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Symmetry
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Symmetry in Computing Algorithms and Applications
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Symmetry in Computing Algorithms and Applications

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

Deadline for manuscript submissions: 31 December 2025 | Viewed by 11438

Special Issue Editors

Dr. Lei Yue

E-Mail Website
Guest Editor
School of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou 510000, China
Interests: intelligent manufacturing system; digital modeling and simulation; digital twin in manufacturing operations; production line balancing; smart optimization algorithms
Dr. Jinhua Zhang

E-Mail Website
Guest Editor
School of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou, China
Interests: mathematical modeling; adaptive robust control; vehicle dynamics

Special Issue Information

Dear Colleagues,

Symmetry plays a crucial role in computing algorithms and their applications, contributing to efficiency, aesthetics, and problem-solving in various domains. In algorithm design, symmetry often leads to elegant solutions that simplify complex problems, since it can help us find patterns and regularities in data and improve the efficiency and accuracy of algorithms. For example, sorting algorithms like Quicksort and Mergesort exploit symmetry to divide and conquer, reducing time complexity. Symmetric data structures, such as binary trees and balanced search trees, ensure efficient data retrieval and insertion. In addition to sorting algorithms, symmetry also appears in other types of algorithms. For example, some machine learning algorithms use symmetry to find patterns in data and classify or cluster similar objects. Symmetry can also help us find regularities in regular expressions and improve the efficiency of pattern-matching algorithms. Moreover, symmetry finds applications in artificial intelligence and machine learning, where it assists in feature extraction, dimensionality reduction, and data preprocessing. Recognizing symmetries in datasets can improve classification accuracy and reduce computational complexity. In summary, symmetry is a powerful concept in computing, with widespread applications across algorithms and various fields. In this Special Issue, we invite submissions focusing on novel models that can predict, detect, and adapt to symmetric solutions in complex mathematic programming. We particularly encourage research that explores the practical applications of these models and algorithms in solving industrial problems.

The focus of this Special Issue is to continue to advance research on topics relating to the Symmetry in Computing Algorithms and Applications. Topics that are invited for submission include (but are not limited to):

  • Symmetries of complex manufacturing systems;
  • Artificial intelligence (AI) in production scheduling;
  • Fuzzy computing;
  • Data analytics for manufacturing;
  • Cloud computing for manufacturing;
  • Predictive maintenance;
  • Real-time monitoring and control;
  • Supply chain optimization;
  • Computing applications;
  • Smart decision support for industry.

Dr. Lei Yue
Dr. Jinhua Zhang
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

  • symmetries of complex manufacturing systems
  • Artificial Intelligence (AI) in production scheduling
  • fuzzy computing
  • data analytics for manufacturing
  • cloud computing for manufacturing
  • predictive maintenance
  • real-time monitoring and control
  • supply chain optimization
  • computing applications
  • smart decision support for industry

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

Published Papers (8 papers)

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Research

30 pages, 2804 KiB  
Article
A Data-Driven Methodology for Hierarchical Production Planning with LSTM-Q Network-Based Demand Forecast
by Dan Luo, Zailin Guan, Linshan Ding, Weikang Fang and Haiping Zhu
Symmetry 2025, 17(5), 655; https://doi.org/10.3390/sym17050655 - 26 Apr 2025
Viewed by 222
Abstract
Mass customization makes it necessary to upgrade production planning systems to improve the flexibility and resilience of production planning in response to volatile demand. The ongoing development of digital twin technologies supports the upgrade of the production planning system. In this paper, we [...] Read more.
Mass customization makes it necessary to upgrade production planning systems to improve the flexibility and resilience of production planning in response to volatile demand. The ongoing development of digital twin technologies supports the upgrade of the production planning system. In this paper, we propose a data-driven methodology for Hierarchical Production Planning (HPP) that addresses the upgrade requests in the production management system of a fuel tank manufacturing workshop. The proposed methodology first introduces a novel hybrid neural network framework with symmetry that integrates a Long Short-Term Memory network and a Q-network (denoted as LSTM-Q network) for real-time iterative demand forecast. The symmetric framework balances the forward and backward flow of information, ensuring continuous extraction of historical order sequence information. Then, we develop two relax-and-fix (R&F) algorithms to solve the mathematical model for medium- and long-term planning. Finally, we use simulation and dispatching rules to realize real-time dynamic adjustment for short-term planning. The case study and numerical experiments demonstrate that the proposed methodology effectively achieves systematic optimization of production planning. Full article
(This article belongs to the Special Issue Symmetry in Computing Algorithms and Applications)
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39 pages, 6495 KiB  
Article
Intelligent Emergency Logistics Route Model Based on Cellular Space AGNES Clustering and Symmetrical Fruit Fly Optimization Algorithm
by Xiao Zhou, Jun Wang, Wenbing Liu, Fan Jiang and Rui Li
Symmetry 2025, 17(5), 649; https://doi.org/10.3390/sym17050649 - 25 Apr 2025
Viewed by 132
Abstract
In response to the current research status and existing problems of material distribution during major emergency events, we construct an intelligent emergency logistics route model based on cellular space AGNES clustering (AGglomerative NESting clustering) and a symmetrical fruit fly optimization algorithm. We establish [...] Read more.
In response to the current research status and existing problems of material distribution during major emergency events, we construct an intelligent emergency logistics route model based on cellular space AGNES clustering (AGglomerative NESting clustering) and a symmetrical fruit fly optimization algorithm. We establish the cellular algorithm based on urban road nodes and node local spaces, and construct the topology algorithm to implement the cellular space in a way that includes distribution centers and delivery points. In the cellular space, we develop an improved AGNES clustering algorithm based on the cellular space model in accordance with the neighboring relationship between distribution centers and delivery points, which quantifies the spatial clustering relationship between the distribution centers and the delivery points. Based on the clustering model, we construct an emergency logistics route model by using a symmetrical fruit fly optimization algorithm. In line with the symmetrical feature of a logistics route from one destination to another, the traveling distances within one route section are the same in both directions. Thus, we construct the logistics sub-intervals and logistics intervals by using distribution centers and delivery points, and the optimal fruit fly individuals and corresponding fitness functions are searched within the two-level intervals to obtain the emergency logistics routes with the lowest costs. Experimental results show that the proposed algorithm can output the optimal logistics routes for each logistics sub-interval and the entire logistics interval. Compared with the traditional route planning methods Dijkstra’s algorithm and the A* algorithm, it can reduce the cost of route planning and achieve optimization rates of 9.89% and 13.12%, respectively. The t-test proves that the constructed algorithm is superior to the traditional route planning algorithms in saving route costs. Full article
(This article belongs to the Special Issue Symmetry in Computing Algorithms and Applications)
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18 pages, 631 KiB  
Article
Prospects for Using Finite Algebraic Rings for Constructing Discrete Coordinate Systems
by Ibragim Suleimenov and Akhat Bakirov
Symmetry 2025, 17(3), 410; https://doi.org/10.3390/sym17030410 - 9 Mar 2025
Viewed by 478
Abstract
The method of non-standard algebraic extensions based on the use of additional formal solutions of the reduced equations is extended to the case corresponding to three-dimensional space. This method differs from the classical one in that it leads to the formation of algebraic [...] Read more.
The method of non-standard algebraic extensions based on the use of additional formal solutions of the reduced equations is extended to the case corresponding to three-dimensional space. This method differs from the classical one in that it leads to the formation of algebraic rings rather than fields. The proposed approach allows one to construct a discrete coordinate system in which the role of three basis vectors is played by idempotent elements of the ring obtained by a non-standard algebraic extension. This approach allows, among other things, the identification of the symmetry properties of objects defined through discrete Cartesian coordinates, which is important, for example, when using advanced methods of digital image processing. An explicit form of solutions of the equations is established that allow one to construct idempotent elements for Galois fields GFp such that p−1 is divisible by three. The possibilities of practical use of the proposed approach are considered; in particular, it is shown that the use of discrete Cartesian coordinates mapped onto algebraic rings is of interest from the point of view of improving UAV swarm control algorithms. Full article
(This article belongs to the Special Issue Symmetry in Computing Algorithms and Applications)
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32 pages, 10468 KiB  
Article
Tourism Recommendation Algorithm Based on the Mobile Intelligent Connected Vehicle Service Platform
by Xiao Zhou, Rui Li, Fei Teng, Juan Pan and Taiping Zhao
Symmetry 2024, 16(11), 1431; https://doi.org/10.3390/sym16111431 - 28 Oct 2024
Viewed by 1803
Abstract
As to the problems in current tourism recommendation, this paper proposes a tourism recommendation algorithm based on the mobile ICV service platform. Firstly, the ICV service system for the Point of Interest (POI) searching and route recommendation is designed. Secondly, the recommendation service [...] Read more.
As to the problems in current tourism recommendation, this paper proposes a tourism recommendation algorithm based on the mobile ICV service platform. Firstly, the ICV service system for the Point of Interest (POI) searching and route recommendation is designed. Secondly, the recommendation service model is set up from two aspects, namely the tourism POI clustering algorithm and the tourism POI searching and route recommendation algorithm. In the aspect of symmetrical-based matching features, the clustered POIs are matched with the tourists’ interests, and the POIs in the neighborhood of the ICV dynamic locations are searched. Then, a POI recommendation algorithm based on the tourists’ interests is constructed, and the POIs that best match the symmetrical interests of the tourists within the dynamic buffer zones of ICV are confirmed. Based on the recommended POIs, the ICV guidance route algorithm is constructed. The experiment verifies the advantages of the proposed algorithm on the aspect of the POI matching tourists’ interests, algorithm stability, traveling time cost, traveling distance cost and computational complexity. As to the iterative sum and the iterative sum average of the POI matching function values, the proposed algorithm has a performance improvement of at least 20.2% and a stability improvement of at least 20.5% compared to the randomly selected POIs in matching tourists’ interests. As to the cost of the guidance routes, the proposed algorithm reduces the average cost by 19.6% compared to the other suboptimal routes. Compared with the control group algorithms, the proposed algorithm is superior in terms of route cost, with an average cost reduction of 13.8% for the output routes compared to the control group. Also, the proposed algorithm is superior in terms of route cost compared to the control group recommendation algorithms, with an average cost reduction of 11.2%. Full article
(This article belongs to the Special Issue Symmetry in Computing Algorithms and Applications)
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46 pages, 10310 KiB  
Article
An Intelligent Connected Vehicle Material Distribution Route Model Based on k-Center Spatial Cellular Clustering and an Improved Cockroach Optimization Algorithm
by Xiao Zhou, Jun Wang, Wenbing Liu, Juan Pan, Taiping Zhao, Fan Jiang and Rui Li
Symmetry 2024, 16(6), 749; https://doi.org/10.3390/sym16060749 - 15 Jun 2024
Viewed by 1282
Abstract
Based on the analysis of the problems in material distribution routes, we propose the idea of integrating the intelligent connected vehicle system with material distribution, and construct an intelligent connected vehicle material distribution route model based on k-center spatial cellular clustering and [...] Read more.
Based on the analysis of the problems in material distribution routes, we propose the idea of integrating the intelligent connected vehicle system with material distribution, and construct an intelligent connected vehicle material distribution route model based on k-center spatial cellular clustering and an improved cockroach optimization algorithm. Firstly, we set the research scope to include the distribution center, the distribution points and the geographical environment. A cellular spatial model of distribution points is constructed to quantify and visualize the neighborhood relationship between the distribution centers and distribution points. On this basis, we construct an intelligent connected vehicle material distribution route model based on the improved cockroach optimization algorithm, and the optimal material distribution center is determined by searching for the corresponding optimal distribution route of each distribution center. In the experiment, we use the concept of symmetry to design routes that start from the initial points. The route passes through the distribution point, and finally reaches the destination. In this mode, the experiment generates symmetrically round-trip routes and generates different distribution time schedules. Case studies and comparative experiments show that the proposed algorithm has a total distance cost 1.2 km lower than the distance cost generated by the Baidu Map method and 2.7 km lower than the distance cost generated by the 360 Map method. In terms of the total time cost of the proposed algorithm, it is 0.06 h lower than the time cost generated by the Baidu Map method and 0.135 h lower than the time cost generated by the 360 Map method. Compared with the commonly used Dijkstra algorithm and the A* algorithm for route optimization, our proposed algorithm also generates a lower cost than the two other types of optimization algorithms. In the case study, the distance generated by the proposed algorithm is 1.8 km lower than that of the Dijkstra algorithm, and the total time cost is 0.09 h lower than that of the Dijkstra algorithm. The distance generated by the proposed algorithm is 1.6 km lower than that of the A* algorithm, and the total time cost is 0.08 h lower than that of the A* algorithm. Meanwhile, the proposed algorithm has a lower time complexity than the two commonly used optimization algorithms. Therefore, our proposed algorithm can find the distribution route with the lowest transportation cost. Compared to the commonly used electronic maps and the optimization algorithms for distribution route planning, our proposed algorithm can output distribution routes with lower costs under the same distribution sequence, and reduce the transportation costs for intelligent connected vehicle material distribution systems to the maximum extent. Full article
(This article belongs to the Special Issue Symmetry in Computing Algorithms and Applications)
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19 pages, 8424 KiB  
Article
Particle Swarm Optimization Algorithm Using Velocity Pausing and Adaptive Strategy
by Kezong Tang and Chengjian Meng
Symmetry 2024, 16(6), 661; https://doi.org/10.3390/sym16060661 - 27 May 2024
Cited by 6 | Viewed by 2875
Abstract
Particle swarm optimization (PSO) as a swarm intelligence-based optimization algorithm has been widely applied to solve various real-world optimization problems. However, traditional PSO algorithms encounter issues such as premature convergence and an imbalance between global exploration and local exploitation capabilities when dealing with [...] Read more.
Particle swarm optimization (PSO) as a swarm intelligence-based optimization algorithm has been widely applied to solve various real-world optimization problems. However, traditional PSO algorithms encounter issues such as premature convergence and an imbalance between global exploration and local exploitation capabilities when dealing with complex optimization tasks. To address these shortcomings, an enhanced PSO algorithm incorporating velocity pausing and adaptive strategies is proposed. By leveraging the search characteristics of velocity pausing and the terminal replacement mechanism, the problem of premature convergence inherent in standard PSO algorithms is mitigated. The algorithm further refines and controls the search space of the particle swarm through time-varying inertia coefficients, symmetric cooperative swarms concepts, and adaptive strategies, balancing global search and local exploitation. The performance of VASPSO was validated on 29 standard functions from Cec2017, comparing it against five PSO variants and seven swarm intelligence algorithms. Experimental results demonstrate that VASPSO exhibits considerable competitiveness when compared with 12 algorithms. The relevant code can be found on our project homepage. Full article
(This article belongs to the Special Issue Symmetry in Computing Algorithms and Applications)
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28 pages, 1809 KiB  
Article
An Adaptive Search Algorithm for Multiplicity Dynamic Flexible Job Shop Scheduling with New Order Arrivals
by Linshan Ding, Zailin Guan, Dan Luo, Mudassar Rauf and Weikang Fang
Symmetry 2024, 16(6), 641; https://doi.org/10.3390/sym16060641 - 22 May 2024
Cited by 4 | Viewed by 1607
Abstract
In today’s customer-centric economy, the demand for personalized products has compelled corporations to develop manufacturing processes that are more flexible, efficient, and cost-effective. Flexible job shops offer organizations the agility and cost-efficiency that traditional manufacturing processes lack. However, the dynamics of modern manufacturing, [...] Read more.
In today’s customer-centric economy, the demand for personalized products has compelled corporations to develop manufacturing processes that are more flexible, efficient, and cost-effective. Flexible job shops offer organizations the agility and cost-efficiency that traditional manufacturing processes lack. However, the dynamics of modern manufacturing, including machine breakdown and new order arrivals, introduce unpredictability and complexity. This study investigates the multiplicity dynamic flexible job shop scheduling problem (MDFJSP) with new order arrivals. To address this problem, we incorporate the fluid model to propose a fluid randomized adaptive search (FRAS) algorithm, comprising a construction phase and a local search phase. Firstly, in the construction phase, a fluid construction heuristic with an online fluid dynamic tracking policy generates high-quality initial solutions. Secondly, in the local search phase, we employ an improved tabu search procedure to enhance search efficiency in the solution space, incorporating symmetry considerations. The results of the numerical experiments demonstrate the superior effectiveness of the FRAS algorithm in solving the MDFJSP when compared to other algorithms. Specifically, the proposed algorithm demonstrates a superior quality of solution relative to existing algorithms, with an average improvement of 29.90%; and exhibits an acceleration in solution speed, with an average increase of 1.95%. Full article
(This article belongs to the Special Issue Symmetry in Computing Algorithms and Applications)
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21 pages, 2144 KiB  
Article
Scheduling Optimization of Compound Operations in Autonomous Vehicle Storage and Retrieval System
by Lili Xu, Jiansha Lu and Yan Zhan
Symmetry 2024, 16(2), 168; https://doi.org/10.3390/sym16020168 - 31 Jan 2024
Cited by 2 | Viewed by 1502
Abstract
The increasing demand for storing various types of goods has led to a raise in the need for storage capacity in warehousing systems. Autonomous vehicle storage and retrieval systems (AVS/RSs) offer high flexibility by allowing different configurations to meet different storage requirements. The [...] Read more.
The increasing demand for storing various types of goods has led to a raise in the need for storage capacity in warehousing systems. Autonomous vehicle storage and retrieval systems (AVS/RSs) offer high flexibility by allowing different configurations to meet different storage requirements. The system mainly completes operations through elevators and multiple rail-guided vehicles (RGVs). This paper focuses on the scheduling optimization of compound operations in the AVS/RS to improve system performance. Compound operations involve the coordinated execution of both single-command and double-command operations. A mathematical model with compound operations was proposed and effectively decomposed into a horizontal component for RGVs and a vertical counterpart for the elevator, which can represent the operations of one elevator cooperating with multiple RGVs. The goal of this model was to minimize the makespan for compound operations and to determine the optimal operation sequence and path for RGVs. An improved discrete particle swarm optimization (DPSO) algorithm called AGDPSO was proposed to solve the model. The algorithm combines DPSO and a genetic algorithm in an adaptive manner to prevent the algorithm from falling into local optima and relying solely on the initial solution. Through rigorous optimization, optimal parameters for the algorithm were identified. When assessing the performance of our improved algorithm against various counterparts, considering different task durations and racking configurations, our results showed that AGDPSO outperformed the alternatives, proving its effectiveness in enhancing system efficiency for the model. The findings of this study not only contribute to the optimization of AVS/RS but also offer valuable insights for designing more efficient warehouses. By streamlining scheduling, improving operations, and leveraging advanced optimization techniques, we can create a more robust and effective storage and retrieval system. Full article
(This article belongs to the Special Issue Symmetry in Computing Algorithms and Applications)
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