Mathematics

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Special Issue Editors

Prof. Dr. Youness El Hamzaoui

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Guest Editor

Engineering College, Carmen Autonomous University, Calle 56, 4, Esq. Avenida Concordia, Col. Benito Juárez, Campeche, Mexico
Interests: machine learning; computational statistics; experimental application research; prediction algorithm; notification and control of the system; operational investigation; optimization

Dr. Homero Toral-Cruz

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Guest Editor

Department of Sciences and Engineering, University of Quintana Roo, Blvd Bahía S/N, Chetumal 77019, Mexico
Interests: VoIP technologies; QoS and network measurements; IP traffic modeling; network performance evaluation; WSN; network security

Special Issue Information

Dear Colleagues,

In this groundbreaking Special Issue of the renowned journal Mathematics, entitled "Mathematical Optimization and Decision-Making Analysis: Innovations and Challenges", we delve into the latest advancements, pressing challenges, and promising potential of harnessing mathematical optimization and decision-making analysis across a variety of disciplines. The focus of this Special Issue is on introducing cutting-edge methodologies and ingenious solutions, underlining their indispensable role in today's complex decision-making dynamics.

The breadth of topics spanned by this Special Issue is both extensive and compelling. It provides an in-depth exploration of traditional areas such as linear and non-linear programming and multi-objective optimization, alongside more contemporary subjects like fuzzy decision-making, robust optimization, stochastic programming, and evolutionary algorithms that adeptly handle constraints.

It proceeds to highlight the practical applications of these techniques, illustrating their transformative potential in sectors as varied as engineering, economics, transport logistics, healthcare, and supply chain management. We particularly underscore the application of mathematical optimization in the emerging areas like green logistics and sustainable supply chains, healthcare informatics, and smart transportation systems, among others.

Moreover, it draws attention to the current trends and developments in machine learning and artificial intelligence, in which mathematical optimization and decision-making analysis are playing increasingly vital roles. It introduces new concepts such as reinforcement learning, deep learning, and algorithmic fairness in the context of optimization and decision-making.

This Special Issue serves as an indispensable guide and resource for researchers, practitioners, and academics invested in state-of-the-art advancements in mathematical optimization and decision-making analysis. With its mix of theory, practical applications, and emphasis on modern advancements, it stands as a critical reference in the current landscape and future direction of these essential disciplines.

Prof. Dr. Youness El Hamzaoui
Dr. Homero Toral-Cruz
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

mathematical optimization
operations research
decision making
convex optimization
integer programming
linear and nonlinear programming
decision tree
game theory
risk analysis

Published Papers (2 papers)

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Research

13 pages, 726 KiB

Open AccessArticle

A Revisit to Sunk Cost Fallacy for Two-Stage Stochastic Binary Decision Making

by Xuecheng Tian, Bo Jiang, King-Wah Pang, Yuquan Du, Yong Jin and Shuaian Wang

Mathematics 2024, 12(10), 1557; https://doi.org/10.3390/math12101557 (registering DOI) - 16 May 2024

Abstract

This paper undertakes a revisit of the sunk cost fallacy, which refers to the tendency of people to persist investing resources into something, even if it is destined to have no good outcome. We emphasize that the utilities associated with different alternatives are not static for decision makers, which is exactly opposite to the traditional perspective. This paper argues that the utility of an option may change due to the choice of another option, suggesting that decisions considered irrational by the traditional analytical method, i.e., sunk cost fallacy, may be rational. We propose a novel analytical method for decision making with sunk cost when considering the utility change and validate the effectiveness of this method through mathematical modeling and computational experiments. This paper mathematically describes such decision-making problems, analyzing the impact of changes in the utilities across different alternatives on decision making with a real-world example. Furthermore, we develop a two-stage stochastic optimization model for such decision-making problems and employ the sample average approximation (SAA) method to solve them. The results from computational experiments indicate that some decisions traditionally considered irrational are, in fact, rational when the utility of an option changes as a result of choosing another option. This paper, therefore, highlights the significance of incorporating utility changes into the decision-making process and stands as a valuable addition to the literature, offering a refreshed and effective decision-making method for improved decision making. Full article

(This article belongs to the Special Issue Mathematical Optimization and Decision Making Analysis)

39 pages, 727 KiB

Open AccessArticle

Chaotic Binarization Schemes for Solving Combinatorial Optimization Problems Using Continuous Metaheuristics

by Felipe Cisternas-Caneo, Broderick Crawford, Ricardo Soto, Giovanni Giachetti, Álex Paz and Alvaro Peña Fritz

Mathematics 2024, 12(2), 262; https://doi.org/10.3390/math12020262 - 12 Jan 2024

Viewed by 666

Abstract

Chaotic maps are sources of randomness formed by a set of rules and chaotic variables. They have been incorporated into metaheuristics because they improve the balance of exploration and exploitation, and with this, they allow one to obtain better results. In the present work, chaotic maps are used to modify the behavior of the binarization rules that allow continuous metaheuristics to solve binary combinatorial optimization problems. In particular, seven different chaotic maps, three different binarization rules, and three continuous metaheuristics are used, which are the Sine Cosine Algorithm, Grey Wolf Optimizer, and Whale Optimization Algorithm. A classic combinatorial optimization problem is solved: the 0-1 Knapsack Problem. Experimental results indicate that chaotic maps have an impact on the binarization rule, leading to better results. Specifically, experiments incorporating the standard binarization rule and the complement binarization rule performed better than experiments incorporating the elitist binarization rule. The experiment with the best results was STD_TENT, which uses the standard binarization rule and the tent chaotic map. Full article

(This article belongs to the Special Issue Mathematical Optimization and Decision Making Analysis)

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