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Mathematics
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Numerical Optimization and Applications
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Numerical Optimization and Applications

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: closed (31 December 2021) | Viewed by 11247

Special Issue Editor

Prof. Dr. Hsien-Chung Wu

E-Mail Website
Guest Editor
Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 802, Taiwan
Interests: : fuzzy optimization; fuzzy real analysis; fuzzy statistical analysis; operations research; computational intelligence; soft computing; fixed point theory; applied functional analysis
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Numerical optimization is a branch of mathematical and numerical analysis. Because of the growing use of optimization in practical problems, almost every problem in science, engineering, and economics can be formulated as an optimization problem in which the computational techniques based on mathematical analysis are frequently designed to solve those problems. Studying the approximate solutions of optimization problems with the presence of computational errors and the convergent behavior of algorithms are the important issues. However, some of the problems are very difficult to solve using the approaches of mathematical analysis. In this case, natural computing is an important tool to solve the hard optimization problems for the purpose of generating the near-optimal solutions, where natural computing is concerned with computing inspired by nature. The topics of this Special Issue include, but are not limited to:

  • Variants of Newton methods
  • Interior-point method
  • Conjugate gradient method
  • Proximal point method
  • Predictor–corrector method
  • Trust-region method
  • Simulation-based optimization

Natural computing (evolutionary computation, neural computation, quantum computation, ant colony optimization, artificial immune systems, swarm intelligence, etc.)

Prof. Dr. Hsien-Chung Wu
Guest Editor

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

  • Convergence analysis
  • Genetic algorithms
  • Gradient and subgradient
  • Metaheuristics
  • Nonsmooth optimization
  • Nondifferentiability and subdifferentiability
  • Near-optimal solution
  • Simulated annealing

Published Papers (4 papers)

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Research

31 pages, 8225 KiB  
Article
Optimal Power Flow Analysis Based on Hybrid Gradient-Based Optimizer with Moth–Flame Optimization Algorithm Considering Optimal Placement and Sizing of FACTS/Wind Power
by Amal Amin Mohamed, Salah Kamel, Mohamed H. Hassan, Mohamed I. Mosaad and Mansour Aljohani
Mathematics 2022, 10(3), 361; https://doi.org/10.3390/math10030361 - 25 Jan 2022
Cited by 37 | Viewed by 3071
Abstract
Optimal power flow (OPF) is one of the most significant electric power network control and management issues. Adding unreliable and intermittent renewable energy sources to the electrical grid increase and complicates the OPF issue, which calls for using modern optimization techniques to solve [...] Read more.
Optimal power flow (OPF) is one of the most significant electric power network control and management issues. Adding unreliable and intermittent renewable energy sources to the electrical grid increase and complicates the OPF issue, which calls for using modern optimization techniques to solve this issue. This work presents the optimal location and size of some FACTS devices in a hybrid power system containing stochastic wind and traditional thermal power plants considering OPF. The FACTS devices used are thyristor-controlled series compensator (TCSC), thyristor-controlled phase shifter (TCPS), and static var compensator (SVC). This optimal location and size of FACTS devices was determined by introducing a multi-objective function containing reserve costs for overestimation and penalty costs for underestimating intermittent renewable sources besides active power losses. The uncertainty in the wind power output is predicted using Weibull probability density functions. This multi-objective function is optimized using a hybrid technique, gradient-based optimizer (GBO), and moth–flame optimization algorithm (MFO). Full article
(This article belongs to the Special Issue Numerical Optimization and Applications)
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52 pages, 513 KiB  
Article
Robust Solutions for Uncertain Continuous-Time Linear Programming Problems with Time-Dependent Matrices
by Hsien-Chung Wu
Mathematics 2021, 9(8), 885; https://doi.org/10.3390/math9080885 - 16 Apr 2021
Cited by 1 | Viewed by 1274
Abstract
The uncertainty for the continuous-time linear programming problem with time-dependent matrices is considered in this paper. In this case, the robust counterpart of the continuous-time linear programming problem is introduced. In order to solve the robust counterpart, it will be transformed into the [...] Read more.
The uncertainty for the continuous-time linear programming problem with time-dependent matrices is considered in this paper. In this case, the robust counterpart of the continuous-time linear programming problem is introduced. In order to solve the robust counterpart, it will be transformed into the conventional form of the continuous-time linear programming problem with time-dependent matrices. The discretization problem is formulated for the sake of numerically calculating the ϵ-optimal solutions, and a computational procedure is also designed to achieve this purpose. Full article
(This article belongs to the Special Issue Numerical Optimization and Applications)
20 pages, 341 KiB  
Article
An Optimisation-Driven Prediction Method for Automated Diagnosis and Prognosis
by Valentino Santucci, Alfredo Milani and Fabio Caraffini
Mathematics 2019, 7(11), 1051; https://doi.org/10.3390/math7111051 - 4 Nov 2019
Cited by 18 | Viewed by 2672
Abstract
This article presents a novel hybrid classification paradigm for medical diagnoses and prognoses prediction. The core mechanism of the proposed method relies on a centroid classification algorithm whose logic is exploited to formulate the classification task as a real-valued optimisation problem. A novel [...] Read more.
This article presents a novel hybrid classification paradigm for medical diagnoses and prognoses prediction. The core mechanism of the proposed method relies on a centroid classification algorithm whose logic is exploited to formulate the classification task as a real-valued optimisation problem. A novel metaheuristic combining the algorithmic structure of Swarm Intelligence optimisers with the probabilistic search models of Estimation of Distribution Algorithms is designed to optimise such a problem, thus leading to high-accuracy predictions. This method is tested over 11 medical datasets and compared against 14 cherry-picked classification algorithms. Results show that the proposed approach is competitive and superior to the state-of-the-art on several occasions. Full article
(This article belongs to the Special Issue Numerical Optimization and Applications)
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50 pages, 490 KiB  
Article
Numerical Method for Solving the Robust Continuous-Time Linear Programming Problems
by Hsien-Chung Wu
Mathematics 2019, 7(5), 435; https://doi.org/10.3390/math7050435 - 16 May 2019
Cited by 1 | Viewed by 2237
Abstract
A robust continuous-time linear programming problem is formulated and solved numerically in this paper. The data occurring in the continuous-time linear programming problem are assumed to be uncertain. In this paper, the uncertainty is treated by following the concept of robust optimization, which [...] Read more.
A robust continuous-time linear programming problem is formulated and solved numerically in this paper. The data occurring in the continuous-time linear programming problem are assumed to be uncertain. In this paper, the uncertainty is treated by following the concept of robust optimization, which has been extensively studied recently. We introduce the robust counterpart of the continuous-time linear programming problem. In order to solve this robust counterpart, a discretization problem is formulated and solved to obtain the ϵ -optimal solution. The important contribution of this paper is to locate the error bound between the optimal solution and ϵ -optimal solution. Full article
(This article belongs to the Special Issue Numerical Optimization and Applications)
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