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Symmetry
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Symmetry in Mathematical Optimization Algorithm and Its Applications
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Symmetry in Mathematical Optimization Algorithm and Its Applications

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

Deadline for manuscript submissions: 1 May 2025 | Viewed by 1876

Special Issue Editor

Dr. Zhe Sun

E-Mail Website
Guest Editor
School of Modern Posts, Nanjing University of Posts and Telecommunications, Nanjing, China
Interests: optimization algorithms; systems optimization; machine learning algorithm

Special Issue Information

Dear Colleagues,

The concept of symmetry is relevant in many real engineering fields and plays a crucial role in mathematical optimization problems, which are widely applied in system control, parameter identification and system modelling. Mathematical optimization algorithms also are an efficient tool for complex engineering problems that require a reasonable system configuration. Mathematical optimization algorithms refer to traditional optimization algorithms and intelligence optimization algorithms such as the machine learning algorithm, heuristic algorithm, swarm optimization algorithm, etc.

This Special Issue focuses on the theoretical and practical application of mathematical optimization algorithms. The scope of this Special Issue includes, but is not limited to, the enhanced application of traditional optimization algorithms, combinatorial optimization algorithms, the evolutionary algorithm and the swarm optimization algorithm. Contributions that explore the application of optimization algorithms in engineering, economics, traffic, logistics and other disciplines are also highly encouraged.

Dr. Zhe Sun
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. 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

  • combinatorial optimization
  • machine learning algorithm
  • heuristic algorithm
  • algorithm design
  • systems optimization and control
  • NP hard Problem optimization
  • parameter identification

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

Published Papers (2 papers)

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Research

34 pages, 17954 KiB  
Article
Unmanned Aerial Vehicle Path Planning Method Based on Improved Dung Beetle Optimization Algorithm
by Fengjun Lv, Yongbo Jian, Kai Yuan and Yubin Lu
Symmetry 2025, 17(3), 367; https://doi.org/10.3390/sym17030367 - 28 Feb 2025
Viewed by 535
Abstract
To address the problem of UAV path planning in complex mountainous terrains, this paper comprehensively considers constraints such as natural mountain and obstacle collision threats, the shortest path, and flight altitude. We propose a more practical UAV path planning model that better reflects [...] Read more.
To address the problem of UAV path planning in complex mountainous terrains, this paper comprehensively considers constraints such as natural mountain and obstacle collision threats, the shortest path, and flight altitude. We propose a more practical UAV path planning model that better reflects the actual UAV path planning situation in complex mountainous areas. In order to solve this model, this paper improves the traditional dung beetle optimization (DBO) algorithm and proposes an improved dung beetle optimization (IDBO) algorithm. The IDBO algorithm optimizes the population initialization method based on the concept of symmetry, ensuring that the population is more evenly distributed within the solution space. Additionally, the algorithm introduces a sine–cosine function-based movement strategy, inspired by the symmetry principle, to enhance the search efficiency of individual population members. Furthermore, a population evolution strategy is incorporated to prevent the algorithm from getting stuck in local optima. To demonstrate the algorithm’s performance, tests were conducted using 23 commonly used benchmark functions provided by the CEC 2005 competition and six commonly used engineering problem models provided by the CEC 2020 competition. The results indicate that IDBO significantly outperforms DBO in terms of convergence performance, effectively solving various engineering optimization problems. Finally, experimental tests under three different threat scenarios show that the proposed IDBO algorithm has scientific validity when applied to UAV path planning. This solution method effectively reduces UAV flight energy consumption costs and obstacle collision threats while improving the efficiency and accuracy of UAV path planning. Full article
(This article belongs to the Special Issue Symmetry in Mathematical Optimization Algorithm and Its Applications)
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22 pages, 2930 KiB  
Article
Type-2 Backstepping T-S Fuzzy Bionic Control Based on Niche Symmetry Function
by Yunli Hao, Maohua Wang, Jian Tang, Ziyue Zhang and Jiangling Xiong
Symmetry 2025, 17(1), 121; https://doi.org/10.3390/sym17010121 - 14 Jan 2025
Viewed by 706
Abstract
Niche can reflect the changes in the quality of the ecological environment and the balance of ecological state. The more advanced the ecosystem, the more complex and higher-order nonlinearities and uncertainties that are presented. For such an uncertain parameter system with complex nonlinearity, [...] Read more.
Niche can reflect the changes in the quality of the ecological environment and the balance of ecological state. The more advanced the ecosystem, the more complex and higher-order nonlinearities and uncertainties that are presented. For such an uncertain parameter system with complex nonlinearity, backstepping fuzzy control is a good control method. When the backstepping control method is introduced into the Type-2 fuzzy T-S control principle, the equality index symmetry function composed of ecological factors is used as the backstepping control consequence, and the Lyapunov function is constructed to analyze the stability and find out the adaptive law of the ecological factors in the equality index symmetry function of the control consequence. This reflects that the individual organisms always develop in their own favorable direction, highlighting the bionic intelligent control of the method. Through simulation analysis, the Type-2 Backstepping control method is effective in stability and parameter tracking, which reflects the self-development ability and self-coordination ability of individual organisms, highlighting the physical background and symmetry of the bionic intelligent control of this method. Full article
(This article belongs to the Special Issue Symmetry in Mathematical Optimization Algorithm and Its Applications)
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