Stochastic Modeling and Optimization Techniques

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

Deadline for manuscript submissions: 28 February 2026 | Viewed by 3736

Special Issue Editors


E-Mail Website
Guest Editor
Faculty of Sciences and Mathematics, University of Priština, Lole Ribara 29, 38220 Kosovska Mitrovica, Serbia
Interests: applied and computational mathematics; reliability theory; failure analysis; optimization

E-Mail Website
Guest Editor
Faculty of Sciences and Mathematics, University of Priština, Lole Ribara 29, 38220 Kosovska Mitrovica, Serbia
Interests: fixed point theory; functional and complex analysis; metric spaces

E-Mail Website
Guest Editor
Faculty of Sciences and Mathematics, University of Priština, Lole Ribara 29, 38220 Kosovska Mitrovica, Serbia
Interests: applied mathematics

Special Issue Information

Dear Colleagues,

It is our pleasure to invite you to submit a paper to this Special issue of the MDPI journal Axioms entitled “Stochastic Modeling and Optimization Techniques”. This Special Issue seeks submissions that explore novel stochastic models, creative optimization techniques that handle unpredictability, and the synergistic blending of these fields to solve real problems.

We welcome papers that extend the theoretical foundations of stochastic modeling and optimization, propose new computational algorithms, and demonstrate applications in areas where uncertainty is a significant factor. Significant theoretical insights or methodological advancements should be provided, ideally supported by rigorous mathematical analysis and proofs. Also, contributions that integrate recent advances in stochastic modeling with machine learning techniques for optimization under uncertainty are especially encouraged.

The scope of this Special Issue includes, but is not limited to, stochastic differential equations, probability theory, statistical analysis, Markov processes, Bayesian optimization, Monte Carlo methods, and game theory under uncertainty. The papers that address challenges in numerical methods for stochastic optimization, the convergence and stability of algorithms, and the application of fixed-point theories in novel contexts are more than welcome.

The presented works should demonstrate originality in concepts and applications while advancing both theoretical foundations and practical impact.

Dr. Natasa Kontrec
Dr. Jelena Vujakovic
Dr. Hranislav Milosevic
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. 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

  • stochastic modeling
  • optimization techniques
  • probability theory
  • statistical analysis
  • fixed point theory
  • game theory

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • e-Book format: Special Issues with more than 10 articles can be published as dedicated e-books, ensuring wide and rapid dissemination.

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

Published Papers (4 papers)

Order results
Result details
Select all
Export citation of selected articles as:

Research

28 pages, 1067 KiB  
Article
Inference Based on Progressive-Stress Accelerated Life-Testing for Extended Distribution via the Marshall-Olkin Family Under Progressive Type-II Censoring with Optimality Techniques
by Ehab M. Almetwally, Osama M. Khaled and Haroon M. Barakat
Axioms 2025, 14(4), 244; https://doi.org/10.3390/axioms14040244 - 23 Mar 2025
Viewed by 231
Abstract
This paper explores a progressive-stress accelerated life test under progressive type-II censoring with binomial random removal. It assumes a cumulative exposure model in which the lifetimes of test units follow a Marshall–Olkin length-biased exponential distribution. The study derives maximum likelihood and Bayes estimates [...] Read more.
This paper explores a progressive-stress accelerated life test under progressive type-II censoring with binomial random removal. It assumes a cumulative exposure model in which the lifetimes of test units follow a Marshall–Olkin length-biased exponential distribution. The study derives maximum likelihood and Bayes estimates of the model parameters and constructs Bayes estimates of the unknown parameters under various loss functions. In addition, this study provides approximate, credible, and bootstrapping confidence intervals for the estimators. Moreover, it evaluates three optimal test methods to determine the most effective censoring approach based on various optimality criteria. A real-life dataset is analyzed to demonstrate the proposed procedures and simulation studies used to compare two different designs of the progressive-stress test. Full article
(This article belongs to the Special Issue Stochastic Modeling and Optimization Techniques)
Show Figures

Figure 1

31 pages, 2537 KiB  
Article
A Novel Framework for Belief and Plausibility Measures in Intuitionistic Fuzzy Sets: Belief and Plausibility Distance, Similarity, and TOPSIS for Multicriteria Decision Making
by Shahid Hussain, Zahid Hussain, Rashid Hussain, Ahmad Bakhet, Hussain Arafat, Mohammed Zakarya, Amirah Ayidh I Al-Thaqfan and Maha Ali
Axioms 2024, 13(12), 858; https://doi.org/10.3390/axioms13120858 - 7 Dec 2024
Viewed by 1235
Abstract
Dempster–Shafer Theory (DST) relies significantly on belief and plausibility measures to handle ambiguity and uncertainty; however, DST has been extended to fuzzy sets (FSs) and intuitionistic fuzzy sets (IFSs) with only a few extensions focusing on belief and plausibility intuitionistic fuzzy distance (BP-distance) [...] Read more.
Dempster–Shafer Theory (DST) relies significantly on belief and plausibility measures to handle ambiguity and uncertainty; however, DST has been extended to fuzzy sets (FSs) and intuitionistic fuzzy sets (IFSs) with only a few extensions focusing on belief and plausibility intuitionistic fuzzy distance (BP-distance) and similarity (BP-similarity) until now. In this work, we propose a novel framework for the belief and plausibility of intuitionistic fuzzy sets (BP-IFSs) and their BP-distance and BP-similarity measures. We modified steps 4 and 5 of the classical TOPSIS method, utilizing both distance and similarity measures to rank the alternatives that satisfy all necessary axioms of distance and similarity. We present numerical examples involving pattern recognition, linguistic variables, and clustering to illustrate the efficiency of these measures, and we develop belief and plausibility TOPSIS (BP-TOPSIS) using the proposed criteria and apply it to complex multicriteria decision-making (MCDM) challenges. The results demonstrate the practicality and effectiveness of our approach. Full article
(This article belongs to the Special Issue Stochastic Modeling and Optimization Techniques)
Show Figures

Figure 1

15 pages, 310 KiB  
Article
Mathematical Optimization of Wind Turbine Maintenance Using Repair Rate Thresholds
by Nataša Kontrec, Stefan Panić, Jelena Vujaković, Dejan Stošović and Sergei Khotnenok
Axioms 2024, 13(11), 809; https://doi.org/10.3390/axioms13110809 - 20 Nov 2024
Viewed by 913
Abstract
As reliance on wind energy intensifies globally, optimizing the efficiency and reliability of wind turbines is becoming vital. This paper explores sophisticated maintenance strategies, crucial for enhancing the operational sustainability of wind turbines. It introduces an innovative approach to maintenance scheduling that utilizes [...] Read more.
As reliance on wind energy intensifies globally, optimizing the efficiency and reliability of wind turbines is becoming vital. This paper explores sophisticated maintenance strategies, crucial for enhancing the operational sustainability of wind turbines. It introduces an innovative approach to maintenance scheduling that utilizes a mathematical model incorporating an alternating renewal process for accurately determining repair rate thresholds. These thresholds are important for identifying optimal maintenance timings, thereby averting failures and minimizing downtime. Central to this study are the obtained generalized analytical expressions that can be used to predict the total repair time for an observed entity. Four key lemmas are developed to establish formal proofs for the probability density function (PDF) and cumulative distribution function (CDF) of repair rates, both above and below critical repair rate thresholds. The core innovation of this study lies in the methodological application of PDFs and CDFs to set repair time thresholds that refine maintenance schedules. The model’s effectiveness is illustrated using simulated data based on typical wind turbine components such as gearboxes, generators, and converters, validating its potential for improving system availability and operational readiness. By establishing measurable repair rate thresholds, the model effectively prioritizes maintenance tasks, extending the life of crucial turbine components and ensuring consistent energy output. Beyond enhancing theoretical understanding, this research provides practical insights that could inform broader maintenance strategies across various renewable energy systems, marking a significant advancement in the field of maintenance engineering Full article
(This article belongs to the Special Issue Stochastic Modeling and Optimization Techniques)
Show Figures

Figure 1

21 pages, 391 KiB  
Article
Randomly Stopped Sums, Minima and Maxima for Heavy-Tailed and Light-Tailed Distributions
by Remigijus Leipus, Jonas Šiaulys, Svetlana Danilenko and Jūratė Karasevičienė
Axioms 2024, 13(6), 355; https://doi.org/10.3390/axioms13060355 - 25 May 2024
Cited by 1 | Viewed by 785
Abstract
This paper investigates the randomly stopped sums, minima and maxima of heavy- and light-tailed random variables. The conditions on the primary random variables, which are independent but generally not identically distributed, and counting random variable are given in order that the randomly stopped [...] Read more.
This paper investigates the randomly stopped sums, minima and maxima of heavy- and light-tailed random variables. The conditions on the primary random variables, which are independent but generally not identically distributed, and counting random variable are given in order that the randomly stopped sum, random minimum and maximum is heavy/light tailed. The results generalize some existing ones in the literature. The examples illustrating the results are provided. Full article
(This article belongs to the Special Issue Stochastic Modeling and Optimization Techniques)
Show Figures

Figure 1

Back to TopTop