youcef Gheraibia
Dr. Jabir Alshehabi Al-Ani
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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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

  • ant colony optimization
  • nature-inspired algorithm (penguin search optimization algorithm, ACO, PSO)
  • discrete optimization
  • multicriteria optimization
  • time complexity analysis
  • dynamic programming
  • heuristics and metaheuristics
  • linear and integer programming
  • deterministic scheduling
  • routing and transportation
  • operations research and decision sciences
  • cognitive neuroscience
  • packing and partitioning
  • optimization in graph problems

 

Published Papers (3 papers)

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Research

21 pages, 760 KiB  
Article
Communication-Efficient Zeroth-Order Adaptive Optimization for Federated Learning
by Ping Xie, Xiangrui Gao, Fan Li, Ling Xing, Yu Zhang and Hanxiao Sun
Mathematics 2024, 12(8), 1148; https://doi.org/10.3390/math12081148 - 11 Apr 2024
Viewed by 347
Abstract
Federated learning has become a prevalent distributed training paradigm, in which local devices collaboratively train learning models without exchanging local data. One of the most dominant frameworks of federated learning (FL) is FedAvg, since it is efficient and simple to implement; here, the [...] Read more.
Federated learning has become a prevalent distributed training paradigm, in which local devices collaboratively train learning models without exchanging local data. One of the most dominant frameworks of federated learning (FL) is FedAvg, since it is efficient and simple to implement; here, the first-order information is generally utilized to train the parameters of learning models. In practice, however, the gradient information may be unavailable or infeasible in some applications, such as federated black-box optimization problems. To solve the issue, we propose an innovative zeroth-order adaptive federated learning algorithm without using the gradient information, referred to as ZO-AdaFL, which integrates the zeroth-order optimization algorithm into the adaptive gradient method. Moreover, we also rigorously analyze the convergence behavior of ZO-AdaFL in a non-convex setting, i.e., where ZO-AdaFL achieves convergence to a region close to a stationary point at a speed of O(1/T) (T represents the total iteration number). Finally, to verify the performance of ZO-AdaFL, simulation experiments are performed using the MNIST and FMNIST datasets. Our experimental findings demonstrate that ZO-AdaFL outperforms other state-of-the-art zeroth-order FL approaches in terms of both effectiveness and efficiency. Full article
(This article belongs to the Special Issue Analysis and Application of Optimization Algorithms)
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23 pages, 5013 KiB  
Article
Enhanced Genetic Method for Optimizing Multiple Sequence Alignment
by Mohammed K. Ibrahim, Umi Kalsom Yusof, Taiseer Abdalla Elfadil Eisa and Maged Nasser
Mathematics 2023, 11(22), 4578; https://doi.org/10.3390/math11224578 - 08 Nov 2023
Cited by 1 | Viewed by 987
Abstract
In the realm of bioinformatics, Multiple Sequence Alignment (MSA) is a pivotal technique used to optimize the alignment of multiple biological sequences, guided by specific scoring criteria. Existing approaches addressing the MSA challenge tend to specialize in distinct biological features, leading to variability [...] Read more.
In the realm of bioinformatics, Multiple Sequence Alignment (MSA) is a pivotal technique used to optimize the alignment of multiple biological sequences, guided by specific scoring criteria. Existing approaches addressing the MSA challenge tend to specialize in distinct biological features, leading to variability in alignment outcomes for the same set of sequences. Consequently, this paper proposes an enhanced evolutionary-based approach that simplifies the sequence alignment problem without considering the sequences in the non-dominated solution. Our method employs a multi-objective optimization technique that uniquely excludes non-dominated solution sets, effectively mitigating computational complexities. Utilizing the Sum of Pairs and the Total Conserved Column as primary objective functions, our approach offers a novel perspective. We adopt an integer coding approach to enhance the computational efficiency, representing chromosomes with sets of integers during the alignment process. Using the SABmark and BAliBASE datasets, extensive experimentation is conducted to compare our method with existing ones. The results affirm the superior solution quality achieved by our approach compared to its predecessors. Furthermore, via the Wilcoxon signed-rank test, a statistical analysis underscores the statistical significance of our model’s improvement (p < 0.05). This comprehensive approach holds promise for advancing Multiple Sequence Alignment in bioinformatics. Full article
(This article belongs to the Special Issue Analysis and Application of Optimization Algorithms)
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16 pages, 707 KiB  
Article
Comprehensive Evaluations of Student Performance Estimation via Machine Learning
by Ahmad Saeed Mohammad, Musab T. S. Al-Kaltakchi, Jabir Alshehabi Al-Ani and Jonathon A. Chambers
Mathematics 2023, 11(14), 3153; https://doi.org/10.3390/math11143153 - 18 Jul 2023
Viewed by 1458
Abstract
Success in student learning is the primary aim of the educational system. Artificial intelligence utilizes data and machine learning to achieve excellence in student learning. In this paper, we exploit several machine learning techniques to estimate early student performance. Two main simulations are [...] Read more.
Success in student learning is the primary aim of the educational system. Artificial intelligence utilizes data and machine learning to achieve excellence in student learning. In this paper, we exploit several machine learning techniques to estimate early student performance. Two main simulations are used for the evaluation. The first simulation used the Traditional Machine Learning Classifiers (TMLCs) applied to the House dataset, and they are Gaussian Naïve Bayes (GNB), Support Vector Machine (SVM), Decision Tree (DT), Multi-Layer Perceptron (MLP), Random Forest (RF), Linear Discriminant Analysis (LDA), and Quadratic Discriminant Analysis (QDA). The best results were achieved with the MLP classifier with a division of 80% training and 20% testing, with an accuracy of 88.89%. The fusion of these seven classifiers was also applied and the highest result was equal to the MLP. Moreover, in the second simulation, the Convolutional Neural Network (CNN) was utilized and evaluated on five main datasets, namely, House, Western Ontario University (WOU), Experience Application Programming Interface (XAPI), University of California-Irvine (UCI), and Analytics Vidhya (AV). The UCI dataset was subdivided into three datasets, namely, UCI-Math, UCI-Por, and UCI-Fused. Moreover, the AV dataset has three targets which are Math, Reading, and Writing. The best accuracy results were achieved at 97.5%, 99.55%, 98.57%, 99.28%, 99.40%, 99.67%, 92.93%, 96.99%, and 96.84% for the House, WOU, XAPI, UCI-Math, UCI-Por, UCI-Fused, AV-Math, AV-Reading, and AV-Writing datasets, respectively, under the same protocol of evaluation. The system demonstrates that the proposed CNN-based method surpasses all seven conventional methods and other state-of-the-art-work. Full article
(This article belongs to the Special Issue Analysis and Application of Optimization Algorithms)
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