Symmetry in Optimization Theory, Algorithm and Applications

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

Deadline for manuscript submissions: closed (30 September 2023) | Viewed by 7015

Special Issue Editors


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Guest Editor
Department of Mathematics and Statistics, Loyola University Maryland, Baltimore, MD 21210, USA
Interests: complementarity problems over symmetric cones; euclidean Jordan algebras; matrix theory; statistical optimization; optimization theory, methods and applications
Special Issues, Collections and Topics in MDPI journals

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Guest Editor
School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai 201620, China
Interests: optimization theory, methods, and applications; interior-point methods; symmetric cone optimization; symmetric cone complementarity problem; statistical optimization; high dimensional statistical inference; financial statistics; biostatistics; portfolio optimization; machine learning; mathematical modelling
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Along with the rapid development of computer science and the urgent need to find solutions for real problems, spectacular progress has also been made in modern optimization theory and its associated methods. These advances have had an important impact on many areas, such as statistics, biology, finance, economics, control, machine learning, and artificial intelligence. All these developments emerge from interdisciplinary work, and it is well known that symmetric cone theory plays a crucial role in this progress.

Although solving large-scale optimization problems arising in science, engineering, and technology has led to breakthrough advancements in numerical optimization, including first-order methods and augmented Lagrange methods, many new questions emerge as the scale of the problems increases.

This Special Issue aims to provide a platform for scholars to present their latest research on symmetry in optimization theory, methods, and applications. Topics of interest include, but are not limited to, symmetric cone optimization; symmetric cone complementarity problems; sparse optimization; statistical optimization; financial statistics; biostatistics; portfolio optimization; interior-point methods; first-order optimization methods; machine learning; artificial intelligence; neural networks; and mathematical modelling.

We invite you to submit your paper and select the journal Symmetry and the Special Issue “Symmetry in Optimization Theory, Methods and Applications” via the MDPI submission system. Papers will be published on a rolling basis, and we will be pleased to receive your submission once you have finished it.

Prof. Dr. Jiyuan Tao
Prof. Dr. Guoqiang Wang
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

  • optimization theory
  • optimization methods
  • symmetric cone optimization
  • symmetric cone complementarity problem
  • sparse optimization
  • optimization in statistics
  • optimization in finance
  • optimization in economics
  • optimization in biology
  • interior-point methods
  • first-order optimization methods
  • data envelopment analysis
  • artificial intelligence
  • machine learning
  • neural networks
  • mathematical modelling

Published Papers (6 papers)

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Editorial

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3 pages, 150 KiB  
Editorial
New Trends in Symmetry in Optimization Theory, Algorithms and Applications
by Guoqiang Wang and Jiyuan Tao
Symmetry 2024, 16(3), 284; https://doi.org/10.3390/sym16030284 - 1 Mar 2024
Viewed by 678
Abstract
Optimization is an important branch of operations research in applied mathematics and computer science, where functions are optimized over a range of feasible solutions [...] Full article
(This article belongs to the Special Issue Symmetry in Optimization Theory, Algorithm and Applications)

Research

Jump to: Editorial

32 pages, 1415 KiB  
Article
An Asymmetric Ensemble Method for Determining the Importance of Individual Factors of a Univariate Problem
by Jelena Mišić, Aleksandar Kemiveš, Milan Ranđelović and Dragan Ranđelović
Symmetry 2023, 15(11), 2050; https://doi.org/10.3390/sym15112050 - 11 Nov 2023
Cited by 2 | Viewed by 737
Abstract
This study proposes an innovative model that determines the importance of selected factors of a univariate problem. The proposed model has been developed based on the example of determining the impact of non-medical factors on the quality of inpatient treatment, but it is [...] Read more.
This study proposes an innovative model that determines the importance of selected factors of a univariate problem. The proposed model has been developed based on the example of determining the impact of non-medical factors on the quality of inpatient treatment, but it is generally applicable to any process of binary classification. In addition, an ensemble stacking model that involves the asymmetric use of two different well-known algorithms is proposed to determine the importance of individual factors. This model is constructed so that the standard logistic regression is first applied as mandatory. Further, the classification algorithms are implemented if the defined conditions are met. Finally, feature selection algorithms, which belong to the optimization group of algorithms, are applied as a combinatorial algorithm. The proposed model is verified through a case study conducted using real data obtained from health institutions in the region connected to the city of Nis, Republic of Serbia. The obtained results show that the proposed model can achieve better results than each of the methods included in it and surpasses several state-of-the-art ensemble algorithms in the field of machine learning. The proposed solution has been implemented in the form of a modern mobile application. Full article
(This article belongs to the Special Issue Symmetry in Optimization Theory, Algorithm and Applications)
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24 pages, 2942 KiB  
Article
An Enhanced Ant Colony System Algorithm Based on Subpaths for Solving the Capacitated Vehicle Routing Problem
by Zakir Hussain Ahmed, Asaad Shakir Hameed, Modhi Lafta Mutar and Habibollah Haron
Symmetry 2023, 15(11), 2020; https://doi.org/10.3390/sym15112020 - 3 Nov 2023
Cited by 1 | Viewed by 957
Abstract
The capacitated vehicle routing problem (CVRP) is regarded as an NP-hard problem. Moreover, the CVRP is described as a model that can be used in many applications such as transport, logistics, and distribution. The exact algorithms can find exact optimal solutions on the [...] Read more.
The capacitated vehicle routing problem (CVRP) is regarded as an NP-hard problem. Moreover, the CVRP is described as a model that can be used in many applications such as transport, logistics, and distribution. The exact algorithms can find exact optimal solutions on the small-sized problem instances; however, for large-sized instances it is difficult to find the exact optimal solutions in polynomial time. This reason motivated the researchers to present heuristic/metaheuristic algorithms to solve large-sized problem instances within a reasonable computational time. One of the good algorithms that deal with the CVRP is the ant colony optimization (ACO) algorithm. Several ACO algorithms have been suggested in the literature, such as the ant system (AS) algorithm, ant colony system (ACS) algorithm, and so on. On the other hand, ACO is designed to solve the path problem that finds the best way. However, this algorithm still lacks exploratory mechanisms, which results in premature convergence and stagnation issues. Therefore, we propose to develop an enhanced ACS (EACS) algorithm for solving the CVRP based on subpaths. In our proposed algorithm, we propose to utilize the K-nearest neighbour (KNN) algorithm for finding the best initial solution and then enhance the diversity mechanism of the proposed algorithm by avoiding the generation of the same solution using subpaths. This uses the diversity of the generated solution to find a better solution with a shorter route in a reasonable amount of computational time. Furthermore, we propose to apply the three-opt algorithm to the completed subtour and the k-opt algorithm to the subpath gained from the experience of the subpath. Finally, to verify the effectiveness of the proposed EACS algorithm, the algorithm is tested on some CVRP instances and is compared with one of the state-of-the-art methods, namely, the enhanced simulated annealing algorithm. The comparative study showed a better performance of our EACS compared to the enhanced simulated annealing algorithm. Full article
(This article belongs to the Special Issue Symmetry in Optimization Theory, Algorithm and Applications)
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26 pages, 393 KiB  
Article
A Three-Dimensional Subspace Algorithm Based on the Symmetry of the Approximation Model and WYL Conjugate Gradient Method
by Guoxin Wang, Shengwei Yao, Mingyang Pei and Jieqiong Xu
Symmetry 2023, 15(6), 1207; https://doi.org/10.3390/sym15061207 - 5 Jun 2023
Cited by 2 | Viewed by 1254
Abstract
In this paper, a three-dimensional subspace method is proposed, in which the search direction is generated by minimizing the approximation model of the objective function in a three-dimensional subspace. The approximation model of the objective function is not unique, and alternatives can be [...] Read more.
In this paper, a three-dimensional subspace method is proposed, in which the search direction is generated by minimizing the approximation model of the objective function in a three-dimensional subspace. The approximation model of the objective function is not unique, and alternatives can be chosen between a symmetric quadratic model and a conic model by specific criteria. Moreover, the idea of a WLY conjugate gradient method is applied to characterize the change of gradient direction between adjacent iteration points. The strategy of initial stepsize and nonmonotone line search are adopted, and the global convergence of the presented algorithm is established under mild assumptions. In numerical experiments, we use a collection of 80 unconstrained optimization test problems to show the competitive performance of the presented method. Full article
(This article belongs to the Special Issue Symmetry in Optimization Theory, Algorithm and Applications)
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10 pages, 430 KiB  
Article
Preassigned-Time Bipartite Flocking Consensus Problem in Multi-Agent Systems
by Xiejun Cheng, Jiashang Yu, Xiurong Chen, Jiaju Yu and Bing Cheng
Symmetry 2023, 15(5), 1105; https://doi.org/10.3390/sym15051105 - 18 May 2023
Cited by 1 | Viewed by 932
Abstract
This article is concerned with the bipartite flocking problem in multi-agent systems. Our contributions can be summarized as follows. Firstly, a class of preassigned-time consensus protocols is proposed to solve the issue of multi-agent systems. Secondly, with the aid of the symmetric properties [...] Read more.
This article is concerned with the bipartite flocking problem in multi-agent systems. Our contributions can be summarized as follows. Firstly, a class of preassigned-time consensus protocols is proposed to solve the issue of multi-agent systems. Secondly, with the aid of the symmetric properties of the graph theory and the Lyapunov stability theorem, we prove that agents can be divided into two disjointed clusters in a finite time, and they move to opposite directions at the same magnitude and speed. The protocol is novel among existing fixed/finite-time protocols in that the associated settling time is a preassigned constant and a parameter of the protocol. Moreover, it is proven that the diameters of the clusters are bounded and independent of other the protocol parameters. These results are demonstrated through both theoretical analysis and simulation examples. Full article
(This article belongs to the Special Issue Symmetry in Optimization Theory, Algorithm and Applications)
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15 pages, 3128 KiB  
Article
An Improved DCC Model Based on Large-Dimensional Covariance Matrices Estimation and Its Applications
by Yan Zhang, Jiyuan Tao, Yongyao Lv and Guoqiang Wang
Symmetry 2023, 15(4), 953; https://doi.org/10.3390/sym15040953 - 21 Apr 2023
Cited by 2 | Viewed by 1688
Abstract
The covariance matrix estimation plays an important role in portfolio optimization and risk management. It is well-known that portfolio is essentially a convex quadratic programming problem, which is also a special case of symmetric cone optimization. Accurate covariance matrix estimation will lead to [...] Read more.
The covariance matrix estimation plays an important role in portfolio optimization and risk management. It is well-known that portfolio is essentially a convex quadratic programming problem, which is also a special case of symmetric cone optimization. Accurate covariance matrix estimation will lead to more reasonable asset weight allocation. However, some existing methods do not consider the influence of time-varying factor on the covariance matrix estimations. To remedy this, in this article, we propose an improved dynamic conditional correlation model (DCC) by using nonconvex optimization model under smoothly clipped absolute deviation and hard-threshold penalty functions. We first construct a nonconvex optimization model to obtain the optimal covariance matrix estimation, and then we use this covariance matrix estimation to replace the unconditional covariance matrix in the DCC model. The result shows that the loss of the proposed estimator is smaller than other variants of the DCC model in numerical experiments. Finally, we apply our proposed model to the classic Markowitz portfolio. The results show that the improved dynamic conditional correlation model performs better than the current DCC models. Full article
(This article belongs to the Special Issue Symmetry in Optimization Theory, Algorithm and Applications)
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