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Symmetry
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Evolutionary Computation, Metaheuristics, Nature-Inspired Algorithms, and Symmetry: 2nd Edition
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Evolutionary Computation, Metaheuristics, Nature-Inspired Algorithms, and Symmetry: 2nd Edition

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

Deadline for manuscript submissions: 30 November 2026 | Viewed by 2734

Special Issue Editors

Dr. Yirui Wang

E-Mail Website
Guest Editor
Faculty of Electrical Engineering and Computer Science, Ningbo University, Ningbo 315211, China
Interests: evolutionary computation; swarm intelligence; computational intelligence; optimization
Special Issues, Collections and Topics in MDPI journals
Dr. Yang Yu

E-Mail Website
Guest Editor
College of Automation & College of Artificial Intelligence, Nanjing University of Posts and Telecommunications, Nanjing 210023, China
Interests: evolutionary computation; neural nets; search problems
Special Issues, Collections and Topics in MDPI journals
Dr. Zhenyu Lei

E-Mail Website
Guest Editor
Department of Intellectual Information Systems Engineering, Faculty of Engineering, University of Toyama, Toyama 930-8555, Japan
Interests: evolutionary computation; machine learning; neural network for real-world applications; optimization problems

Special Issue Information

Dear Colleagues,

Computational intelligence is an important branch of artificial intelligence and, nowadays, evolutionary computation, as a subset of computational intelligence, is widely used to solve various numerical problems and real-world engineering problems. Its application and development provide a great contribution to the optimization domain. Thus, it is of great interest to investigate the role and significance of evolutionary computation, metaheuristics, and nature-inspired algorithms in optimizing distinctive problems such as model symmetry/asymmetry, model architecture and hyperparameters, numerical functions, and industrial processing.

This Special Issue aims to bring together both experts and newcomers from either academia or industry to discuss new and existing issues concerning evolutionary computation and optimization. The research topics include single-objective optimization, multi-objective optimization, combinatorial optimization, and real-world problems, as well as industrial control, job-shop scheduling, pattern recognition, and computer vision. There is no limit on the number of pages, but the submissions must demonstrate an understanding of the theme and contribute to the specified topic.

Dr. Yirui Wang
Dr. Yang Yu
Dr. Zhenyu Lei
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 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

  • evolutionary computation
  • metaheuristics
  • nature-inspired algorithms
  • single-objective optimization
  • multi-objective optimization
  • real-world engineering application
  • intelligent systems
  • artificial Intelligence

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Published Papers (5 papers)

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Research

57 pages, 13008 KB  
Article
Corrosion Diagnosis of Hydroelectric Grounding Grids Based on Voltage Distribution Symmetry Deviation via a Quantum-Inspired Candidate Pool Guided Sine Cosine Algorithm
by Xinyue Zhang, Keying Wang and Liangliang Li
Symmetry 2026, 18(5), 753; https://doi.org/10.3390/sym18050753 - 27 Apr 2026
Viewed by 264
Abstract
Hydropower stations, as critical infrastructure for basic energy supply, play a pivotal role in ensuring the reliability of power systems through their safe and stable operation. Grounding grids operating long-term in complex soil environments are prone to corrosion and degradation, disrupting current distribution [...] Read more.
Hydropower stations, as critical infrastructure for basic energy supply, play a pivotal role in ensuring the reliability of power systems through their safe and stable operation. Grounding grids operating long-term in complex soil environments are prone to corrosion and degradation, disrupting current distribution balance and causing spatial asymmetry in the voltage field, thereby compromising system safety. Corrosion branch resistance increment identification based on the electrical network method is typically modeled as a parameter inversion optimization problem. However, this problem exhibits underdetermination and other characteristics, making it difficult for traditional analytical methods to obtain stable solutions. To address this, this paper proposes a quantum perturbation scheduling candidate pool-guided sine–cosine algorithm (QSPSCA). Building upon the classical sine–cosine algorithm framework, it incorporates a dynamic candidate pool with multi-source attractor points and a quantum-inspired long-tail scheduling local refinement operator. This achieves an enhanced and smooth transition between global exploration and local refinement. Comparative experiments based on the CEC2017 benchmark and a hydropower station grounding grid corrosion diagnosis case demonstrate that QSPSCA outperforms multiple comparison algorithms in terms of average optimality and result stability. Furthermore, QSPSCA is applied to three typical engineering-constrained optimization problems. Results demonstrate that, whilst satisfying engineering constraints, this method consistently yields higher-quality feasible solutions with superior convergence accuracy and stability compared to alternative algorithms. Therefore, QSPSCA is not only applicable to underdetermined inversion diagnostics but also provides a solution framework with broad applicability for complex engineering optimization problems under structural symmetry perturbations. Full article
(This article belongs to the Special Issue Evolutionary Computation, Metaheuristics, Nature-Inspired Algorithms, and Symmetry: 2nd Edition)
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39 pages, 28158 KB  
Article
Improved Arithmetic Optimization Algorithm Based on Curriculum Education for Numerical Optimization and Practical Problems
by Ke Shen, Shiyi Guo, Wanqing Tang and Meng Wang
Symmetry 2026, 18(3), 544; https://doi.org/10.3390/sym18030544 - 23 Mar 2026
Viewed by 414
Abstract
The arithmetic optimization algorithm (AOA) is a recently proposed swarm intelligence optimizer with a simple structure and few control parameters. However, the original AOA relies on a single update mechanism, which often leads to premature convergence and limited adaptability in complex optimization problems. [...] Read more.
The arithmetic optimization algorithm (AOA) is a recently proposed swarm intelligence optimizer with a simple structure and few control parameters. However, the original AOA relies on a single update mechanism, which often leads to premature convergence and limited adaptability in complex optimization problems. To address these limitations, this paper proposes a multi-strategy improved arithmetic optimization algorithm (IAOA). The proposed algorithm constructs a heterogeneous strategy pool composed of six search strategies, including arithmetic update, differential evolution operators, competitive elite learning, interpolation-based acceleration, and curriculum education learning. Furthermore, an adaptive strategy regulation mechanism based on fitness improvement contribution is introduced to dynamically adjust the selection probability of each strategy. Extensive experiments conducted on the CEC2017 and CEC2022 benchmark suites demonstrate that IAOA achieves a superior optimization accuracy, convergence speed, and stability compared with several classical algorithms, recent metaheuristics, and AOA variants. Statistical tests including the Wilcoxon rank-sum test and Friedman mean rank test confirm the significance of the performance improvements. In addition, the algorithm is successfully applied to a three-dimensional path planning problem for amphibious unmanned aerial vehicles, demonstrating its effectiveness in solving complex engineering optimization problems. Full article
(This article belongs to the Special Issue Evolutionary Computation, Metaheuristics, Nature-Inspired Algorithms, and Symmetry: 2nd Edition)
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36 pages, 5695 KB  
Article
Red-Billed Blue Magpie Optimization Algorithm-Based Aquila Optimizer: Numerical Optimization, Engineering Problem, and Cybersecurity Intrusion Prediction
by Oluwatayomi Rereloluwa Adegboye, Afi Kekeli Feda and Huseyin Kusetogullari
Symmetry 2026, 18(3), 503; https://doi.org/10.3390/sym18030503 - 15 Mar 2026
Cited by 1 | Viewed by 407
Abstract
A hybrid metaheuristic methodology that combines the Red-billed Blue Magpie Optimization (RBMO) algorithm with the Aquila Optimizer (AO) is introduced in this work as the RBMOAO method. The novel algorithm addresses a critical shortcoming of the standard AO: its exploration-to-exploitation ratio across different [...] Read more.
A hybrid metaheuristic methodology that combines the Red-billed Blue Magpie Optimization (RBMO) algorithm with the Aquila Optimizer (AO) is introduced in this work as the RBMOAO method. The novel algorithm addresses a critical shortcoming of the standard AO: its exploration-to-exploitation ratio across different optimization stages is inefficient, yielding premature convergence and low diversity within the population. This is achieved by using RBMO’s Group-Based Directional Perturbation (GDP) and its dynamic convergence factor (CF) as part of the methodology. The early stages of the optimization process are characterized by a grouping methodology to maintain population diversity through coordinated exploration across subgroups of varying sizes using GDP. Later iterations are characterized by a CF-guided updating process that increases the resolution of the search for the best areas, thereby improving convergence precision without sacrificing solution quality. Empirical testing of the proposed methodology using the CEC 2015 and CEC 2020 test sets demonstrated RBMOAO’s superior performance compared to other metaheuristics, outperforming other optimizers in 73.33% of CEC 2015 functions and 80% of CEC 2020 functions, with statistical significance in the increased precision and robustness of solutions across all problem types. Additionally, the RBMOAO methodology demonstrated outstanding performance in constrained engineering design problems. In addition to optimization, an RBMOAO-optimized ensemble architecture was implemented to predict cybersecurity intrusion threats, achieving an accuracy of 89.6%. Through the dynamic calibration of the base learner weights via metaheuristic search, the RBMOAO ensemble achieved the top ranking. These results illustrate the wide range of applications of the RBMOAO methodology and provide support for its deployment in the context of high-stakes predictive analytics. Full article
(This article belongs to the Special Issue Evolutionary Computation, Metaheuristics, Nature-Inspired Algorithms, and Symmetry: 2nd Edition)
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41 pages, 19065 KB  
Article
Student Psychological Optimization Algorithm Based on Teaching and Learning for Global Optimization Problems and Optimal Scheduling Problems
by Minnan Chen, Yinghao Wang and Mingfei Jin
Symmetry 2026, 18(2), 341; https://doi.org/10.3390/sym18020341 - 12 Feb 2026
Viewed by 572
Abstract
To overcome the limitations of the standard Student Psychology-Based Optimization (SPBO) algorithm, such as strategy homogeneity, insufficient elite-guided diversity, and inefficient evolution of low-quality individuals, this paper proposes a Hierarchical Teaching–Learning Enhanced Student Psychology-Based Optimization (HTL-SPBO) algorithm. The proposed method introduces a fitness-based [...] Read more.
To overcome the limitations of the standard Student Psychology-Based Optimization (SPBO) algorithm, such as strategy homogeneity, insufficient elite-guided diversity, and inefficient evolution of low-quality individuals, this paper proposes a Hierarchical Teaching–Learning Enhanced Student Psychology-Based Optimization (HTL-SPBO) algorithm. The proposed method introduces a fitness-based three-layer teaching mechanism to realize differentiated learning behaviors for individuals with different evolutionary states. In addition, a multi-elite mentor pool strategy is employed to generalize elite guidance and alleviate premature convergence, while an elite-neighborhood-guided restart mechanism is designed to improve the evolutionary efficiency of poorly performing individuals. The effectiveness of HTL-SPBO is comprehensively evaluated on the CEC2017 and CEC2022 benchmark test suites under multiple dimensional settings. Experimental results demonstrate that HTL-SPBO achieves superior performance in terms of convergence accuracy, convergence speed, and robustness when compared with several State-of-the-Art optimization algorithms. The convergence behavior shows that the proposed algorithm is capable of rapid early-stage exploration followed by stable and accurate exploitation in later iterations. Furthermore, HTL-SPBO is applied to an optimal scheduling problem for a grid-connected microgrid to verify its practical applicability. The results indicate that HTL-SPBO attains the lowest average operating cost while maintaining small performance variance across multiple independent runs, highlighting its effectiveness and stability in solving complex engineering optimization problems. Overall, the proposed HTL-SPBO provides a robust and efficient optimization framework and exhibits strong potential for application in large-scale and real-world optimization scenarios. Full article
(This article belongs to the Special Issue Evolutionary Computation, Metaheuristics, Nature-Inspired Algorithms, and Symmetry: 2nd Edition)
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35 pages, 8270 KB  
Article
Multi-Strategy Variable Secretary Bird Optimization Algorithm (MSVSBOA) for Global Optimization and UAV 3D Path Planning
by Amir Seyyedabbasi
Symmetry 2026, 18(2), 273; https://doi.org/10.3390/sym18020273 - 31 Jan 2026
Cited by 1 | Viewed by 511
Abstract
In this study, an enhanced variant of the Secretary Bird Optimization Algorithm (SBOA), named MSVSBOA, is proposed to address the limitations of the SBOA in global optimization and UAV 3D path-planning. The proposed MSVSBOA integrates three complementary strategies to achieve a balanced exploration [...] Read more.
In this study, an enhanced variant of the Secretary Bird Optimization Algorithm (SBOA), named MSVSBOA, is proposed to address the limitations of the SBOA in global optimization and UAV 3D path-planning. The proposed MSVSBOA integrates three complementary strategies to achieve a balanced exploration and exploitation trade-off. First, a Levy-based Directed Exploration mechanism is introduced to enrich the global search capability and prevent premature convergence. Second, a spiral movement mechanism is incorporated to strengthen the local exploitation behavior and improve convergence accuracy. Third, a Differential Evolution-inspired refinement strategy (DE-Refinement) is employed to accelerate fine-grained exploitation during the later stages of optimization. The performance of the MSVSBOA is extensively evaluated on the CEC 2014 and CEC 2022 benchmark suites. Experimental results demonstrate that the MSVSBOA achieves superior accuracy, faster convergence, and improved robustness compared to the SBOA and other multi-strategy variants. Furthermore, the MSVSBOA is applied to a challenging UAV 3D path planning problem, where it successfully generates safe, smooth, and collision-free trajectories while outperforming competing algorithms. These findings confirm the effectiveness of the proposed MSVSBOA for both global optimization problems and real-world UAV applications. Full article
(This article belongs to the Special Issue Evolutionary Computation, Metaheuristics, Nature-Inspired Algorithms, and Symmetry: 2nd Edition)
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