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Symmetry
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Symmetry in Intelligent Algorithms
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Symmetry in Intelligent Algorithms

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

Deadline for manuscript submissions: 31 May 2025 | Viewed by 5858

Special Issue Editors

Dr. Hongwei Kang

E-Mail Website
Guest Editor
1. School of Software, Yunnan University, Kunming 650500, China
2. Yunnan key laboratory of software engineering, Yunnan University, Kunming 650504, China
Interests: evolutionary algorithm; cooperative coevolution; differential evolution
Dr. Xinping Sun

E-Mail Website
Guest Editor
School of Software, Yunnan University, Kunming 650500, China
Interests: swarm intelligence; evolutionary computation; evolutionary game; machine learning

Special Issue Information

Dear Colleagues,

We are delighted to announce the launch of a new Special Issue entitled "Symmetry in Intelligent Algorithms". Intelligent Algorithms, which range from machine learning to evolutionary computation, are pivotal in modern computing.  However, challenges persist in understanding their intricacies, ensuring fairness, and maximizing efficiency. From swarm intelligence to evolutionary computation and machine learning, symmetry can be leveraged to optimize algorithmic behavior, streamline computational processes, and enhance the quality of solutions.  Understanding and harnessing symmetry can lead to more robust, scalable, and interpretable algorithms. This Special Issue aims to explore the integration of symmetry into the design and application of intelligent algorithms.  It seeks to connect researchers, practitioners, and experts to discuss novel approaches, theoretical foundations, and real-world applications.  By providing a platform for sharing insights and fostering collaboration, this Special Issue seeks to advance the understanding and application of symmetry in intelligent algorithms, addressing current challenges and setting the stage for future developments. Below is an outline of topics, key areas of interest, and the significance of this Special Issue. 

  • Fundamentals and Theoretical Advances
    • Theoretical foundations and mathematical modeling of swarm intelligence and evolutionary algorithms.
    • Comparative analyses and benchmarks of different swarm and evolutionary algorithms.
    • Hybrid models combining swarm intelligence with evolutionary computation or other optimization techniques.
    • Convergence analysis and performance metrics for swarm and evolutionary algorithms. 
  • Algorithm Design and Optimization
    • Novel swarm intelligence algorithms (e.g., Ant Colony Optimization, Particle Swarm Optimization, Artificial Bee Colony).
    • Innovative evolutionary computation techniques (e.g., Genetic Algorithms, Genetic Programming, Differential Evolution).
    • Enhancements and modifications to existing algorithms to enhance performance and robustness.
    • Parallel and distributed implementations of swarm and evolutionary algorithms.
  • Applications in Engineering and Industry
    • Applications in robotics, including multi-robot systems, path planning, and control.
    • Use of swarm and evolutionary algorithms in manufacturing, logistics, and supply chain optimization.
    • Optimization of telecommunications and network design.
    • Applications in energy systems, including smart grids, renewable energy, and resource management.
    • Data Science and Artificial Intelligence 
  • Machine learning and data mining using swarm intelligence and evolutionary algorithms.
    • Feature selection, parameter tuning, and model optimization.
    • Applications in natural language processing and text mining.
    • Image and video analysis using evolutionary and swarm-based approaches.
    • Symmetry in Swarm Intelligence 
  • Behavioral symmetry in intelligence algorithms.
    • Spatial symmetry in swarm formations and movement patterns.
    • Communication symmetry and its effects on information dissemination and coordination.l  Symmetrical task allocation and role distribution in swarm systems.
    • Symmetry in Evolutionary Computation
    • Symmetric crossover, mutation, and other genetic operations.
    • Fitness evaluation symmetry and its impact on evolutionary search efficiency.
    • Symmetry-breaking techniques that avoid local optima and enhance diversity.
    • Symmetry in Machine Learning Algorithms
    • Data augmentation and transformation using symmetrical properties.
    • Group-equivariant neural networks and applications in pattern recognition.
    • Symmetry in training, optimization, and regularization techniques.

Dr. Hongwei Kang
Dr. Xinping Sun
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 100 words) can be sent to the Editorial Office for announcement on this website.

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

  • swarm intelligence
  • evolutionary computation
  • machine learning
  • behavioral symmetry
  • spatial symmetry
  • genetic algorithms
  • particle swarm optimization
  • ant colony optimization
  • artificial bee colony
  • genetic programming
  • differential evolution
  • neural networks
  • group-equivariant neural networks
  • symmetry in neural architectures
  • fitness evaluation
  • hybrid algorithms
  • natural language processing
  • text analysis
  • bioinformatics
  • environmental modeling
  • optimization problems
  • algorithm performance
  • scalability
  • convergence analysis
  • diversity in algorithms
  • hybrid approaches
  • real-world applications
  • symmetry

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

Published Papers (6 papers)

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Research

30 pages, 595 KiB  
Article
Dual-Performance Multi-Subpopulation Adaptive Restart Differential Evolutionary Algorithm
by Yong Shen, Yunlu Xie and Qingyi Chen
Symmetry 2025, 17(2), 223; https://doi.org/10.3390/sym17020223 (registering DOI) - 3 Feb 2025
Abstract
To cope with common local optimum traps and balance exploration and development in complex multi-peak optimisation problems, this paper puts forth a Dual-Performance Multi-subpopulation Adaptive Restart Differential Evolutionary Algorithm (DPR-MGDE) as a potential solution. The algorithm employs a novel approach by utilising the [...] Read more.
To cope with common local optimum traps and balance exploration and development in complex multi-peak optimisation problems, this paper puts forth a Dual-Performance Multi-subpopulation Adaptive Restart Differential Evolutionary Algorithm (DPR-MGDE) as a potential solution. The algorithm employs a novel approach by utilising the fitness and historical update frequency as dual-performance metrics to categorise the population into three distinct sub-populations: PM (the promising individual set), MM (the medium individual set) and UM (the un-promising individual set). The multi-subpopulation division mechanism enables the algorithm to achieve a balance between global exploration, local exploitation and diversity maintenance, thereby enhancing its overall optimisation capability. Furthermore, the DPR-MGDE incorporates an adaptive cross-variation strategy, which enables the dynamic adjustment of the variation factor and crossover probability in accordance with the performance of the individuals. This enhances the flexibility of the algorithm, allowing for the prioritisation of local exploitation among the more excellent individuals and the exploration of new search space among the less excellent individuals. Furthermore, the algorithm employs a collision-based Gaussian wandering restart strategy, wherein the collision frequency serves as the criterion for triggering a restart. Upon detecting population stagnation, the updated population is subjected to optimal solution-guided Gaussian wandering, effectively preventing the descent into local optima. Through experiments on the CEC2017 benchmark functions, we verified that DPR-MGDE has higher solution accuracy compared to newer differential evolution algorithms, and proved its significant advantages in complex optimisation tasks with the Wilcoxon test. In addition to this, we also conducted experiments on real engineering problems to demonstrate the effectiveness and superiority of DPR-MGDE in dealing with real engineering problems. Full article
(This article belongs to the Special Issue Symmetry in Intelligent Algorithms)
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45 pages, 1703 KiB  
Article
NLAPSMjSO-EDA: A Nonlinear Shrinking Population Strategy Algorithm for Elite Group Exploration with Symmetry Applications
by Yong Shen, Jiaxuan Liang, Hongwei Kang, Xingping Sun and Qingyi Chen
Symmetry 2025, 17(2), 153; https://doi.org/10.3390/sym17020153 - 21 Jan 2025
Viewed by 479
Abstract
This work effectively modifies APSM-jSO (a novel jSO variant with an adaptive parameter selection mechanism and a new external archive updating mechanism) to offer a new jSO (single objective real-parameter optimization: Algorithm jSO) version called NLAPSMjSO-EDA. There are three main distinctions between NLAPSMjSO-EDA [...] Read more.
This work effectively modifies APSM-jSO (a novel jSO variant with an adaptive parameter selection mechanism and a new external archive updating mechanism) to offer a new jSO (single objective real-parameter optimization: Algorithm jSO) version called NLAPSMjSO-EDA. There are three main distinctions between NLAPSMjSO-EDA and APSM-jSO. Firstly, in the linear population reduction strategy, the number of individuals eliminated in each generation is insufficient. This results in a higher number of inferior individuals remaining, and since the total number of iterations is fixed, these inferior individuals will also consume iteration counts for their evolution. Therefore, it is essential to allocate more iterations to the elite population to promote the emergence of superior individuals. The nonlinear population reduction strategy effectively addresses this issue. Secondly, we have introduced an Estimation of Distribution Algorithm (EDA) to sample and generate individuals from the elite population, aiming to produce higher-quality individuals that can drive the iterative evolution of the population. Furthermore, to enhance algorithmic diversity, we increased the number of individuals in the initial population during subsequent experiments to ensure a diverse early population while maintaining a constant total number of iterations. Symmetry plays an essential role in the design and performance of NLAPSMjSO-EDA. The nonlinear population reduction strategy inherently introduces a form of asymmetry that mimics natural evolutionary processes, favoring elite individuals while reducing the influence of inferior ones. This asymmetric yet balanced approach ensures a dynamic equilibrium between exploration and exploitation, aligning with the principles of symmetry and asymmetry in optimization. Additionally, the incorporation of EDA utilizes probabilistic symmetry in sampling from the elite population, maintaining structural coherence while promoting diversity. Such applications of symmetry in algorithm design not only improve performance but also provide insights into balancing diverse algorithmic components. NLAPSMjSO-EDA, evaluated on the CEC 2017 benchmark suite, significantly outperforms recent differential evolution algorithms. In conclusion, NLAPSMjSO-EDA effectively enhances the overall performance of APSM-jSO, establishing itself as an outstanding variant combining jSO and EDA algorithms. The algorithm code has been open-sourced. Full article
(This article belongs to the Special Issue Symmetry in Intelligent Algorithms)
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17 pages, 1145 KiB  
Article
Weighted Multiview K-Means Clustering with L2 Regularization
by Ishtiaq Hussain, Yessica Nataliani, Mehboob Ali, Atif Hussain, Hana M. Mujlid, Faris A. Almaliki and Nouf M. Rahimi
Symmetry 2024, 16(12), 1646; https://doi.org/10.3390/sym16121646 - 12 Dec 2024
Viewed by 627
Abstract
In the era of big data, cloud, internet of things, virtual communities, and interconnected networks, the prominence of multiview data is undeniable. This type of data encapsulates diverse feature components across varying perspectives, each offering unique insights into the same underlying samples. Despite [...] Read more.
In the era of big data, cloud, internet of things, virtual communities, and interconnected networks, the prominence of multiview data is undeniable. This type of data encapsulates diverse feature components across varying perspectives, each offering unique insights into the same underlying samples. Despite being sourced from diverse settings and domains, these data serve the common purpose of describing the same samples, establishing a significant interrelation among them. Thus, there arises a necessity for the development of multiview clustering methodologies capable of leveraging the wealth of information available across multiple views. This study introduces two novel weighted multiview k-means algorithms, W-MV-KM and weighted multiview k-means using L2 regularization, W-MV-KM-L2, designed specifically for clustering multiview data. These algorithms incorporate feature weights and view weights within the k-means (KM) framework. Our approach emphasizes a weighted multiview learning strategy, which assigns varying degrees of importance to individual views. We evaluate the clustering performance of our algorithms on seven diverse benchmark datasets spanning dermatology, textual, image, and digit domains. Through extensive experimentation and comparisons with existing methods, we showcase the superior effectiveness and utility of our newly introduced W-MV-KM-L2 algorithm. Full article
(This article belongs to the Special Issue Symmetry in Intelligent Algorithms)
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27 pages, 12449 KiB  
Article
A Novel Reinforcement Learning-Based Particle Swarm Optimization Algorithm for Better Symmetry between Convergence Speed and Diversity
by Fan Zhang and Zhongsheng Chen
Symmetry 2024, 16(10), 1290; https://doi.org/10.3390/sym16101290 - 1 Oct 2024
Cited by 1 | Viewed by 1368
Abstract
This paper introduces a novel Particle Swarm Optimization (RLPSO) algorithm based on reinforcement learning, embodying a fundamental symmetry between global and local search processes. This symmetry aims at addressing the trade-off issue between convergence speed and diversity in traditional algorithms. Traditional Particle Swarm [...] Read more.
This paper introduces a novel Particle Swarm Optimization (RLPSO) algorithm based on reinforcement learning, embodying a fundamental symmetry between global and local search processes. This symmetry aims at addressing the trade-off issue between convergence speed and diversity in traditional algorithms. Traditional Particle Swarm Optimization (PSO) algorithms often struggle to maintain good convergence speed and particle diversity when solving multi-modal function problems. To tackle this challenge, we propose a new algorithm that incorporates the principles of reinforcement learning, enabling particles to intelligently learn and adjust their behavior for better convergence speed and richer exploration of the search space. This algorithm guides particle learning behavior through online updating of a Q-table, allowing particles to selectively learn effective information from other particles and dynamically adjust their strategies during the learning process, thus finding a better balance between convergence speed and diversity. The results demonstrate the superior performance of this algorithm on 16 benchmark functions of the CEC2005 test suite compared to three other algorithms. The RLPSO algorithm can find all global optimum solutions within a certain error range on all 16 benchmark functions, exhibiting outstanding performance and better robustness. Additionally, the algorithm’s performance was tested on 13 benchmark functions from CEC2017, where it outperformed six other algorithms by achieving the minimum value on 11 benchmark functions. Overall, the RLPSO algorithm shows significant improvements and advantages over traditional PSO algorithms in aspects such as local search strategy, parameter adaptive adjustment, convergence speed, and multi-modal problem handling, resulting in better performance and robustness in solving optimization problems. This study provides new insights and methods for the further development of Particle Swarm Optimization algorithms. Full article
(This article belongs to the Special Issue Symmetry in Intelligent Algorithms)
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23 pages, 5712 KiB  
Article
Sparse Fuzzy C-Means Clustering with Lasso Penalty
by Shazia Parveen and Miin-Shen Yang
Symmetry 2024, 16(9), 1208; https://doi.org/10.3390/sym16091208 - 13 Sep 2024
Viewed by 1119
Abstract
Clustering is a technique of grouping data into a homogeneous structure according to the similarity or dissimilarity measures between objects. In clustering, the fuzzy c-means (FCM) algorithm is the best-known and most commonly used method and is a fuzzy extension of k-means in [...] Read more.
Clustering is a technique of grouping data into a homogeneous structure according to the similarity or dissimilarity measures between objects. In clustering, the fuzzy c-means (FCM) algorithm is the best-known and most commonly used method and is a fuzzy extension of k-means in which FCM has been widely used in various fields. Although FCM is a good clustering algorithm, it only treats data points with feature components under equal importance and has drawbacks for handling high-dimensional data. The rapid development of social media and data acquisition techniques has led to advanced methods of collecting and processing larger, complex, and high-dimensional data. However, with high-dimensional data, the number of dimensions is typically immaterial or irrelevant. For features to be sparse, the Lasso penalty is capable of being applied to feature weights. A solution for FCM with sparsity is sparse FCM (S-FCM) clustering. In this paper, we propose a new S-FCM, called S-FCM-Lasso, which is a new type of S-FCM based on the Lasso penalty. The irrelevant features can be diminished towards exactly zero and assigned zero weights for unnecessary characteristics by the proposed S-FCM-Lasso. Based on various clustering performance measures, we compare S-FCM-Lasso with the S-FCM and other existing sparse clustering algorithms on several numerical and real-life datasets. Comparisons and experimental results demonstrate that, in terms of these performance measures, the proposed S-FCM-Lasso performs better than S-FCM and existing sparse clustering algorithms. This validates the efficiency and usefulness of the proposed S-FCM-Lasso algorithm for high-dimensional datasets with sparsity. Full article
(This article belongs to the Special Issue Symmetry in Intelligent Algorithms)
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28 pages, 16506 KiB  
Article
A Modified Osprey Optimization Algorithm for Solving Global Optimization and Engineering Optimization Design Problems
by Liping Zhou, Xu Liu, Ruiqing Tian, Wuqi Wang and Guowei Jin
Symmetry 2024, 16(9), 1173; https://doi.org/10.3390/sym16091173 - 6 Sep 2024
Cited by 1 | Viewed by 1748
Abstract
The osprey optimization algorithm (OOA) is a metaheuristic algorithm with a simple framework, which is inspired by the hunting process of ospreys. To enhance its searching capabilities and overcome the drawbacks of susceptibility to local optima and slow convergence speed, this paper proposes [...] Read more.
The osprey optimization algorithm (OOA) is a metaheuristic algorithm with a simple framework, which is inspired by the hunting process of ospreys. To enhance its searching capabilities and overcome the drawbacks of susceptibility to local optima and slow convergence speed, this paper proposes a modified osprey optimization algorithm (MOOA) by integrating multiple advanced strategies, including a Lévy flight strategy, a Brownian motion strategy and an RFDB selection method. The Lévy flight strategy and Brownian motion strategy are used to enhance the algorithm’s exploration ability. The RFDB selection method is conducive to search for the global optimal solution, which is a symmetrical strategy. Two sets of benchmark functions from CEC2017 and CEC2022 are employed to evaluate the optimization performance of the proposed method. By comparing with eight other optimization algorithms, the experimental results show that the MOOA has significant improvements in solution accuracy, stability, and convergence speed. Moreover, the efficacy of the MOOA in tackling real-world optimization problems is demonstrated using five engineering optimization design problems. Therefore, the MOOA has the potential to solve real-world complex optimization problems more effectively. Full article
(This article belongs to the Special Issue Symmetry in Intelligent Algorithms)
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