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Challenges and New Trends in Optimization and Control Theory in...
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Challenges and New Trends in Optimization and Control Theory in the Era of AI: Analysis, Modelling, and Symmetrical Mathematical Methods

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Computer".

Deadline for manuscript submissions: 1 December 2024 | Viewed by 2465

Special Issue Editors

Dr. Ahmed Aberqi

E-Mail Website
Guest Editor
ENSA, Sidi Mohamed Ben Abdellah University, Fez, Morocco
Interests: functional analysis; operator theory; numerical analysis; nonlinear partial differential equations; nonlinear analysis; optimal control theory
Special Issues, Collections and Topics in MDPI journals
Dr. Touria Karite

E-Mail Website
Guest Editor
Department of Applied Mathematics Engineering Department, National School of Applied Sciences of Fez, Sidi Mohamed Ben Abdellah University, Fez 30000, Morocco
Interests: control theory; controllability; nonlinear dynamics; optimal control; distributed systems; optimization methods; systems theory; fractional calculus
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Karim El Moutaouakil

E-Mail Website
Guest Editor
Engineering Science Laboratory, Department of Mathematics, Multidisciplinary Faculty of Taza, University Sidi Mohamed Ben Abdellah of Fez, Fes, Morocco
Interests: Artificial Intelligence; machine learning; optimization and operation; numeric for equations and optimal control

Special Issue Information

Dear Colleagues,

This Special Issue offers an in-depth exploration of optimization and control theory, examining the intricate relationship between traditional methodologies and the burgeoning influence of artificial intelligence (AI). Contributors may delve into the integration of AI techniques with conventional methods, navigating the evolving landscape of optimization and control to harness AI algorithms for improved predictive accuracy and real-time decision-making. With a focus on symmetrical mathematical techniques, the collection spans diverse domains, from fractional and ordinary differential equations to the complexities of biomathematics, providing insightful analyses and innovative modeling approaches.

Within mathematical methods, the exploitation of symmetry serves to reduce computational complexity and derive efficient algorithms. For example, leveraging symmetry in matrix computations can yield faster solutions for linear systems or eigenvalue problems. A comprehensive understanding of both symmetry and asymmetry in mathematical analysis enables researchers and practitioners to approach problem solving and optimization with versatility and effectiveness. This Special Issue serves as a compendium of cutting-edge research, illuminating the challenges and new trends at the intersection of optimization and control theory with the transformative influence of AI. Through rigorous analysis, innovative modeling, and the application of symmetrical mathematical methods, this compilation aims to propel the field toward new frontiers of understanding and practical application.

Dr. Ahmed Aberqi
Dr. Touria Karite
Prof. Dr. Karim El Moutaouakil
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. Symmetry 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

  • symmetric methods for solving fractional and ordinary differential equations
  • fractals and fractional calculus
  • PDE: deterministic, stochastic, and fuzzy
  • symmetrical/asymmetrical models in biomathematics
  • symmetry analysis and methods
  • optimization
  • control theory
  • AI and ML

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Published Papers (2 papers)

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Research

22 pages, 1067 KiB  
Article
Enhancing Symmetry and Memory in the Fractional Economic Growing Quantity (FEGQ) Model
by Azedine Ouhmid, Karim El Moutaouakil, Fatima Belhabib and Alina-Mihaela Patriciu
Symmetry 2024, 16(8), 1057; https://doi.org/10.3390/sym16081057 - 16 Aug 2024
Viewed by 967
Abstract
In this paper, we present a novel approach to inventory management modeling, specifically tailored for growing items. We extend traditional economic growth quantity (EGQ) models by introducing the fractional economic growing quantity (FEGQ) model. This new approach improves the model’s symmetry and dynamic [...] Read more.
In this paper, we present a novel approach to inventory management modeling, specifically tailored for growing items. We extend traditional economic growth quantity (EGQ) models by introducing the fractional economic growing quantity (FEGQ) model. This new approach improves the model’s symmetry and dynamic responsiveness, providing a more precise representation of the changing nature of inventory items. Additionally, the use of fractional derivatives allows our model to incorporate the memory effect, introducing a new dynamic concept in inventory management. This advancement enables us to select the optimal business policy to maximize profit. We adopt the fractional derivative in terms of Caputo derivative sense to model the inventory level associated with the items. To analytically solve the (FEGQ) model, we use the Laplacian transform to obtain an algebraic equation. As for the logistic function, known for its symmetrical S-shaped curve, it closely mirrors real-life growth patterns and is defined using fractional calculus. We apply an iterative approximation method, specifically the Adomian decomposition method, to solve the fractional logistic function. Through a sensitivity analysis, we delve for the first time into the discussion of the initial weights, which have a massive impact on the total profit level. The provided numerical data indicate that the firm began with a favorable policy. In the following years, several misguided practices were implemented that led to a decrease in profitability. The healing process began once again by selecting more effective strategies. Full article
(This article belongs to the Special Issue Challenges and New Trends in Optimization and Control Theory in the Era of AI: Analysis, Modelling, and Symmetrical Mathematical Methods)
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21 pages, 712 KiB  
Article
OPT-FRAC-CHN: Optimal Fractional Continuous Hopfield Network
by Karim El Moutaouakil, Zakaria Bouhanch, Abdellah Ahourag, Ahmed Aberqi and Touria Karite
Symmetry 2024, 16(7), 921; https://doi.org/10.3390/sym16070921 - 18 Jul 2024
Cited by 2 | Viewed by 754
Abstract
The continuous Hopfield network (CHN) is a common recurrent neural network. The CHN tool can be used to solve a number of ranking and optimization problems, where the equilibrium states of the ordinary differential equation (ODE) related to the CHN give the solution [...] Read more.
The continuous Hopfield network (CHN) is a common recurrent neural network. The CHN tool can be used to solve a number of ranking and optimization problems, where the equilibrium states of the ordinary differential equation (ODE) related to the CHN give the solution to any given problem. Because of the non-local characteristic of the “infinite memory” effect, fractional-order (FO) systems have been proved to describe more accurately the behavior of real dynamical systems, compared to the model’s ODE. In this paper, a fractional-order variant of a Hopfield neural network is introduced to solve a Quadratic Knap Sac Problem (QKSP), namely the fractional CHN (FRAC-CHN). Firstly, the system is integrated with the quadratic method for fractional-order equations whose trajectories have shown erratic paths and jumps to other basin attractions. To avoid these drawbacks, a new algorithm for obtaining an equilibrium point for a CHN is introduced in this paper, namely the optimal fractional CHN (OPT-FRAC-CHN). This is a variable time-step method that converges to a good local minima in just a few iterations. Compared with the non-variable time-stepping CHN method, the optimal time-stepping CHN method (OPT-CHN) and the FRAC-CHN method, the OPT-FRAC-CHN method, produce the best local minima for random CHN instances and for the optimal feeding problem. Full article
(This article belongs to the Special Issue Challenges and New Trends in Optimization and Control Theory in the Era of AI: Analysis, Modelling, and Symmetrical Mathematical Methods)
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