Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
5.3
2.2
Journals
Symmetry
Special Issues
Symmetry in Optimization Algorithms and Applications
share announcement

Symmetry in Optimization Algorithms and Applications

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

Deadline for manuscript submissions: 31 March 2027 | Viewed by 3024

Special Issue Editor

Prof. Dr. Adrián González

E-Mail Website
Guest Editor
Departamento de Ingeniería Electro-Fotónica, Universidad de Guadalajara (CUCEI), Blvd. Marcelino García Barragán #1421, Guadalajara 44430, Mexico
Interests: evolutionary algorithms

Special Issue Information

Dear Colleagues,

This Special Issue, "Symmetry in Optimization Algorithms and Applications", examines how symmetry, present in many optimization problems, impacts the efficiency and performance of algorithms. It explores methods to identify and leverage symmetries to simplify problems, reduce search spaces, and speed up convergence. Practical applications are discussed in fields such as mathematical programming, artificial intelligence, and combinatorial optimization. The Issue will also address challenges such as breaking unnecessary symmetries to avoid redundant solutions and ensuring algorithm robustness in real-world scenarios.  

Prof. Dr. Adrián González
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
  • optimization algorithms
  • problem simplification
  • search space reduction
  • algorithm efficiency
  • symmetry breaking
  • mathematical programming
  • combinatorial optimization
  • convergence acceleration

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • Reprint: MDPI Books provides the opportunity to republish successful Special Issues in book format, both online and in print.

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

Published Papers (5 papers)

Download All Papers
Order results
Result details
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:

Research

46 pages, 8934 KB  
Article
An Adaptive Multi-Strategy Enhanced Educational Competition Optimizer for Global Optimization and Real-World Problems
by Yiwen Liu, Yang Liu and Haoxiang Zhou
Symmetry 2026, 18(6), 924; https://doi.org/10.3390/sym18060924 (registering DOI) - 28 May 2026
Abstract
The Educational Competition Optimizer (ECO) shows promise on simple tasks but struggles with high-dimensional and complex landscapes due to rigid stage division and limited search operators. This paper proposes a Hybrid Strategy Enhanced ECO (HSECO) featuring: (i) a self-adaptive parameter evolution mechanism for [...] Read more.
The Educational Competition Optimizer (ECO) shows promise on simple tasks but struggles with high-dimensional and complex landscapes due to rigid stage division and limited search operators. This paper proposes a Hybrid Strategy Enhanced ECO (HSECO) featuring: (i) a self-adaptive parameter evolution mechanism for individual-level flexibility, (ii) a multi-operator adaptive selection scheme switching between learning and differential evolution strategies based on real-time feedback, and (iii) an archive-assisted diversity preservation module to mitigate premature convergence. HSECO is validated on CEC2017, CEC2020 and CEC2022, and a continuous engineering benchmark. Statistical tests confirm its superiority over nine State-of-the-Art and parameter-free algorithms in accuracy, convergence speed, and robustness. Ablation and diversity analyses verify its balanced exploration–exploitation dynamics. Finally, HSECO is applied to a three-dimensional UAV path-planning problem, where path length, altitude variation, and turning smoothness are integrated into a single fitness function using a weighted-sum formulation. Therefore, from a metaheuristic optimization perspective, the UAV case is treated as a single-objective constrained optimization problem rather than a Pareto-based multi-objective problem. Experimental results show that HSECO obtains shorter, safer, and smoother trajectories with lower overall weighted fitness. Full article
(This article belongs to the Special Issue Symmetry in Optimization Algorithms and Applications)
►▼ Show Figures

Figure 1

40 pages, 32270 KB  
Article
Teaching–Learning–Studying-Based Optimization with Dance Learning Strategies for Global Optimization Problems and Real-World Applications
by Keyu Shi, Wenchen Sun and Jianfeng Wang
Symmetry 2026, 18(5), 837; https://doi.org/10.3390/sym18050837 - 13 May 2026
Viewed by 142
Abstract
This paper addresses two key challenges: low solution accuracy and premature convergence in high-dimensional optimization problems, as well as the difficulty of jointly optimizing coverage, redundancy, and movement cost in wireless sensor network (WSN) deployment. To solve these issues, an improved Teaching–Learning–Studying-Based Optimization [...] Read more.
This paper addresses two key challenges: low solution accuracy and premature convergence in high-dimensional optimization problems, as well as the difficulty of jointly optimizing coverage, redundancy, and movement cost in wireless sensor network (WSN) deployment. To solve these issues, an improved Teaching–Learning–Studying-Based Optimization algorithm, named TLSBO-DLS, is proposed. Within the original TLSBO framework, three enhancement strategies are incorporated: (1) a dimension-adaptive update probability mechanism to improve fine-grained search capability; (2) a dance learning strategy that enhances dynamic exploration through oscillatory cooperative learning; and (3) an elite adaptive perturbation mechanism based on a Cauchy–Gaussian hybrid distribution to improve convergence accuracy and help escape local optima. Empirical evaluations conducted on the CEC2017, CEC2020, and CEC2022 benchmark datasets indicate that TLSBO-DLS achieves superior performance compared to nine alternative algorithms, exhibiting higher solution precision and faster convergence behavior. Furthermore, its advantage is rigorously confirmed through statistical analyses using the Wilcoxon rank-sum test and the Friedman ranking test. Furthermore, a two-dimensional multi-objective WSN node deployment model is constructed, and TLSBO-DLS is applied to a practical scenario with 30 sensor nodes. The results show that the proposed algorithm achieves a coverage rate of 85.50%, a redundant coverage rate of only 5.15%, and an average node movement distance as low as 15.8471. In terms of global performance, the proposed method surpasses PSO, GWO, WOA, as well as several enhanced TLSBO variants, thereby demonstrating its strong capability and practical value when addressing high-dimensional challenging optimization tasks and real-world engineering problems. Full article
(This article belongs to the Special Issue Symmetry in Optimization Algorithms and Applications)
►▼ Show Figures

Figure 1

62 pages, 15310 KB  
Article
A Multi-Strategy Improved Information Acquisition Algorithm for Numerical Optimization and Artistic Image Segmentation
by Xiaoyan Zhang, Bin Wang, Yu Shao and Jianfeng Wang
Symmetry 2026, 18(5), 708; https://doi.org/10.3390/sym18050708 - 23 Apr 2026
Viewed by 193
Abstract
To address the shortcomings of the information acquisition optimizer (IAO)—specifically its susceptibility to premature convergence, insufficient exploitation capability during later stages, and population diversity decay when applied to complex optimization problems—this paper proposes a multi-strategy improved information acquisition optimizer (MIIAO). Centered on balancing [...] Read more.
To address the shortcomings of the information acquisition optimizer (IAO)—specifically its susceptibility to premature convergence, insufficient exploitation capability during later stages, and population diversity decay when applied to complex optimization problems—this paper proposes a multi-strategy improved information acquisition optimizer (MIIAO). Centered on balancing exploration and exploitation capabilities during the search process, this method incorporates several key strategies: an adaptive differential perturbation factor is designed to dynamically adjust the search step size; an elite-guided information acquisition mechanism is introduced to enhance convergence efficiency within high-quality regions; a diversity-based restart perturbation strategy is integrated to mitigate the risk of entrapment in local optima; and a mirror boundary handling technique is adopted to bolster the resilience of solutions near boundaries and improve the effectiveness of searching within the feasible domain. To validate the efficacy of the proposed method, MIIAO was applied to the CEC2014, CEC2017, and CEC2022 benchmark test suites and systematically compared against various representative intelligent optimization algorithms. Furthermore, the method was applied to multi-threshold image segmentation tasks based on Otsu’s criterion. Experimental results demonstrate that MIIAO consistently exhibits superior solution accuracy, convergence speed, stability, and statistical ranking across various dimensions and a diverse range of complex test functions; the results of the Wilcoxon rank-sum test and Friedman mean ranking further substantiate its comprehensive performance advantages. In the image segmentation experiments, MIIAO achieved superior Otsu objective function values across multiple test images and under various threshold settings, while also demonstrating higher segmentation quality and greater robustness across evaluation metrics such as PSNR, SSIM, and FSIM. In summary, the proposed MIIAO effectively enhances the original IAO’s global search capability, local exploitation capability, and ability to maintain population diversity, thereby demonstrating significant potential for practical application in both numerical optimization and multi-threshold image segmentation tasks. Full article
(This article belongs to the Special Issue Symmetry in Optimization Algorithms and Applications)
►▼ Show Figures

Figure 1

34 pages, 22620 KB  
Article
Improved Secretary Bird Optimization Algorithm Based on Financial Investment Strategy for Global Optimization and Real Application Problems
by Yiming Liu, Bingchun Yuan and Shuqi Yuan
Symmetry 2026, 18(4), 688; https://doi.org/10.3390/sym18040688 - 21 Apr 2026
Viewed by 393
Abstract
This paper proposes a multi-strategy Secretary Bird Optimization Algorithm (MS-SBOA) for solving global optimization problems and 3D wireless sensor network deployment. While preserving the original two-phase search framework of SBOA, the proposed algorithm achieves a dynamic balance between global exploration and local exploitation [...] Read more.
This paper proposes a multi-strategy Secretary Bird Optimization Algorithm (MS-SBOA) for solving global optimization problems and 3D wireless sensor network deployment. While preserving the original two-phase search framework of SBOA, the proposed algorithm achieves a dynamic balance between global exploration and local exploitation through the synergistic integration of multiple enhancement strategies, including a hybrid initialization scheme combining Latin hypercube sampling and quasi-opposition-based learning, a success-history-based adaptive parameter learning mechanism, a finance-inspired market-state trading operator, and an elite-guided population regulation strategy. Experimental results on the IEEE CEC2020 and CEC2022 benchmark test suites demonstrate that MS-SBOA significantly outperforms nine comparative algorithms, including VPPSO, IAGWO, and QHSBOA, under both 10-dimensional and 20-dimensional settings. The proposed algorithm exhibits superior optimization accuracy, faster convergence speed, and stronger robustness. Statistical analyses using the Wilcoxon rank-sum test and the Friedman mean rank test further confirm that the observed performance improvements are statistically significant. Moreover, MS-SBOA is applied to three-dimensional wireless sensor network (3D WSN) deployment optimization problems, where the average coverage rates reach 76.22% and 82.32% for 30-node and 50-node deployment scenarios, respectively. The resulting node distributions are more uniform, and the computational efficiency is improved compared with competing algorithms. Full article
(This article belongs to the Special Issue Symmetry in Optimization Algorithms and Applications)
►▼ Show Figures

Figure 1

26 pages, 2942 KB  
Article
An Improved Whale Migration Algorithm for Global Optimization of Collaborative Symmetric Balanced Learning and Cloud Task Scheduling
by Honggan Lu, Shenghao Cheng and Xinsheng Zhang
Symmetry 2025, 17(6), 841; https://doi.org/10.3390/sym17060841 - 27 May 2025
Cited by 3 | Viewed by 1303
Abstract
In today’s complex and ever-changing fields of science and engineering, intelligent optimization algorithms have become a key tool. However, the complexity of the problem itself often poses a severe challenge to the performance of the algorithm. The whale migration algorithm stands out among [...] Read more.
In today’s complex and ever-changing fields of science and engineering, intelligent optimization algorithms have become a key tool. However, the complexity of the problem itself often poses a severe challenge to the performance of the algorithm. The whale migration algorithm stands out among numerous optimization algorithms with its simple and efficient implementation and has received extensive attention. However, when confronted with complex issues such as global optimization and task scheduling, it still exposes some deficiencies including low initial population symmetry (i.e., poor distribution uniformity and insufficient balance between exploration and exploitation in iterative processes). The development ability of the algorithm is relatively weak, making it difficult to conduct an effective search and optimization in the complex problem space. The task scheduling strategy is not optimized enough, which affects the application of the algorithm in actual task scheduling scenarios. To overcome these challenges, this paper proposes an improved whale migration algorithm. Based on inheriting the original advantages of the whale migration algorithm, this algorithm effectively solves the above problems by introducing a new mechanism. The CEC2021 test function set was selected, and the effectiveness of the proposed strategy was verified through point-by-point ablation experiments. The algorithm was comprehensively verified through the CEC2022 test problem set, verifying the effectiveness and robustness of the algorithm in global optimization problems. Furthermore, the proposed algorithm was tested for cloud task scheduling problems of different scales. The experimental results show that the proposed algorithm can reduce the total scheduling cost by about 9% or more. Full article
(This article belongs to the Special Issue Symmetry in Optimization Algorithms and Applications)
►▼ Show Figures

Figure 1

Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-5
Back to TopTop