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Mathematics
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Mathematical Optimization and Control: Methods and Applications
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Mathematical Optimization and Control: Methods and Applications

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

Deadline for manuscript submissions: 31 December 2024 | Viewed by 2860

Special Issue Editors

Prof. Dr. Jose de Jesus Rubio

E-Mail Website
Guest Editor
School of Engineering, National Polytechnic Institute, Mexico City 02250, Mexico
Interests: intelligent control; neural network; optimal control
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Jeff Pieper

E-Mail Website
Guest Editor
Department of Mechanical and Manufacturing Engineering, University of Calgary, Calgary, AB, Canada
Interests: control; optimization
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Jaime Pacheco Martinez

E-Mail Website
Guest Editor
Seccion de Estudios de Posgrado e Investigacion, Esime Azcapotzalco, Instituto Politecnico Nacional, Mexico City 02250, Mexico
Interests: control; optimization
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Mu-Yen Chen

E-Mail Website
Guest Editor
Department of Information Management, National Taichung University of Science and Technology, Taichung, Taiwan
Interests: mathematical optimization and control
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Mathematical optimization is the discipline of adjusting a mathematical process so as to optimize (make the best use of) a specified set of parameters without violating certain constraints. The most common goals are minimizing cost and maximizing efficiency. Mathematical optimization uses optimization algorithms as the random research for the maximization or minimization of functions without violating certain constraints. It brings the necessity to research for optimization algorithms. Examples of these optimization algorithms are the genetic, bat, butterfly, grey wolf, particle swarm, ant colony, bee colony, and Bayesian algorithm. Additionally, the convergence of the mentioned optimization algorithms could be analyzed.

Mathematical control compares the value of a variable being controlled with the desired value, and applies the control signal to bring the variable to a desired value. The most common goals are regulation, trajectory tracking, stabilization, synchronization, nonlineariy compensation, obstacle avoidance, or disturbance rejection. It brings the necessity to research for control algorithms. Examples of these control algorithms are the adaptive, neural network, fuzzy, backstepping, sliding mode, robust, feedback, observer-based algorithms. Additionally, the stability of the mentioned control algorithms could be analyzed.

The objective of this Special Issue of Mathematics is to cover the optimization and control algorithms.

Original contributions are solicited from, but are not limited, the following topics of interest:

  • genetic optimization;
  • bat optimization;
  • butterfly optimization;
  • grey wolf optimization;
  • particle swarm optimization;
  • ant colony optimization;
  • bee colony optimization;
  • bayesian optimization;
  • adaptive control;
  • neural network control;
  • fuzzy control;
  • backstepping control;
  • feedback control;
  • sliding mode control; 
  • robust control;
  • observer-based control;
  • other alternative optimization or control.

Prof. Dr. Jose de Jesus Rubio
Prof. Dr. Jeff Pieper
Prof. Dr. Jaime Pacheco Martinez
Prof. Dr. Mu-Yen Chen
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

  • genetic optimization
  • bat optimization
  • butterfly optimization
  • grey wolf optimization
  • particle swarm optimization
  • ant colony optimization
  • bee colony optimization
  • bayesian optimization
  • adaptive control
  • neural network control
  • fuzzy control
  • backstepping control
  • feedback control
  • sliding mode control
  • robust control
  • observer-based control
  • other alternative optimization or control

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Further information on MDPI's Special Issue polices can be found here.

Published Papers (4 papers)

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Research

19 pages, 2501 KiB  
Article
Cost Optimization in Sintering Process on the Basis of Bulk Queueing System with Diverse Services Modes and Vacation
by Subramani Palani Niranjan, Suthanthira Raj Devi Latha and Sorin Vlase
Mathematics 2024, 12(22), 3535; https://doi.org/10.3390/math12223535 - 12 Nov 2024
Viewed by 433
Abstract
This research investigated a single bulk server queuing model where service modes and server vacations are dependent on the number of clients. The server operates in three different service modes: single service, fixed batch service, and variable batch service. Modes will be determined [...] Read more.
This research investigated a single bulk server queuing model where service modes and server vacations are dependent on the number of clients. The server operates in three different service modes: single service, fixed batch service, and variable batch service. Modes will be determined by queue length. The service starts only when the minimum number of customers, say ‘a’, has accumulated in the queue. At this point, the server selects one of three service modes. Transitions between duty modes are permitted only at the beginning of a duty period. At the end of the service, the server can go on vacation if the queue length drops below ‘a’. When returning from vacation, if threshold ‘a’ is not reached, the server will remain inactive until it is reached. A special technique called the Supplementary Variables Technique (SVT) was used to determine the probability-generating function when estimating the queue size at a given time. Appropriate numerical examples exemplify the method developed in the paper. An optimal cost analysis was performed to set the threshold values for different server modes with the intention of minimizing the aggregate average cost. Full article
(This article belongs to the Special Issue Mathematical Optimization and Control: Methods and Applications)
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21 pages, 389 KiB  
Article
Constraint Qualifications and Optimality Conditions for Nonsmooth Semidefinite Multiobjective Programming Problems with Mixed Constraints Using Convexificators
by Balendu Bhooshan Upadhyay, Shubham Kumar Singh and Ioan Stancu-Minasian
Mathematics 2024, 12(20), 3202; https://doi.org/10.3390/math12203202 - 12 Oct 2024
Viewed by 559
Abstract
In this article, we investigate a class of non-smooth semidefinite multiobjective programming problems with inequality and equality constraints (in short, NSMPP). We establish the convex separation theorem for the space of symmetric matrices. Employing the properties of the convexificators, we establish Fritz John [...] Read more.
In this article, we investigate a class of non-smooth semidefinite multiobjective programming problems with inequality and equality constraints (in short, NSMPP). We establish the convex separation theorem for the space of symmetric matrices. Employing the properties of the convexificators, we establish Fritz John (in short, FJ)-type necessary optimality conditions for NSMPP. Subsequently, we introduce a generalized version of Abadie constraint qualification (in short, NSMPP-ACQ) for the considered problem, NSMPP. Employing NSMPP-ACQ, we establish strong Karush-Kuhn-Tucker (in short, KKT)-type necessary optimality conditions for NSMPP. Moreover, we establish sufficient optimality conditions for NSMPP under generalized convexity assumptions. In addition to this, we introduce the generalized versions of various other constraint qualifications, namely Kuhn-Tucker constraint qualification (in short, NSMPP-KTCQ), Zangwill constraint qualification (in short, NSMPP-ZCQ), basic constraint qualification (in short, NSMPP-BCQ), and Mangasarian-Fromovitz constraint qualification (in short, NSMPP-MFCQ), for the considered problem NSMPP and derive the interrelationships among them. Several illustrative examples are furnished to demonstrate the significance of the established results. Full article
(This article belongs to the Special Issue Mathematical Optimization and Control: Methods and Applications)
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13 pages, 335 KiB  
Article
Optimal L(d,1)-Labeling of Certain Direct Graph Bundles Cycles over Cycles and Cartesian Graph Bundles Cycles over Cycles
by Irena Hrastnik Ladinek
Mathematics 2024, 12(19), 3121; https://doi.org/10.3390/math12193121 - 5 Oct 2024
Viewed by 563
Abstract
An L(d,1)-labeling of a graph G=(V,E) is a function f from the vertex set V(G) to the set of nonnegative integers such that the labels on adjacent vertices [...] Read more.
An L(d,1)-labeling of a graph G=(V,E) is a function f from the vertex set V(G) to the set of nonnegative integers such that the labels on adjacent vertices differ by at least d and the labels on vertices at distance two differ by at least one, where d≥1. The span of f is the difference between the largest and the smallest numbers in f(V). The λ1d-number of G, denoted by λ1d(G), is the minimum span over all L(d,1)-labelings of G. We prove that λ1d(X)≤2d+2, with equality if 1≤d≤4, for direct graph bundle X=Cm×σℓCn and Cartesian graph bundle X=Cm□σℓCn, if certain conditions are imposed on the lengths of the cycles and on the cyclic ℓ-shift σℓ. Full article
(This article belongs to the Special Issue Mathematical Optimization and Control: Methods and Applications)
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19 pages, 1785 KiB  
Article
Representing the Information of Multiplayer Online Battle Arena (MOBA) Video Games Using Convolutional Accordion Auto-Encoder (A2E) Enhanced by Attention Mechanisms
by José A. Torres-León, Marco A. Moreno-Armendáriz and Hiram Calvo
Mathematics 2024, 12(17), 2744; https://doi.org/10.3390/math12172744 - 3 Sep 2024
Viewed by 689
Abstract
In this paper, we propose a representation of the visual information about Multiplayer Online Battle Arena (MOBA) video games using an adapted unsupervised deep learning architecture called Convolutional Accordion Auto-Encoder (Conv_A2E). Our study includes a presentation of current representations of MOBA [...] Read more.
In this paper, we propose a representation of the visual information about Multiplayer Online Battle Arena (MOBA) video games using an adapted unsupervised deep learning architecture called Convolutional Accordion Auto-Encoder (Conv_A2E). Our study includes a presentation of current representations of MOBA video game information and why our proposal offers a novel and useful solution to this task. This approach aims to achieve dimensional reduction and refined feature extraction of the visual data. To enhance the model’s performance, we tested several attention mechanisms for computer vision, evaluating algorithms from the channel attention and spatial attention families, and their combination. Through experimentation, we found that the best reconstruction of the visual information with the Conv_A2E was achieved when using a spatial attention mechanism, deformable convolution, as its mean squared error (MSE) during testing was the lowest, reaching a value of 0.003893, which means that its dimensional reduction is the most generalist and representative for this case study. This paper presents one of the first approaches to applying attention mechanisms to the case study of MOBA video games, representing a new horizon of possibilities for research. Full article
(This article belongs to the Special Issue Mathematical Optimization and Control: Methods and Applications)
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