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Symmetry
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Applications Based on Symmetry/Asymmetry in Optimization Algorithms
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Applications Based on Symmetry/Asymmetry in Optimization Algorithms

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

Deadline for manuscript submissions: 31 December 2026 | Viewed by 1561

Editors

Dr. Yu Sun

E-Mail Website
Guest Editor
School of Computer, Electronics and Information, Guangxi University, Nanning 530004, China
Interests: intelligent algorithms; intelligent algorithms and their applications in image processing
Dr. Xin Nie

E-Mail Website
Guest Editor
School of Computer Science and Engineering, Wuhan Institute of Technology, Wuhan, China
Interests: software engineering; intelligent optimization algorithms; SOC system design

Special Issue Information

Dear Colleagues,

Symmetry often underlies hidden redundancies that inflate search spaces and degenerate gradients, while asymmetry frequently encodes the real-world imbalance that intelligent algorithms must cope with. This Special Issue welcomes original contributions that discover, quantify, or break symmetry and those that deliberately introduce beneficial asymmetry into optimization algorithms. We focus on advanced evolutionary and swarm intelligence methods (genetic algorithms, differential evolution, ant colony, particle swarm, estimation of distribution, and memetic frameworks), gradient-based and hybrid learning systems, and their deployment in machine learning tasks—especially computer vision problems such as symmetric/asymmetric object detection, equivariant network design, imbalance-aware classification, and neural architecture search. Review articles that offer systematic comparisons or unveil new benchmark suites are also encouraged. By gathering high-quality theoretical analyses, novel algorithmic designs, and real-world vision applications, this Special Issue aims to provide a comprehensive snapshot of how symmetry and asymmetry can be exploited to enhance convergence speed, solution quality, model compression, and generalization capability across complex optimization landscapes.

Dr. Yu Sun
Dr. Xin Nie
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-anonymized 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 breaking
  • asymmetric search operators
  • evolutionary computation
  • swarm intelligence
  • equivariant neural networks
  • neural architecture search
  • imbalanced learning
  • computer vision optimization
  • real-world applications

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

Published Papers (3 papers)

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Research

75 pages, 85508 KB  
Article
Symmetry-Guided Multi-Elite Gekko Japonicus Optimization Algorithm for Global Optimization and Artistic Image Segmentation
by Yulong Zhang, Jianfeng Wang and Xiaoyan Zhang
Symmetry 2026, 18(7), 1183; https://doi.org/10.3390/sym18071183 - 13 Jul 2026
Viewed by 456
Abstract
This paper presents a symmetry-guided multi-elite Gekko Japonicus Algorithm, termed MIGJA, for global optimization and multi-threshold image segmentation. The method modifies the original GJA from three aspects. In the movement stage, a success-rate feedback mechanism is used to adapt the Lévy-flight probability and [...] Read more.
This paper presents a symmetry-guided multi-elite Gekko Japonicus Algorithm, termed MIGJA, for global optimization and multi-threshold image segmentation. The method modifies the original GJA from three aspects. In the movement stage, a success-rate feedback mechanism is used to adapt the Lévy-flight probability and step-size coefficient according to recent search behavior, allowing the population to switch more flexibly between exploration and exploitation. In the guidance stage, several elite individuals are combined to form a weighted collaborative center, which reduces the excessive dependence on a single best solution and provides a more balanced search direction. In the reconstruction stage, historical memory and differential information are introduced into the tail reconstruction process to help inferior or stagnant individuals move out of local regions during the later search phase. The proposed MIGJA is tested on the CEC2017 and CEC2020 benchmark suites and further applied to Otsu-based multi-threshold image segmentation. The numerical results show that MIGJA performs competitively in terms of convergence accuracy and stability. According to the Friedman mean-rank results, MIGJA ranks first in all test settings, with mean-rank reductions of about 78.8–84.5% compared with the original GJA and 66.7–76.1% compared with the strongest competitor. In the segmentation experiments, MIGJA also obtains favorable objective function values and image quality metrics, including PSNR, FSIM, and SSIM. These findings suggest that the proposed algorithm is suitable for both benchmark optimization and multi-threshold image segmentation tasks. Full article
(This article belongs to the Special Issue Applications Based on Symmetry/Asymmetry in Optimization Algorithms)
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43 pages, 20683 KB  
Article
A Human Behavior Optimization Algorithm Based on Legal and Ethical Constraints for Numerical Optimization and Practical Applications
by Changheng Li and Chengpeng Li
Symmetry 2026, 18(6), 958; https://doi.org/10.3390/sym18060958 - 2 Jun 2026
Viewed by 261
Abstract
This paper proposes an improved metaheuristic algorithm named LHBBO, which incorporates legal and moral constraints into a human behavior-based optimization framework to tackle the limitations of conventional methods in high-dimensional and multimodal problem spaces. Three key innovations are introduced: a dual-layer normative audit [...] Read more.
This paper proposes an improved metaheuristic algorithm named LHBBO, which incorporates legal and moral constraints into a human behavior-based optimization framework to tackle the limitations of conventional methods in high-dimensional and multimodal problem spaces. Three key innovations are introduced: a dual-layer normative audit mechanism that enforces hard legal and soft moral constraints during candidate evaluation; a jury-guided collaborative consultation strategy that diversifies search direction references; and a directional migration mechanism triggered by population diversity and stagnation metrics. The proposed LHBBO is evaluated on the CEC2017 and CEC2022 benchmark suites, where it demonstrates significantly better convergence behavior and solution quality compared to several state-of-the-art algorithms. Notably, in 100-dimensional tests, LHBBO improves optimization precision by over 97% relative to the standard HBBO. When applied to unsupervised visual anomaly detection in industrial settings using the M2AD dataset, LHBBO effectively optimizes key parameters of a collaborative discrepancy-based model. The resulting system achieves a 9.05% increase in pixel-level localization accuracy (AUPRO) compared to the baseline CDO model, confirming its practical utility in complex, non-convex industrial optimization tasks. Full article
(This article belongs to the Special Issue Applications Based on Symmetry/Asymmetry in Optimization Algorithms)
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44 pages, 13105 KB  
Article
An Artistic Image Segmentation Method Based on an Art-Design-Strategy-Improved Parrot Optimizer
by Xiaoning Wang and Hui Zhang
Symmetry 2026, 18(5), 709; https://doi.org/10.3390/sym18050709 - 23 Apr 2026
Viewed by 391
Abstract
Multi-threshold image segmentation is an important research topic in the fields of computer vision and image processing. Its core objective is to efficiently determine the optimal threshold combination within a high-dimensional and complex search space. However, as the number of thresholds and image [...] Read more.
Multi-threshold image segmentation is an important research topic in the fields of computer vision and image processing. Its core objective is to efficiently determine the optimal threshold combination within a high-dimensional and complex search space. However, as the number of thresholds and image complexity increase, the computational cost of traditional exhaustive search methods grows exponentially. Meanwhile, conventional swarm intelligence algorithms often suffer from unstable convergence, premature stagnation, and parameter sensitivity when dealing with high-dimensional composite functions. To address these issues, this paper proposes an enhanced optimization algorithm termed the Parrot Optimizer with Artistic Design Strategy (PO-ADS). The proposed method constructs a multi-strategy cooperative optimization framework that integrates an Evolution Feedback–Based Adaptive Control Strategy (EFACS), a Multi-Operator Cooperative Evolution Strategy (MOCES), and an Artistic Design Strategy (ADS). These strategies enable dynamic parameter adjustment, adaptive balance between global exploration and local exploitation, and structured perturbation enhancement mechanisms. Experimental results on the CEC2020 and CEC2022 benchmark suites demonstrate that PO-ADS significantly outperforms seven state-of-the-art optimization algorithms across different dimensional settings in terms of optimization accuracy, convergence speed, and stability. The Friedman test results show that, on the CEC2020 benchmark suite, PO-ADS achieves average ranks of 1.72 (30-dimensional) and 1.85 (50-dimensional), both statistically superior to the comparative algorithms. Furthermore, PO-ADS is applied to multi-threshold image segmentation based on the Otsu criterion. The results indicate that the proposed method achieves optimal or near-optimal performance in terms of SSIM, PSNR, FSIM, and objective function values. Overall, the experimental findings confirm that PO-ADS not only possesses strong numerical optimization capability but also demonstrates robust and practical applicability in real-world image segmentation tasks. Full article
(This article belongs to the Special Issue Applications Based on Symmetry/Asymmetry in Optimization Algorithms)
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