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Symmetry
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Symmetry in Optimization: From Algorithmic Design to Applications
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Symmetry in Optimization: From Algorithmic Design to Applications

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

Deadline for manuscript submissions: 31 August 2026 | Viewed by 805

Special Issue Editor

Dr. Touqeer Ahmed Jumani

E-Mail Website
Guest Editor
Department of Electrical Engineering and Computer Science, College of Engineering, A’Sharqiyah University, Ibra 400, Oman
Interests: swarm intelligence; microgrid controls; meta-heuristic techniques; machine learning based classification methods; evolutionary algorithms

Special Issue Information

Dear Colleagues,

This Special Issue focuses on advancing optimization research through the systematic exploitation of symmetry. Many real-world optimization problems exhibit inherent symmetric structures due to variable permutations, model formulations, constraints, and system configurations. Identifying and leveraging these symmetries can significantly reduce computational complexity, shrink search spaces, and improve convergence speed and solution quality.

The aim of this Special Issue is to highlight recent developments in symmetry-aware optimization methods, including exact algorithms, metaheuristics, evolutionary computation, and learning-based optimization frameworks. Topics of interest include symmetry detection and breaking, symmetry reduction techniques, invariant modeling, and group-theoretic approaches in optimization. Particular emphasis is placed on algorithmic design and performance enhancement through structural exploitation.

Furthermore, the Special Issue welcomes application-oriented studies where symmetry-based optimization plays a central role, such as large-scale engineering optimization, network optimization, scheduling, energy systems, and resource allocation. Both theoretical contributions and practical implementations with experimental validation are encouraged. This Special Issue seeks to provide a comprehensive platform for researchers developing next-generation optimization algorithms that effectively leverage symmetry.

Dr. Touqeer Ahmed Jumani
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 in optimization
  • optimization algorithms
  • symmetry reduction
  • symmetry breaking
  • metaheuristic optimization
  • evolutionary algorithms
  • invariant optimization
  • computational optimization
  • large-scale optimization

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

Published Papers (2 papers)

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Research

40 pages, 29804 KB  
Article
A Multi-Strategy Improved Love Evolution Algorithm for Global Optimization Problems and Real-World Problems
by Xiaoyu Hu and Chengpeng Li
Symmetry 2026, 18(6), 926; https://doi.org/10.3390/sym18060926 (registering DOI) - 29 May 2026
Abstract
This paper proposes a Multi-strategy Improved Love Evolution Algorithm, named MSILEA, to overcome the limitations of the original Love Evolution Algorithm (LEA) in complex optimization tasks. Although LEA has a distinctive stimulus–value–role interaction mechanism, its linear search-radius control, distance-dominated behavioral decision rule, and [...] Read more.
This paper proposes a Multi-strategy Improved Love Evolution Algorithm, named MSILEA, to overcome the limitations of the original Love Evolution Algorithm (LEA) in complex optimization tasks. Although LEA has a distinctive stimulus–value–role interaction mechanism, its linear search-radius control, distance-dominated behavioral decision rule, and weak directional learning in the value phase make it prone to insufficient exploitation, ineffective behavioral switching, and local optimum trapping on rotated, hybrid, and composition functions. To address these issues, MSILEA introduces three complementary strategies: a nonlinear two-stage search radius regulation strategy, a quality–distance joint decision strategy, and a winner-direction differential learning strategy. These strategies respectively improve stage-dependent search control, multi-criteria behavioral selection, and directional learning ability. From the perspective of the symmetry concept, the proposed MSILEA can be regarded as an optimization framework that dynamically regulates the symmetry and asymmetry of population interactions. The encounter and role mechanisms preserve paired interaction symmetry among candidate solutions, whereas the quality–distance joint decision and winner-direction differential learning strategies introduce controlled symmetry breaking to guide the population toward higher-quality regions of the search space. MSILEA is evaluated on the CEC2017 and CEC2022 benchmark suites and compared with nine representative classical and advanced metaheuristic algorithms. On the 30-dimensional CEC2017 suite, MSILEA achieves the best Friedman mean rank of 1.93, outperforming the original LEA with a mean rank of 4.60. On the CEC2022 suite, MSILEA also obtains the best mean ranks of 2.50 and 2.00 in the 10-dimensional and 20-dimensional cases, respectively. In the microgrid day-ahead optimal scheduling problem, MSILEA obtains the lowest mean operating cost of 1.23 × 106 CNY and reduces the cost by approximately 50.80% compared with LEA. The average CPU time of MSILEA is 18.47 s, which is comparable to LEA and lower than several improved competitors. These results indicate that MSILEA can improve optimization accuracy, convergence robustness, and engineering feasibility without increasing the theoretical computational complexity. Full article
(This article belongs to the Special Issue Symmetry in Optimization: From Algorithmic Design to Applications)
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39 pages, 11265 KB  
Article
A Multi-Strategy Hybrid-Enhanced Educational Competition Optimizer for Global Optimization and Real-World Engineering Applications
by Min Sun, Shicen Zhang and Wenjun Jiang
Symmetry 2026, 18(4), 602; https://doi.org/10.3390/sym18040602 - 1 Apr 2026
Viewed by 518
Abstract
This paper proposes a multi-strategy hybrid-enhanced Educational Competition Optimizer (MEECO) to improve the performance of swarm-based optimization algorithms in complex search environments. From the perspective of symmetry, population-based optimization algorithms inherently rely on the symmetric distribution and evolution of individuals in the search [...] Read more.
This paper proposes a multi-strategy hybrid-enhanced Educational Competition Optimizer (MEECO) to improve the performance of swarm-based optimization algorithms in complex search environments. From the perspective of symmetry, population-based optimization algorithms inherently rely on the symmetric distribution and evolution of individuals in the search space, while the imbalance between exploration and exploitation often leads to symmetry breaking, resulting in premature convergence and loss of diversity. Unlike the standard ECO, which suffers from limited information exchange, premature convergence, and boundary stagnation, the proposed method integrates three complementary mechanisms: adaptive differential evolution, vertical crossover, and global-best-guided boundary handling. Specifically, the adaptive differential evolution strategy enhances global exploration and maintains population distribution symmetry through dynamic mutation, the vertical crossover mechanism improves inter-dimensional symmetry and information interaction, and the boundary-handling strategy restores symmetry by guiding infeasible solutions back to promising regions. These strategies jointly improve population diversity, exploration–exploitation balance, and convergence efficiency while preserving structural symmetry in the search process. Extensive experiments on CEC2017 and CEC2022 benchmark suites demonstrate that MEECO consistently achieves superior optimization accuracy, faster convergence speed, and stronger robustness compared with several state-of-the-art algorithms. Statistical analyses further confirm the significance and reliability of the improvements. In addition, the proposed method is applied to a wireless sensor network node deployment problem, where it significantly improves coverage rate and deployment uniformity. The results indicate that MEECO provides an effective, robust, and symmetry-preserving optimization framework for both benchmark problems and real-world engineering applications. Full article
(This article belongs to the Special Issue Symmetry in Optimization: From Algorithmic Design to Applications)
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