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Symmetry
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Symmetry and Metaheuristic Algorithms
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Symmetry and Metaheuristic Algorithms

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

Deadline for manuscript submissions: 31 October 2026 | Viewed by 5315

Special Issue Editor

Dr. Erik V. Cuevas

E-Mail Website
Guest Editor
Departamento de Eléctro-Fotónica, Universidad de Guadalajara, Campus CUCEI, Guadalajara 44430, Jalisco, Mexico
Interests: artificial intelligence; computer vision
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleague,

Metaheuristic algorithms have emerged as powerful and versatile tools in the field of optimization, addressing the increasing complexity of problems that traditional methods struggle to efficiently solve. These algorithms are designed to explore and exploit the search space in innovative ways to find optimal or near-optimal solutions. They offer practical and effective approaches for tackling optimization challenges across a myriad of domains, from engineering and logistics to healthcare and artificial intelligence. The growing need for these methods is evidence of their adaptability and effectiveness for solving complex real-world problems. In recent years, the application of metaheuristic algorithms has increased, underscoring their significance and versatility in various scientific areas.

"Symmetry and Metaheuristic Algorithms" is a field of study that explores the relationship between symmetry and the design and optimization of metaheuristic algorithms. Metaheuristic algorithms are approximate solution methods used for optimization problems that cannot be easily solved using traditional optimization techniques. Researchers in this field investigate how symmetry properties in optimization problems can be utilized or preserved to enhance the performance of metaheuristic algorithms. By leveraging symmetry, researchers aim to develop more effective and efficient algorithms for solving complex optimization problems.

We invite scientists and practitioners from around the globe to contribute high-quality papers to a Special Issue titled "Symmetry and Metaheuristic Algorithms". The objective is to capture a comprehensive snapshot of the current advancements and a wide array of applications of metaheuristic algorithms. We seek submissions that not only push the boundaries of algorithmic design, but also demonstrate the practical implications and innovations driven by these methods in diverse scientific and engineering fields. Through this Special Issue, we aim to highlight the latest state-of-the-art developments and foster a deeper understanding of the potential and future directions of metaheuristic algorithms and their significant impact on solving the complex optimization problems of today and tomorrow.

This Special Issue includes (but are not limited to) the following topics:

  • Symmetry-based optimization;
  • The improvement in traditional metaheuristic algorithms (pso, sa, de, etc.) using new mechanisms;
  • New metaheuristic algorithms;
  • Hybridization of metaheuristic methods;
  • Multi-objective optimization;
  • Theoretical insights into metaheuristic algorithms;
  • Metaheuristics in artificial intelligence and machine learning;
  • Metaheuristics for image processing;
  • Metaheuristic applications in healthcare and biomedical engineering;
  • Emerging trends and future directions in metaheuristic research.

Dr. Erik V. Cuevas
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 250 words) can be sent to the Editorial Office for assessment.

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

  • symmetry-based optimization
  • the improvement in traditional metaheuristic algorithms (pso, sa, de, etc.) using new mechanisms
  • new metaheuristic algorithms
  • hybridization of metaheuristic methods
  • multi-objective optimization
  • theoretical insights into metaheuristic algorithms
  • metaheuristics in artificial intelligence and machine learning
  • metaheuristics for image processing
  • metaheuristic applications in healthcare and biomedical engineering
  • emerging trends and future directions in metaheuristic research

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

Published Papers (5 papers)

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Research

46 pages, 17303 KB  
Article
Multi-Strategy Enhanced Beaver Behavior Optimizer for Global Optimization and Enterprise Bankruptcy Prediction
by Haoyuan He and Mingyang Yu
Symmetry 2026, 18(5), 848; https://doi.org/10.3390/sym18050848 (registering DOI) - 15 May 2026
Viewed by 112
Abstract
Enterprise bankruptcy prediction is a critical research issue in financial risk early warning, credit evaluation, and investment decision-making. To address the limitations of traditional methods in handling high-dimensional, nonlinear, and complex financial data, including parameter sensitivity, susceptibility to local optima, and insufficient prediction [...] Read more.
Enterprise bankruptcy prediction is a critical research issue in financial risk early warning, credit evaluation, and investment decision-making. To address the limitations of traditional methods in handling high-dimensional, nonlinear, and complex financial data, including parameter sensitivity, susceptibility to local optima, and insufficient prediction stability, this study proposes a multi-strategy enhanced Beaver Behavior Optimizer and applies it to optimize kernel extreme learning machines, constructing the MEBBO KELM prediction model. Three improvement mechanisms are introduced, including an elite pool enhanced exploration strategy, a stochastic centroid reverse learning strategy, and a leader guided boundary control strategy, which improve population diversity, global search capability, boundary handling capacity, and convergence accuracy. The proposed algorithm is evaluated on CEC2017 and CEC2022 benchmark datasets and compared with EWOA, HPHHO, MELGWO, TACPSO, CFOA, ALA, AOO, RIME, and BBO. Statistical analyses are conducted using the Wilcoxon rank sum test and the Friedman test. The results demonstrate that MEBBO achieves superior solution accuracy and stability, indicating strong global optimization capability and robustness. Further experiments on the Wieslaw Corporate Bankruptcy Dataset show that MEBBO-KELM achieves strong and robust performance across multiple evaluation metrics, including ACC, MCC, Sensitivity, Specificity, Precision, Recall, and F1 score. Specifically, ACC reaches 79.7578, MCC reaches 0.6050, and F1 score reaches 78.8504, confirming its effectiveness. Full article
(This article belongs to the Special Issue Symmetry and Metaheuristic Algorithms)
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58 pages, 87068 KB  
Article
Enhanced Enterprise Development Optimization Algorithm with Business Management Strategies for Global Optimization and Real-World Engineering Applications
by Xiao Lin and Yu Fang
Symmetry 2026, 18(5), 786; https://doi.org/10.3390/sym18050786 (registering DOI) - 3 May 2026
Viewed by 222
Abstract
Wireless sensor network (WSN) coverage optimization is a challenging high-dimensional and nonlinear problem that directly affects network performance, including sensing quality, energy efficiency, and system reliability. Although metaheuristic algorithms have been widely applied to this problem, many existing methods still suffer from premature [...] Read more.
Wireless sensor network (WSN) coverage optimization is a challenging high-dimensional and nonlinear problem that directly affects network performance, including sensing quality, energy efficiency, and system reliability. Although metaheuristic algorithms have been widely applied to this problem, many existing methods still suffer from premature convergence, insufficient population diversity, and an imbalance between exploration and exploitation. To address these issues, this paper proposes a multi-strategy enhanced enterprise development optimization algorithm (MEEDOA) inspired by business management mechanisms. The proposed method integrates a hybrid population initialization strategy, an adaptive activity switching mechanism based on performance feedback, a multi-elite collaborative learning strategy, and a Lévy flight-based stagnation escape mechanism. These strategies are tightly coupled within a unified adaptive framework to improve global search capability, convergence speed, and robustness. Furthermore, a mathematical model for WSN deployment is constructed based on a binary sensing model and discrete coverage evaluation. From the perspective of symmetry, the sensing regions of sensor nodes exhibit significant geometric symmetry in both two-dimensional and three-dimensional deployment spaces. In the two-dimensional case, the sensing and communication regions are modeled as concentric circular structures, while in the three-dimensional case, the sensing regions are represented by isotropic spheres with symmetric spatial distributions. Such symmetry properties provide an effective basis for describing coverage behavior, reducing redundant overlap, and improving the uniformity of node deployment. Meanwhile, the proposed MEEDOA preserves population diversity and enhances search balance, enabling the algorithm to better capture symmetric coverage patterns and more effectively explore complex spatial deployment configurations. Extensive experiments on CEC2014, CEC2017, CEC2020, and CEC2022 benchmark functions demonstrate that MEEDOA achieves superior convergence accuracy, faster convergence speed, and stronger robustness compared with several state-of-the-art algorithms. Additional simulation results in WSN deployment applications verify its effectiveness in improving coverage performance under both symmetric and irregular spatial deployment scenarios. The results indicate that the proposed MEEDOA provides a reliable and efficient solution for complex global optimization problems and practical engineering applications. Full article
(This article belongs to the Special Issue Symmetry and Metaheuristic Algorithms)
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51 pages, 10042 KB  
Article
A Symmetry-Guided Multi-Strategy Differential Hybrid Slime Mold Algorithm for Sustainable Microgrid Dispatch Under Refined Battery Degradation Models
by Xingyu Lai, Minjie Dai, Yuhang Luo and Xin Song
Symmetry 2026, 18(4), 692; https://doi.org/10.3390/sym18040692 - 21 Apr 2026
Viewed by 308
Abstract
Optimized dispatch of microgrids is crucial for improving the economic performance and long-term sustainability of modern low-carbon power systems. In particular, accurate economic dispatch modeling for battery energy storage systems (BESSs) is essential for properly evaluating the operational benefits and lifetime costs of [...] Read more.
Optimized dispatch of microgrids is crucial for improving the economic performance and long-term sustainability of modern low-carbon power systems. In particular, accurate economic dispatch modeling for battery energy storage systems (BESSs) is essential for properly evaluating the operational benefits and lifetime costs of microgrids. However, when both battery cycle aging and calendar aging are considered, the resulting scheduling model becomes highly nonlinear, high-dimensional, non-convex, and multimodal, which poses substantial challenges to conventional optimization methods. To alleviate the above problem, a symmetry-guided multi-strategy differential hybrid slime mold algorithm (MDHSMA) is introduced for the day-ahead economic dispatch of microgrids under a refined battery degradation framework. First, a chaotic bimodal mirrored Latin hypercube sampling strategy is designed to exploit symmetry during population initialization, thereby enhancing diversity and improving structured coverage of the search space. Second, a history-driven adaptive differential evolution mechanism is integrated to balance global exploration and local exploitation more effectively during the iterative search process. Third, a state-aware stagnation handling framework is incorporated to maintain population vitality and further improve convergence accuracy and robustness. MDHSMA is evaluated against 12 state-of-the-art optimizers on the CEC2017 and CEC2022 benchmark suites and two representative engineering optimization problems to verify its overall performance. In addition, it is applied to a microgrid case study with refined BESS degradation modeling. The results show that MDHSMA achieves the lowest comprehensive operating cost by effectively coordinating electricity arbitrage and battery life consumption. Moreover, it guides the energy storage system toward shallow charge–-discharge patterns, thereby mitigating accelerated degradation caused by excessive cycling. These results confirm the effectiveness and practical value of the proposed method for sustainable microgrid dispatch in complex nonconvex optimization scenarios. Full article
(This article belongs to the Special Issue Symmetry and Metaheuristic Algorithms)
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41 pages, 33044 KB  
Article
An Improved DOA for Global Optimization and Cloud Task Scheduling
by Shinan Xu and Wentao Zhang
Symmetry 2025, 17(10), 1670; https://doi.org/10.3390/sym17101670 - 6 Oct 2025
Viewed by 1219
Abstract
Symmetry is an essential characteristic in both solution spaces and cloud task scheduling loads, as it reflects a structural balance that can be exploited to enhance algorithmic efficiency and robustness. In recent years, with the rapid development of 6G networks, the number of [...] Read more.
Symmetry is an essential characteristic in both solution spaces and cloud task scheduling loads, as it reflects a structural balance that can be exploited to enhance algorithmic efficiency and robustness. In recent years, with the rapid development of 6G networks, the number of tasks requiring computation in the cloud has surged, prompting an increasing number of researchers to focus on how to efficiently schedule these tasks to idle computing nodes at low cost to enhance system resource utilization. However, developing reliable and cost-effective scheduling schemes for cloud computing tasks in real-world environments remains a significant challenge. This paper proposes a method for cloud computing task scheduling in real-world environments using an improved dhole optimization algorithm (IDOA). First, we enhance the quality of the initial population by employing a uniform distribution initialization method based on the Sobol sequence. Subsequently, we further improve the algorithm’s search capabilities using a sine elite population search method based on adaptive factors, enabling it to more effectively explore promising solution spaces. Additionally, we propose a random mirror perturbation boundary control method to better address individual boundary violations and enhance the algorithm’s robustness. By explicitly leveraging symmetry characteristics, the proposed algorithm maintains balanced exploration and exploitation, thereby improving convergence stability and scheduling fairness. To evaluate the effectiveness of the proposed algorithm, we compare it with nine other algorithms using the IEEE CEC2017 test set and assess the differences through statistical analysis. Experimental results demonstrate that the IDOA exhibits significant advantages. Finally, to verify its applicability in real-world scenarios, we applied IDOA to cloud computing task scheduling problems in actual environments, achieving excellent results and successfully completing cloud computing task scheduling planning. Full article
(This article belongs to the Special Issue Symmetry and Metaheuristic Algorithms)
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24 pages, 5652 KB  
Article
Detection of COVID-19: A Metaheuristic-Optimized Maximally Stable Extremal Regions Approach
by Víctor García-Gutiérrez, Adrián González, Erik Cuevas, Fernando Fausto and Marco Pérez-Cisneros
Symmetry 2024, 16(7), 870; https://doi.org/10.3390/sym16070870 - 9 Jul 2024
Cited by 2 | Viewed by 2116
Abstract
The challenges associated with conventional methods of COVID-19 detection have prompted the exploration of alternative approaches, including the analysis of lung X-ray images. This paper introduces a novel algorithm designed to identify abnormalities in X-ray images indicative of COVID-19 by combining the maximally [...] Read more.
The challenges associated with conventional methods of COVID-19 detection have prompted the exploration of alternative approaches, including the analysis of lung X-ray images. This paper introduces a novel algorithm designed to identify abnormalities in X-ray images indicative of COVID-19 by combining the maximally stable extremal regions (MSER) method with metaheuristic algorithms. The MSER method is efficient and effective under various adverse conditions, utilizing symmetry as a key property to detect regions despite changes in scaling or lighting. However, calibrating the MSER method is challenging. Our approach transforms this calibration into an optimization task, employing metaheuristic algorithms such as Particle Swarm Optimization (PSO), Grey Wolf Optimizer (GWO), Firefly (FF), and Genetic Algorithms (GA) to find the optimal parameters for MSER. By automating the calibration process through metaheuristic optimization, we overcome the primary disadvantage of the MSER method. This innovative combination enables precise detection of abnormal regions characteristic of COVID-19 without the need for extensive datasets of labeled training images, unlike deep learning methods. Our methodology was rigorously tested across multiple databases, and the detection quality was evaluated using various indices. The experimental results demonstrate the robust capability of our algorithm to support healthcare professionals in accurately detecting COVID-19, highlighting its significant potential and effectiveness as a practical and efficient alternative for medical diagnostics and precise image analysis. Full article
(This article belongs to the Special Issue Symmetry and Metaheuristic Algorithms)
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