Circular rail-guided vehicles (RGVs) are widely used in automated warehouses, and their efficiency directly determines the transportation efficiency of the entire system. The congestion frequency of RGVs greatly increases when facing dense multi-type entry and delivery tasks, affecting overall transportation efficiency. This article focuses on the RGV scheduling problem of multi-type parallel transportation tasks in a real-world automated warehouse, considering maximizing efficiency while reducing energy consumption and thus establishing the RGV scheduling optimization model. At the same time, an improved genetic algorithm (GA) based on symmetry selection function and offspring population structure symmetry is proposed to solve the above RGV scheduling problem, achieving the model solution. The case study demonstrates the superiority of the proposed method in breaking local optima and achieving bi-objective optimization in genetic algorithms.
{"title":"Bi-Objective Circular Multi-Rail-Guided Vehicle Scheduling Optimization Considering Multi-Type Entry and Delivery Tasks: A Combined Genetic Algorithm and Symmetry Algorithm","authors":"Xinlin Li, Xuzhen Wu, Peipei Wang, Yalu Xu, Yue Gao, Yiyang Chen","doi":"10.3390/sym16091205","DOIUrl":"https://doi.org/10.3390/sym16091205","url":null,"abstract":"Circular rail-guided vehicles (RGVs) are widely used in automated warehouses, and their efficiency directly determines the transportation efficiency of the entire system. The congestion frequency of RGVs greatly increases when facing dense multi-type entry and delivery tasks, affecting overall transportation efficiency. This article focuses on the RGV scheduling problem of multi-type parallel transportation tasks in a real-world automated warehouse, considering maximizing efficiency while reducing energy consumption and thus establishing the RGV scheduling optimization model. At the same time, an improved genetic algorithm (GA) based on symmetry selection function and offspring population structure symmetry is proposed to solve the above RGV scheduling problem, achieving the model solution. The case study demonstrates the superiority of the proposed method in breaking local optima and achieving bi-objective optimization in genetic algorithms.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209349","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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.
{"title":"Sparse Fuzzy C-Means Clustering with Lasso Penalty","authors":"Shazia Parveen, Miin-Shen Yang","doi":"10.3390/sym16091208","DOIUrl":"https://doi.org/10.3390/sym16091208","url":null,"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 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.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209353","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Zahra Abdelmalek, Mohammad Yaghoub Abdollahzadeh Jamalabadi
The journal retracts the article titled “Numerical Simulation of Micromixing of Particles and Fluids with Galloping Cylinder” [...]
该杂志撤销了题为 "利用绞龙式圆筒对颗粒和流体的微混合进行数值模拟 "的文章 [...]
{"title":"RETRACTED: Abdelmalek, Z.; Abdollahzadeh Jamalabadi, M.Y. Numerical Simulation of Micromixing of Particles and Fluids with Galloping Cylinder. Symmetry 2020, 12, 580","authors":"Zahra Abdelmalek, Mohammad Yaghoub Abdollahzadeh Jamalabadi","doi":"10.3390/sym16091204","DOIUrl":"https://doi.org/10.3390/sym16091204","url":null,"abstract":"The journal retracts the article titled “Numerical Simulation of Micromixing of Particles and Fluids with Galloping Cylinder” [...]","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":"24 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209348","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Lorenzo Ledda, Annalisa Greco, Ilaria Fiore, Ivo Caliò
The dynamic stiffness method is developed to analyze the natural vibration characteristics of functionally graded beams, where material properties change continuously across the beam thickness following a symmetric law distribution. The governing equations of motion and associated natural boundary conditions for free vibration analysis are derived using Hamilton’s principle and closed-form exact solutions are obtained for both Euler–Bernoulli and Timoshenko beam models. The dynamic stiffness matrix, which governs the relationship between force and displacements at the beam ends, is determined. Using the Wittrick–Williams algorithm, the dynamic stiffness matrix is employed to compute natural frequencies and mode shapes. The proposed procedure is validated by comparing the obtained frequencies with those given by approximated well-known formulas. Finally, a parametric investigation is conducted by varying the geometry of the structure and the characteristic mechanical parameters of the functionally graded material.
{"title":"Closed-Form Exact Solution for Free Vibration Analysis of Symmetric Functionally Graded Beams","authors":"Lorenzo Ledda, Annalisa Greco, Ilaria Fiore, Ivo Caliò","doi":"10.3390/sym16091206","DOIUrl":"https://doi.org/10.3390/sym16091206","url":null,"abstract":"The dynamic stiffness method is developed to analyze the natural vibration characteristics of functionally graded beams, where material properties change continuously across the beam thickness following a symmetric law distribution. The governing equations of motion and associated natural boundary conditions for free vibration analysis are derived using Hamilton’s principle and closed-form exact solutions are obtained for both Euler–Bernoulli and Timoshenko beam models. The dynamic stiffness matrix, which governs the relationship between force and displacements at the beam ends, is determined. Using the Wittrick–Williams algorithm, the dynamic stiffness matrix is employed to compute natural frequencies and mode shapes. The proposed procedure is validated by comparing the obtained frequencies with those given by approximated well-known formulas. Finally, a parametric investigation is conducted by varying the geometry of the structure and the characteristic mechanical parameters of the functionally graded material.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":"35 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209354","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The problem of machining complex surfaces with non-ball-end cutters by strip-width-maximization machining is formulated as a kind of surface fitting problem in which the tool surface envelope feature line approximates the design surface under the movement transform. The theory of surface envelope−approximation is proposed as a general method for optimizing tool movement in single-contact strip-width-maximization machining of sculptured surfaces with non-ball-end cutters. Based on the surface moving frame, the velocity equations and transformation matrices for the tool motion relative to the workpiece, described by the motion-invariant parameters of the tool surface and design surface, are derived. A functional extremum model for optimizing the tool position ensures continuous and symmetrical motion relative to the workpiece to achieve the highest machining efficiency and accuracy. Finally, a Matlab-based simulation example verifies the machining efficiency and accuracy of the envelope approximation theory.
{"title":"Optimized Tool Motion Symmetry for Strip-Width-Max Mfg of Sculptured Surfaces with Non-Ball Tools Based on Envelope Approximation","authors":"Kaihong Zhou, Haixu Liu, Shu Li","doi":"10.3390/sym16091207","DOIUrl":"https://doi.org/10.3390/sym16091207","url":null,"abstract":"The problem of machining complex surfaces with non-ball-end cutters by strip-width-maximization machining is formulated as a kind of surface fitting problem in which the tool surface envelope feature line approximates the design surface under the movement transform. The theory of surface envelope−approximation is proposed as a general method for optimizing tool movement in single-contact strip-width-maximization machining of sculptured surfaces with non-ball-end cutters. Based on the surface moving frame, the velocity equations and transformation matrices for the tool motion relative to the workpiece, described by the motion-invariant parameters of the tool surface and design surface, are derived. A functional extremum model for optimizing the tool position ensures continuous and symmetrical motion relative to the workpiece to achieve the highest machining efficiency and accuracy. Finally, a Matlab-based simulation example verifies the machining efficiency and accuracy of the envelope approximation theory.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209350","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Large language models (LLMs) are widely integrated into autonomous driving systems to enhance their operational intelligence and responsiveness and improve self-driving vehicles’ overall performance. Despite these advances, LLMs still struggle between hallucinations—when models either misinterpret the environment or generate imaginary parts for downstream use cases—and taxing computational overhead that relegates their performance to strictly non-real-time operations. These are essential problems to solve to make autonomous driving as safe and efficient as possible. This work is thus focused on symmetrical trade-offs between the reduction of hallucination and optimization, leading to a framework for these two combined and at least specifically motivated by these limitations. This framework intends to generate a symmetry of mapping between real and virtual worlds. It helps in minimizing hallucinations and optimizing computational resource consumption reasonably. In autonomous driving tasks, we use multimodal LLMs that combine an image-encoding Visual Transformer (ViT) and a decoding GPT-2 with responses generated by the powerful new sequence generator from OpenAI known as GPT4. Our hallucination reduction and optimization framework leverages iterative refinement loops, RLHF—reinforcement learning from human feedback (RLHF)—along with symmetric performance metrics, e.g., BLEU, ROUGE, and CIDEr similarity scores between machine-generated answers specific to other human reference answers. This ensures that improvements in model accuracy are not overused to the detriment of increased computational overhead. Experimental results show a twofold improvement in decision-maker error rate and processing efficiency, resulting in an overall decrease of 30% for the model and a 25% improvement in processing efficiency across diverse driving scenarios. Not only does this symmetrical approach reduce hallucination, but it also better aligns the virtual and real-world representations.
{"title":"Hallucination Reduction and Optimization for Large Language Model-Based Autonomous Driving","authors":"Jue Wang","doi":"10.3390/sym16091196","DOIUrl":"https://doi.org/10.3390/sym16091196","url":null,"abstract":"Large language models (LLMs) are widely integrated into autonomous driving systems to enhance their operational intelligence and responsiveness and improve self-driving vehicles’ overall performance. Despite these advances, LLMs still struggle between hallucinations—when models either misinterpret the environment or generate imaginary parts for downstream use cases—and taxing computational overhead that relegates their performance to strictly non-real-time operations. These are essential problems to solve to make autonomous driving as safe and efficient as possible. This work is thus focused on symmetrical trade-offs between the reduction of hallucination and optimization, leading to a framework for these two combined and at least specifically motivated by these limitations. This framework intends to generate a symmetry of mapping between real and virtual worlds. It helps in minimizing hallucinations and optimizing computational resource consumption reasonably. In autonomous driving tasks, we use multimodal LLMs that combine an image-encoding Visual Transformer (ViT) and a decoding GPT-2 with responses generated by the powerful new sequence generator from OpenAI known as GPT4. Our hallucination reduction and optimization framework leverages iterative refinement loops, RLHF—reinforcement learning from human feedback (RLHF)—along with symmetric performance metrics, e.g., BLEU, ROUGE, and CIDEr similarity scores between machine-generated answers specific to other human reference answers. This ensures that improvements in model accuracy are not overused to the detriment of increased computational overhead. Experimental results show a twofold improvement in decision-maker error rate and processing efficiency, resulting in an overall decrease of 30% for the model and a 25% improvement in processing efficiency across diverse driving scenarios. Not only does this symmetrical approach reduce hallucination, but it also better aligns the virtual and real-world representations.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209357","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Cemil Tunç, Jen-Chih Yao, Mouffak Benchohra, Ahmed M. A. El-Sayed
The fractional calculus is a specific case of classical calculus, as is well known [...]
众所周知，分数微积分是经典微积分的一种特殊情况 [...] 。
{"title":"Editorial for the Special Issue of “Fractional Differential and Fractional Integro-Differential Equations: Qualitative Theory, Numerical Simulations, and Symmetry Analysis”","authors":"Cemil Tunç, Jen-Chih Yao, Mouffak Benchohra, Ahmed M. A. El-Sayed","doi":"10.3390/sym16091193","DOIUrl":"https://doi.org/10.3390/sym16091193","url":null,"abstract":"The fractional calculus is a specific case of classical calculus, as is well known [...]","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":"176 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209355","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The novelty and main contributions of this paper are reflected in four aspects. First, we introduce multi-fractional phasor in Theorem 1. Second, we propose the motion phasor equations of seven types of multi-fractional vibrators in Theorems 2, 12, 22, 32, 43, 54, and 65, respectively. Third, we present the analytical expressions of response phasors of seven types of multi-fractional vibrators in Theorems 10, 20, 30, 41, 52, 63, and 74, respectively. Fourth, we bring forward the analytical expressions of stationary sinusoidal responses of seven types of multi-fractional vibrators in Theorems 11, 21, 31, 42, 53, 64, and 75, respectively. In addition, by using multi-fractional phasor, we put forward the analytical expressions of vibration parameters (equivalent mass, equivalent damping, equivalent stiffness, equivalent damping ratio, equivalent damping free natural angular frequency, equivalent damped natural angular frequency, equivalent frequency ratio) and frequency transfer functions of seven types of multi-fractional vibrators. Demonstrations exhibit that the effects of multi-fractional orders on stationary sinusoidal responses of those multi-fractional vibrators are considerable.
{"title":"Dealing with Stationary Sinusoidal Responses of Seven Types of Multi-Fractional Vibrators Using Multi-Fractional Phasor","authors":"Ming Li","doi":"10.3390/sym16091197","DOIUrl":"https://doi.org/10.3390/sym16091197","url":null,"abstract":"The novelty and main contributions of this paper are reflected in four aspects. First, we introduce multi-fractional phasor in Theorem 1. Second, we propose the motion phasor equations of seven types of multi-fractional vibrators in Theorems 2, 12, 22, 32, 43, 54, and 65, respectively. Third, we present the analytical expressions of response phasors of seven types of multi-fractional vibrators in Theorems 10, 20, 30, 41, 52, 63, and 74, respectively. Fourth, we bring forward the analytical expressions of stationary sinusoidal responses of seven types of multi-fractional vibrators in Theorems 11, 21, 31, 42, 53, 64, and 75, respectively. In addition, by using multi-fractional phasor, we put forward the analytical expressions of vibration parameters (equivalent mass, equivalent damping, equivalent stiffness, equivalent damping ratio, equivalent damping free natural angular frequency, equivalent damped natural angular frequency, equivalent frequency ratio) and frequency transfer functions of seven types of multi-fractional vibrators. Demonstrations exhibit that the effects of multi-fractional orders on stationary sinusoidal responses of those multi-fractional vibrators are considerable.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209358","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We studied the photoproduction of dileptons from strong electromagnetic fields generated by the nucleus in relativistic heavy-ion collisions. The production of dileptons is calculated based on the Equivalent Photon Approximation (EPA) method, which depends on the strength of the electromagnetic fields and the density of protons in the nucleus. With the EPA method, we construct the connections between dilepton photoproduction and the electromagnetic form factors in the nucleus. Finally, the nuclear proton densities can be determined with the dilepton photoproduction, which is employed to extract the neutron skin in the nucleus. Our calculations indicate that the dilepton photoproduction varies evidently with different proton densities in the nucleus, suggesting a deeper symmetry underlying the connections between proton density (or the neutron skin) and the dilepton photoproduction. This offers a new way to study the neutron skin in the nucleus.
{"title":"A Study of the Neutron Skin of Nuclei with Dileptons in Nuclear Collisions","authors":"Ke Xu, Baoyi Chen","doi":"10.3390/sym16091195","DOIUrl":"https://doi.org/10.3390/sym16091195","url":null,"abstract":"We studied the photoproduction of dileptons from strong electromagnetic fields generated by the nucleus in relativistic heavy-ion collisions. The production of dileptons is calculated based on the Equivalent Photon Approximation (EPA) method, which depends on the strength of the electromagnetic fields and the density of protons in the nucleus. With the EPA method, we construct the connections between dilepton photoproduction and the electromagnetic form factors in the nucleus. Finally, the nuclear proton densities can be determined with the dilepton photoproduction, which is employed to extract the neutron skin in the nucleus. Our calculations indicate that the dilepton photoproduction varies evidently with different proton densities in the nucleus, suggesting a deeper symmetry underlying the connections between proton density (or the neutron skin) and the dilepton photoproduction. This offers a new way to study the neutron skin in the nucleus.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":"47 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209362","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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