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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: 31 December 2025 | Viewed by 4102

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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Published Papers (6 papers)

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Research

22 pages, 3412 KB  
Article
Fault Identification Method for Photovoltaic Power Grids Based on an Improved GABP Neural Network and Fuzzy System
by Xiaofeng Dong, Houtao Sun, Zhongxiu Han, Yuanchen Xia, Hongjun Wang and Qingwen Mou
Symmetry 2025, 17(9), 1476; https://doi.org/10.3390/sym17091476 - 7 Sep 2025
Abstract
Fault detection and classification localization in photovoltaic power grids is a key challenge in photovoltaic power systems. Due to the greater fluctuation of power data in photovoltaic power grids, traditional grid fault detection methods suffer from inefficiency, low accuracy, and inaccurate fault localization [...] Read more.
Fault detection and classification localization in photovoltaic power grids is a key challenge in photovoltaic power systems. Due to the greater fluctuation of power data in photovoltaic power grids, traditional grid fault detection methods suffer from inefficiency, low accuracy, and inaccurate fault localization in photovoltaic scenarios. In this paper, a fuzzy control technique combined with an improved GABP neural network is used to identify potential fault nodes in the photovoltaic distribution network. The symmetric crossover operator of the genetic algorithm and the symmetry constraints of the neural network weight matrix are used to improve the model’s ability to capture the symmetric fluctuation characteristics of photovoltaic data, while a classification module consisting of three fuzzy controllers is used for fault identification. The simulation results show that the recognition method proposed in this paper has good performance and the fault classification accuracy reaches 92.75%, which provides a practical reference value for the management of photovoltaic distribution network. Full article
(This article belongs to the Special Issue Symmetry in Mathematical Optimization Algorithm and Its Applications)
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25 pages, 2525 KB  
Article
Symmetry-Enhanced Locally Adaptive COA-ELM for Short-Term Load Forecasting
by Shiyu Dai, Zhe Sun and Zhixin Sun
Symmetry 2025, 17(8), 1335; https://doi.org/10.3390/sym17081335 - 15 Aug 2025
Viewed by 400
Abstract
Reliable short-term electricity usage prediction is essential for preserving the stability of topologically symmetric power networks and their dynamic supply–demand equilibrium. To tackle this challenge, this paper proposes a novel approach derived from the standard Extreme Learning Machine (ELM) by integrating an enhanced [...] Read more.
Reliable short-term electricity usage prediction is essential for preserving the stability of topologically symmetric power networks and their dynamic supply–demand equilibrium. To tackle this challenge, this paper proposes a novel approach derived from the standard Extreme Learning Machine (ELM) by integrating an enhanced Crayfish Optimization Algorithm (DSYCOA). This algorithm combines Logistic chaotic mapping, local precise search, and dynamic parameter adjustment strategies designed to achieve a dynamic balance between exploration and exploitation, thereby optimizing the initial thresholds and weights of the ELM. Consequently, a new short-term power load forecasting model, namely the DSYCOA-ELM model, is developed. Experimental validation demonstrates that the improved DSYCOA exhibits fast convergence speed and high convergence accuracy, and successfully harmonizes global exploration and local exploitation capabilities while maintaining an empirical balance between exploration and exploitation. To additionally verify the effectiveness of DSYCOA in improving ELM, this paper conducts simulation comparison experiments among six models, including DSYCOA-ELM, ELM, and ELM improved by BWO (BWO-ELM). The findings demonstrate that the DSYCOA-ELM model outperforms the other five forecasting models in terms of Mean Absolute Percentage Error (MAPE), Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), and other indicators. Specifically, in terms of MAPE, DSYCOA-ELM reduces the error by 96.9% compared to ELM. This model demonstrates feasibility and effectiveness in solving the problem of short-term power load prediction, providing critical support for maintaining the stability of grid topological symmetry and supply–demand balance. Full article
(This article belongs to the Special Issue Symmetry in Mathematical Optimization Algorithm and Its Applications)
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22 pages, 8629 KB  
Article
3D UAV Route Optimization in Complex Environments Using an Enhanced Artificial Lemming Algorithm
by Yuxuan Xie, Zhe Sun, Kai Yuan and Zhixin Sun
Symmetry 2025, 17(6), 946; https://doi.org/10.3390/sym17060946 - 13 Jun 2025
Cited by 1 | Viewed by 436
Abstract
The use of UAVs for logistics delivery has become a hot topic in current research, and how to plan a reasonable delivery route is the key to the problem. Therefore, this paper proposes a multi-environment logistics delivery route planning model that is based [...] Read more.
The use of UAVs for logistics delivery has become a hot topic in current research, and how to plan a reasonable delivery route is the key to the problem. Therefore, this paper proposes a multi-environment logistics delivery route planning model that is based on UAVs, is characterized by a 3D environment model, and aims at the shortest delivery route with minimum flight undulation. In order to find the optimal route in various environments, a multi-strategy improved artificial lemming algorithm, which integrates the Cubic chaotic map initialization, double adaptive t-distribution perturbation, and population dynamic optimization, is proposed. The symmetric nature of the t-distribution ensures that the lemmings conduct extensive searches in both directions within the solution space, thus improving the convergence speed and preventing them from falling into local optimal solutions. Through data experiments and simulation analysis, the improved algorithm can be successfully applied to the 3D route planning model, and the route quality is superior. Full article
(This article belongs to the Special Issue Symmetry in Mathematical Optimization Algorithm and Its Applications)
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22 pages, 482 KB  
Article
A Novel Symmetrical Inertial Alternating Direction Method of Multipliers with Proximal Term for Nonconvex Optimization with Applications
by Ji-Hong Li, Heng-You Lan and Si-Yuan Lin
Symmetry 2025, 17(6), 887; https://doi.org/10.3390/sym17060887 - 5 Jun 2025
Viewed by 372
Abstract
In this paper, we propose a novel alternating direction method of multipliers based on acceleration technique involving two symmetrical inertial terms for a class of nonconvex optimization problems with a two-block structure. To address the nonconvex subproblem, we introduce a proximal term to [...] Read more.
In this paper, we propose a novel alternating direction method of multipliers based on acceleration technique involving two symmetrical inertial terms for a class of nonconvex optimization problems with a two-block structure. To address the nonconvex subproblem, we introduce a proximal term to reduce the difficulty of solving this subproblem. For the smooth subproblem, we employ a gradient descent method on the augmented Lagrangian function, which significantly reduces the computational complexity. Under appropriate assumptions, we prove subsequential convergence of the algorithm. Moreover, when the generated sequence is bounded and the auxiliary function satisfies Kurdyka–Łojasiewicz property, we establish global convergence of the algorithm. Finally, effectiveness and superior performance of the proposed algorithm are validated through numerical experiments in signal processing and smoothly clipped absolute deviation penalty problems. Full article
(This article belongs to the Special Issue Symmetry in Mathematical Optimization Algorithm and Its Applications)
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34 pages, 17954 KB  
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
Cited by 3 | Viewed by 1040
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 KB  
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 894
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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