Jianjun Deng, Junjie Wang, Xiaojun Wang, Yiqiao Cai, Peizhong Liu
The vehicle routing problem with time windows (VRPTW) is a widely studied combinatorial optimization problem in supply chains and logistics within the last decade. Recent research has explored the potential of deep reinforcement learning (DRL) as a promising solution for the VRPTW. However, the challenge of addressing the VRPTW with many conflicting objectives (MOVRPTW) still remains for DRL. The MOVRPTW considers five conflicting objectives simultaneously: minimizing the number of vehicles required, the total travel distance, the travel time of the longest route, the total waiting time for early arrivals, and the total delay time for late arrivals. To tackle the MOVRPTW, this study introduces the MTMO/DRP-AT, a multi-task multi-objective evolutionary search algorithm, by making full use of both DRL and the multitasking mechanism. In the MTMO/DRL-AT, a two-objective MOVRPTW is constructed as an assisted task, with the objectives being to minimize the total travel distance and the travel time of the longest route. Both the main task and the assisted task are simultaneously solved in a multitasking scenario. Each task is decomposed into scalar optimization subproblems, which are then solved by an attention model trained using DRL. The outputs of these trained models serve as the initial solutions for the MTMO/DRL-AT. Subsequently, the proposed algorithm incorporates knowledge transfer and multiple local search operators to further enhance the quality of these promising solutions. The simulation results on real-world benchmarks highlight the superior performance of the MTMO/DRL-AT compared to several other algorithms in solving the MOVRPTW.
{"title":"Multi-Task Multi-Objective Evolutionary Search Based on Deep Reinforcement Learning for Multi-Objective Vehicle Routing Problems with Time Windows","authors":"Jianjun Deng, Junjie Wang, Xiaojun Wang, Yiqiao Cai, Peizhong Liu","doi":"10.3390/sym16081030","DOIUrl":"https://doi.org/10.3390/sym16081030","url":null,"abstract":"The vehicle routing problem with time windows (VRPTW) is a widely studied combinatorial optimization problem in supply chains and logistics within the last decade. Recent research has explored the potential of deep reinforcement learning (DRL) as a promising solution for the VRPTW. However, the challenge of addressing the VRPTW with many conflicting objectives (MOVRPTW) still remains for DRL. The MOVRPTW considers five conflicting objectives simultaneously: minimizing the number of vehicles required, the total travel distance, the travel time of the longest route, the total waiting time for early arrivals, and the total delay time for late arrivals. To tackle the MOVRPTW, this study introduces the MTMO/DRP-AT, a multi-task multi-objective evolutionary search algorithm, by making full use of both DRL and the multitasking mechanism. In the MTMO/DRL-AT, a two-objective MOVRPTW is constructed as an assisted task, with the objectives being to minimize the total travel distance and the travel time of the longest route. Both the main task and the assisted task are simultaneously solved in a multitasking scenario. Each task is decomposed into scalar optimization subproblems, which are then solved by an attention model trained using DRL. The outputs of these trained models serve as the initial solutions for the MTMO/DRL-AT. Subsequently, the proposed algorithm incorporates knowledge transfer and multiple local search operators to further enhance the quality of these promising solutions. The simulation results on real-world benchmarks highlight the superior performance of the MTMO/DRL-AT compared to several other algorithms in solving the MOVRPTW.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":"59 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141947546","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 Wintgen inequality is a significant result in the field of differential geometry, specifically related to the study of submanifolds in Riemannian manifolds. It was discovered by Pierre Wintgen. In the present work, we deal with the Riemannian maps between Riemannian manifolds that serve as a superb method for comparing the geometric structures of the source and target manifolds. This article is the first to explore a well-known conjecture, called DDVV inequality (a conjecture for Wintgen inequality on Riemannian submanifolds in real space forms proven by P.J. De Smet, F. Dillen, L. Verstraelen and L. Vrancken), for Riemannian maps, where we consider different space forms as target manifolds. There are numerous research problems related to such inequality in various ambient manifolds. These problems can all be explored within the general framework of Riemannian maps between various Riemannian manifolds equipped with notable geometric structures.
温特根不等式是微分几何领域的一个重要结果，特别是与黎曼流形中子流形的研究有关。它是由皮埃尔-温特根发现的。在本文中，我们将讨论黎曼流形之间的黎曼映射，它是比较源流形和目标流形几何结构的绝佳方法。本文首次针对黎曼映射探讨了一个著名的猜想，即 DDVV 不等式（由 P.J. De Smet、F. Dillen、L. Verstraelen 和 L. Vrancken 证明的实空间形式中黎曼子流形的温特根不等式猜想），我们将不同的空间形式视为目标流形。在各种环境流形中，与此类不等式相关的研究问题不胜枚举。这些问题都可以在具有显著几何结构的各种黎曼流形之间的黎曼映射的一般框架内进行探讨。
{"title":"A DDVV Conjecture for Riemannian Maps","authors":"Aliya Naaz Siddiqui, Fatemah Mofarreh","doi":"10.3390/sym16081029","DOIUrl":"https://doi.org/10.3390/sym16081029","url":null,"abstract":"The Wintgen inequality is a significant result in the field of differential geometry, specifically related to the study of submanifolds in Riemannian manifolds. It was discovered by Pierre Wintgen. In the present work, we deal with the Riemannian maps between Riemannian manifolds that serve as a superb method for comparing the geometric structures of the source and target manifolds. This article is the first to explore a well-known conjecture, called DDVV inequality (a conjecture for Wintgen inequality on Riemannian submanifolds in real space forms proven by P.J. De Smet, F. Dillen, L. Verstraelen and L. Vrancken), for Riemannian maps, where we consider different space forms as target manifolds. There are numerous research problems related to such inequality in various ambient manifolds. These problems can all be explored within the general framework of Riemannian maps between various Riemannian manifolds equipped with notable geometric structures.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":"22 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141947545","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}
A new formalism is introduced that makes it possible to elucidate the physical and geometric content of quantum space–time. It is based on the Minimum Group Representation Principle (MGRP). Within this framework, new results for entanglement and geometrical/topological phases are found and implemented in cosmological and black hole space–times. Our main results here are as follows: (i) We find the Berry phases for inflation and for the cosmological perturbations and express them in terms of the observables, such as the spectral scalar and tensor indices, nS and nT, and the tensor-to-scalar ratio r. The Berry phase for de Sitter inflation is imaginary with the sign describing the exponential acceleration. (ii) The pure entangled states in the minimum group (metaplectic) Mp(n) representation for quantum de Sitter space–time and black holes are found. (iii) For entanglement, the relation between the Schmidt type representation and the physical states of the Mp(n) group is found: This is a new non-diagonal coherent state representation complementary to the known Sudarshan diagonal one. (iv) Mean value generators of Mp(2) are related to the adiabatic invariant and topological charge of the space–time, (matrix element of the transition −∞
本文引入了一种新的形式主义，使阐明量子时空的物理和几何内容成为可能。它以最小群表示原理（MGRP）为基础。在这一框架内，我们发现了纠缠和几何/拓扑相位的新结果，并在宇宙学和黑洞时空中加以实现。我们的主要成果如下(i) 我们找到了暴胀和宇宙学扰动的贝里相位，并用光谱标量和张量指数 nS 和 nT 以及张量与标量之比 r 等观测指标来表示。(ii) 发现了量子德西特时空和黑洞在最小群（元映射）Mp(n) 表示中的纯纠缠态。(iii) 就纠缠而言，找到了施密特型表示与 Mp(n) 群物理状态之间的关系：这是一种新的非对角相干态表示，是对已知须弥对角表示的补充。(iv) Mp(2) 的均值发生器与绝热不变量和时空拓扑电荷有关（转换的矩阵元素-∞
{"title":"Entanglement and Generalized Berry Geometrical Phases in Quantum Gravity","authors":"Diego J. Cirilo-Lombardo, Norma G. Sanchez","doi":"10.3390/sym16081026","DOIUrl":"https://doi.org/10.3390/sym16081026","url":null,"abstract":"A new formalism is introduced that makes it possible to elucidate the physical and geometric content of quantum space–time. It is based on the Minimum Group Representation Principle (MGRP). Within this framework, new results for entanglement and geometrical/topological phases are found and implemented in cosmological and black hole space–times. Our main results here are as follows: (i) We find the Berry phases for inflation and for the cosmological perturbations and express them in terms of the observables, such as the spectral scalar and tensor indices, nS and nT, and the tensor-to-scalar ratio r. The Berry phase for de Sitter inflation is imaginary with the sign describing the exponential acceleration. (ii) The pure entangled states in the minimum group (metaplectic) Mp(n) representation for quantum de Sitter space–time and black holes are found. (iii) For entanglement, the relation between the Schmidt type representation and the physical states of the Mp(n) group is found: This is a new non-diagonal coherent state representation complementary to the known Sudarshan diagonal one. (iv) Mean value generators of Mp(2) are related to the adiabatic invariant and topological charge of the space–time, (matrix element of the transition −∞<t<∞). (v) The basic even and odd n-sectors of the Hilbert space are intrinsic to the quantum space–time and its discrete levels (in particular, continuum for n→∞), they do not require any extrinsic generation process such as the standard Schrodinger cat states, and are entangled. (vi) The gravity or cosmological on one side and another of the Planck scale are entangled. Examples: The quantum primordial trans-Planckian de Sitter vacuum and the classical late de Sitter vacuum today; the central quantum gravity region and the external classical gravity region of black holes. The classical and quantum dual gravity regions of the space–time are entangled. (vii) The general classical-quantum gravity duality is associated with the Metaplectic Mp(n) group symmetry which provides the complete full covering of the phase space and of the quantum space–time mapped from it.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":"26 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141947543","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}
In active noise control (ANC) systems, the traditional filtered-x least mean square (FxLMS) algorithm has poor control effect on impulsive noise. To overcome this drawback, a robust cost function was designed in this paper by embedding the cost function of the FxLMS algorithm into the framework of hyperbolic tangent function; this paper thus proposes a robust filtered-x least hyperbolic tangent (FxLHT) algorithm in ANC systems. Moreover, the value of λ in the FxLHT algorithm greatly affects the robustness and convergence performance of the algorithm. Therefore, a variable λ-parameter was proposed to enhance the performance of the FxLHT algorithm. Simulation results show that in the active control of impulsive noise, compared with the FxLMS algorithm and other robust ANC algorithms, the proposed FxLHT algorithm and variable λ-parameter FxLHT algorithm not only exhibit good robustness and noise reduction performance but also have a better tracking ability.
{"title":"A Robust Filtered-x Least Mean Square Algorithm with Adjustable Parameters for Active Impulsive Noise Control","authors":"Pucha Song, Kang Yan, Li Luo","doi":"10.3390/sym16081031","DOIUrl":"https://doi.org/10.3390/sym16081031","url":null,"abstract":"In active noise control (ANC) systems, the traditional filtered-x least mean square (FxLMS) algorithm has poor control effect on impulsive noise. To overcome this drawback, a robust cost function was designed in this paper by embedding the cost function of the FxLMS algorithm into the framework of hyperbolic tangent function; this paper thus proposes a robust filtered-x least hyperbolic tangent (FxLHT) algorithm in ANC systems. Moreover, the value of λ in the FxLHT algorithm greatly affects the robustness and convergence performance of the algorithm. Therefore, a variable λ-parameter was proposed to enhance the performance of the FxLHT algorithm. Simulation results show that in the active control of impulsive noise, compared with the FxLMS algorithm and other robust ANC algorithms, the proposed FxLHT algorithm and variable λ-parameter FxLHT algorithm not only exhibit good robustness and noise reduction performance but also have a better tracking ability.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":"90 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141947548","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}
Murugan Kaviyarasu, Luminița-Ioana Cotîrlă, Daniel Breaz, Murugesan Rajeshwari, Eleonora Rapeanu
This study introduces the notion of complex t-neutrosophic graphs (CTNGs) as a powerful tool for understanding and displaying complex interactions that are sometimes difficult to understand. It demonstrates that CTNGs may accurately reflect complicated interactions involving several components or dimensions within a particular scenario. It also instructs the basic set operations of CTNGs and analyzes notions like homomorphism and isomorphism within this framework. Furthermore, the research describes a practical application of CTNGs. It illustrates their value in addressing biodiversity conservation by taking into account a variety of relevant factors. The paper uses this application to highlight the flexibility and effectiveness of CTNGs as a tool for decision-makers to visualize and prioritize activities targeted at improving biodiversity conservation.
{"title":"A Study on Complex t-Neutrosophic Graph with Intention to Preserve Biodiversity","authors":"Murugan Kaviyarasu, Luminița-Ioana Cotîrlă, Daniel Breaz, Murugesan Rajeshwari, Eleonora Rapeanu","doi":"10.3390/sym16081033","DOIUrl":"https://doi.org/10.3390/sym16081033","url":null,"abstract":"This study introduces the notion of complex t-neutrosophic graphs (CTNGs) as a powerful tool for understanding and displaying complex interactions that are sometimes difficult to understand. It demonstrates that CTNGs may accurately reflect complicated interactions involving several components or dimensions within a particular scenario. It also instructs the basic set operations of CTNGs and analyzes notions like homomorphism and isomorphism within this framework. Furthermore, the research describes a practical application of CTNGs. It illustrates their value in addressing biodiversity conservation by taking into account a variety of relevant factors. The paper uses this application to highlight the flexibility and effectiveness of CTNGs as a tool for decision-makers to visualize and prioritize activities targeted at improving biodiversity conservation.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141947547","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}
In recent years, computer vision technology has been extensively applied in the field of defect detection for transportation infrastructure, particularly in the detection of road surface cracks. Given the variations in performance and parameters across different models, this paper proposes an improved Faster R-CNN crack recognition model that incorporates attention mechanisms. The main content of this study includes the use of the residual network ResNet50 as the basic backbone network for feature extraction in Faster R-CNN, integrated with the Squeeze-and-Excitation Network (SENet) to enhance the model’s attention mechanisms. We thoroughly explored the effects of integrating SENet at different layers within each bottleneck of the Faster R-CNN and its specific impact on model performance. Particularly, SENet was added to the third convolutional layer, and its performance enhancement was investigated through 20 iterations. Experimental results demonstrate that the inclusion of SENet in the third convolutional layer significantly improves the model’s accuracy in detecting road surface cracks and optimizes resource utilization after 20 iterations, thereby proving that the addition of SENet substantially enhances the model’s performance.
{"title":"The Improvement of Faster-RCNN Crack Recognition Model and Parameters Based on Attention Mechanism","authors":"Qiule Li, Xiangyang Xu, Jijie Guan, Hao Yang","doi":"10.3390/sym16081027","DOIUrl":"https://doi.org/10.3390/sym16081027","url":null,"abstract":"In recent years, computer vision technology has been extensively applied in the field of defect detection for transportation infrastructure, particularly in the detection of road surface cracks. Given the variations in performance and parameters across different models, this paper proposes an improved Faster R-CNN crack recognition model that incorporates attention mechanisms. The main content of this study includes the use of the residual network ResNet50 as the basic backbone network for feature extraction in Faster R-CNN, integrated with the Squeeze-and-Excitation Network (SENet) to enhance the model’s attention mechanisms. We thoroughly explored the effects of integrating SENet at different layers within each bottleneck of the Faster R-CNN and its specific impact on model performance. Particularly, SENet was added to the third convolutional layer, and its performance enhancement was investigated through 20 iterations. Experimental results demonstrate that the inclusion of SENet in the third convolutional layer significantly improves the model’s accuracy in detecting road surface cracks and optimizes resource utilization after 20 iterations, thereby proving that the addition of SENet substantially enhances the model’s performance.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141947544","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}
Xu Liu, Lei Wang, Chengwu Shen, Wenjia Ma, Shaojin Liu, Yan Han, Zhiqian Wang
In this study, an optimization method for the motion trajectory of attitude actuators was investigated in order to improve assembly efficiency in the automatic docking process of large components. The self-developed dual-attitude adjustment mechanism (2-PPPR) is used as the research object, and the structure is symmetrical. Based on the modified Denavit–Hartenberg (MDH) parameter description method, a kinematic model of the attitude mechanism is established, and its end trajectory is parametrically expressed using a five-order B-spline curve. Based on the constraints of the dynamics and kinematics of the dual-posture mechanism, the total posturing time, the degree of urgency of each joint, and the degree of difficulty of the mechanism’s posturing are selected as the optimization objectives. The Lévy flight and Cauchy variation algorithms are introduced into the salp swarm algorithm (SSA) to solve the parameters of the multi-objective trajectory optimization model. By combining the evaluation method of the multi-objective average optimal solution, the optimal trajectory of the dual-tuning mechanism and the motion trajectory of each joint are obtained. The simulation and experiment results show that the trajectory planning method proposed in this paper is effective and feasible and can ensure that the large-part dual-posture mechanism can complete the automatic docking task smoothly and efficiently.
本研究探讨了姿态执行器运动轨迹的优化方法，以提高大型部件自动对接过程中的装配效率。以自主研发的双姿态调整机构（2-PPPR）为研究对象，结构对称。基于改进的 Denavit-Hartenberg (MDH) 参数描述方法，建立了姿态机构的运动学模型，并用五阶 B 样条曲线对其末端轨迹进行了参数化表达。根据双姿态机构动力学和运动学的约束条件，选择总姿态时间、各关节的紧迫程度和机构姿态的难易程度作为优化目标。在萨尔普群算法（SSA）中引入了莱维飞行算法和考奇变异算法来求解多目标轨迹优化模型的参数。结合多目标平均最优解的评价方法，得到了双调谐机构的最优轨迹和各关节的运动轨迹。仿真和实验结果表明，本文提出的轨迹规划方法有效可行，能够保证大部件双姿态机构平稳高效地完成自动对接任务。
{"title":"Research on the Optimal Trajectory Planning Method for the Dual-Attitude Adjustment Mechanism Based on an Improved Multi-Objective Salp Swarm Algorithm","authors":"Xu Liu, Lei Wang, Chengwu Shen, Wenjia Ma, Shaojin Liu, Yan Han, Zhiqian Wang","doi":"10.3390/sym16081028","DOIUrl":"https://doi.org/10.3390/sym16081028","url":null,"abstract":"In this study, an optimization method for the motion trajectory of attitude actuators was investigated in order to improve assembly efficiency in the automatic docking process of large components. The self-developed dual-attitude adjustment mechanism (2-PPPR) is used as the research object, and the structure is symmetrical. Based on the modified Denavit–Hartenberg (MDH) parameter description method, a kinematic model of the attitude mechanism is established, and its end trajectory is parametrically expressed using a five-order B-spline curve. Based on the constraints of the dynamics and kinematics of the dual-posture mechanism, the total posturing time, the degree of urgency of each joint, and the degree of difficulty of the mechanism’s posturing are selected as the optimization objectives. The Lévy flight and Cauchy variation algorithms are introduced into the salp swarm algorithm (SSA) to solve the parameters of the multi-objective trajectory optimization model. By combining the evaluation method of the multi-objective average optimal solution, the optimal trajectory of the dual-tuning mechanism and the motion trajectory of each joint are obtained. The simulation and experiment results show that the trajectory planning method proposed in this paper is effective and feasible and can ensure that the large-part dual-posture mechanism can complete the automatic docking task smoothly and efficiently.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":"59 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141947452","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}
Khawla Abdullah Alqablan, Kholood Mohammad Alsager
This study introduces a novel mathematical tool for representing imprecise and ambiguous data: the multi-q cubic bipolar fuzzy soft set. Building upon established bipolar fuzzy sets and soft sets, this paper fist defines the concept of multi-q cubic bipolar fuzzy sets and their fundamental properties. Mathematical operations such as complement, union, and intersection are then developed for these sets. The core contribution lies in the introduction of multi-q cubic bipolar fuzzy soft sets. This new tool allows for a more nuanced representation of imprecise data compared to existing approaches. Key operations for manipulating these sets, including complement, restriction, and expansion, are defined. The applicability of multi-q cubic bipolar fuzzy soft sets extends to various domains, including multi-criteria decision making and problem solving. Illustrative examples demonstrate the practical utility of this innovative concept.
{"title":"Multi-Q Cubic Bipolar Fuzzy Soft Sets and Cosine Similarity Methods for Multi-Criteria Decision Making","authors":"Khawla Abdullah Alqablan, Kholood Mohammad Alsager","doi":"10.3390/sym16081032","DOIUrl":"https://doi.org/10.3390/sym16081032","url":null,"abstract":"This study introduces a novel mathematical tool for representing imprecise and ambiguous data: the multi-q cubic bipolar fuzzy soft set. Building upon established bipolar fuzzy sets and soft sets, this paper fist defines the concept of multi-q cubic bipolar fuzzy sets and their fundamental properties. Mathematical operations such as complement, union, and intersection are then developed for these sets. The core contribution lies in the introduction of multi-q cubic bipolar fuzzy soft sets. This new tool allows for a more nuanced representation of imprecise data compared to existing approaches. Key operations for manipulating these sets, including complement, restriction, and expansion, are defined. The applicability of multi-q cubic bipolar fuzzy soft sets extends to various domains, including multi-criteria decision making and problem solving. Illustrative examples demonstrate the practical utility of this innovative concept.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141969542","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 Game of Life (GoL) is a paradigmatic computer simulation that exhibits the emergence of complex properties of the whole from relatively simple sets of heuristic rules operating at lower organizational levels. Therefore, it is widely understood as a valuable tool for investigating global properties of evolutionary processes. Cognizant of refined concepts that emerged in recent debates on the central role of historical contingency (historicity) in evolution, we modify the original GoL rules by introducing an updating feedback loop and a probability factor that reflect the degree of historicity in pattern evolution as both stochastic path dependence and sensitivity to initial conditions. We examine this trait in simulations of the emergence and breaking of bilateral and radial symmetries commonly observed in the evolution of life, most prominently as evolving body plans. We show that the implementation of historicity parameters leads to a more realistic sequential and gradual alternating emergence and the breaking of new symmetries than the original set of rules. Apart from its more realistic representations of evolutionary processes, the new approach allows for easier exploration of the parameter space, demonstrates the sequential and gradual emergence and breaking of symmetries, and provides a publicly available and modular simulation tool. We discuss the exploratory potential of the modified GoL platform we designed as an extended thought experiment to study the parameter space defining the historicity of biological processes.
生命游戏（GoL）是一种典型的计算机模拟游戏，它展示了在较低组织层次上运行的相对简单的启发式规则集合所产生的复杂的整体特性。因此，它被广泛认为是研究进化过程整体特性的重要工具。考虑到最近关于历史偶然性（历史性）在进化中的核心作用的辩论中出现的精炼概念，我们通过引入一个更新反馈回路和一个概率因子来修改原始的 GoL 规则，以反映模式进化中的历史性程度，即随机路径依赖性和对初始条件的敏感性。我们在模拟生命进化过程中常见的双边和径向对称性的出现和打破时检验了这一特性，其中最突出的是不断进化的身体计划。我们发现，与原始规则集相比，历史性参数的实施导致了更真实的顺序和渐进交替出现以及新对称性的打破。除了更真实地表现进化过程外，新方法还能更容易地探索参数空间，展示对称性的顺序和渐进交替出现和打破，并提供一个公开可用的模块化模拟工具。我们讨论了修改后的 GoL 平台的探索潜力，该平台是我们设计的一个扩展思想实验，用于研究定义生物过程历史性的参数空间。
{"title":"Symmetry and Historicity in the Game of Life: Modifying Rules to Simulate Evolutionary Dynamics","authors":"Jovan M. Tadić, Andrej Korenić, Slobodan Perović","doi":"10.3390/sym16081024","DOIUrl":"https://doi.org/10.3390/sym16081024","url":null,"abstract":"The Game of Life (GoL) is a paradigmatic computer simulation that exhibits the emergence of complex properties of the whole from relatively simple sets of heuristic rules operating at lower organizational levels. Therefore, it is widely understood as a valuable tool for investigating global properties of evolutionary processes. Cognizant of refined concepts that emerged in recent debates on the central role of historical contingency (historicity) in evolution, we modify the original GoL rules by introducing an updating feedback loop and a probability factor that reflect the degree of historicity in pattern evolution as both stochastic path dependence and sensitivity to initial conditions. We examine this trait in simulations of the emergence and breaking of bilateral and radial symmetries commonly observed in the evolution of life, most prominently as evolving body plans. We show that the implementation of historicity parameters leads to a more realistic sequential and gradual alternating emergence and the breaking of new symmetries than the original set of rules. Apart from its more realistic representations of evolutionary processes, the new approach allows for easier exploration of the parameter space, demonstrates the sequential and gradual emergence and breaking of symmetries, and provides a publicly available and modular simulation tool. We discuss the exploratory potential of the modified GoL platform we designed as an extended thought experiment to study the parameter space defining the historicity of biological processes.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":"36 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141947559","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}
Multi-criteria decision-making methods based on reference points and distances from them are essential for evaluating alternatives across multiple criteria. These methods provide structured approaches to comparing and ranking alternatives relative to specified reference points. The main objective of this paper is to present the Multi-Criteria Method Integrating Distances to Ideal and Anti-ideal Points (MIDIA), which, through a weighted system, allows for the consideration of balance and asymmetry in assessing alternatives based on their distances from the ideal and anti-ideal points. As a multi-criteria algorithm, MIDIA is user-friendly and reflects the human mind’s natural tendency to assess objects based on fundamental concepts—comparison with the ideal solution and the anti-ideal solution—that are familiar from everyday experiences and provide valuable insights from a behavioral perspective. Moreover, the proposed method can be seen as an extension of Hellwig’s approach, designed to facilitate the ranking of alternatives based on two reference points: the ideal point and the anti-ideal point, measuring the distance between the alternative and the ideal point and the distance between the ideal and anti-ideal points. The MIDIA method integrates elements from both TOPSIS and VIKOR, by incorporating the structure of TOPSIS and the compromise perspective of VIKOR, offering a balanced approach to multi-criteria decision-making by focusing on the distances from ideal and anti-ideal points. Illustrative examples are given to demonstrate the usability of the proposed tool in situations where the decision-maker has asymmetrical preferences concerning the importance of ideal and anti-ideal points in ranking alternatives. Moreover, the MIDIA method is applied to one of the Sustainable Development Goals, in the area of education (SDG4), to obtain the rankings of EU member countries in 2022. The results obtained using the MIDIA method were compared with those obtained using the TOPSIS and VIKOR approaches. The study concludes that the ranking of alternatives depends on the coefficients of the importance of the distances to reference points and the data setup.
{"title":"A Multi-Criteria Method Integrating Distances to Ideal and Anti-Ideal Points","authors":"Ewa Roszkowska, Marzena Filipowicz-Chomko","doi":"10.3390/sym16081025","DOIUrl":"https://doi.org/10.3390/sym16081025","url":null,"abstract":"Multi-criteria decision-making methods based on reference points and distances from them are essential for evaluating alternatives across multiple criteria. These methods provide structured approaches to comparing and ranking alternatives relative to specified reference points. The main objective of this paper is to present the Multi-Criteria Method Integrating Distances to Ideal and Anti-ideal Points (MIDIA), which, through a weighted system, allows for the consideration of balance and asymmetry in assessing alternatives based on their distances from the ideal and anti-ideal points. As a multi-criteria algorithm, MIDIA is user-friendly and reflects the human mind’s natural tendency to assess objects based on fundamental concepts—comparison with the ideal solution and the anti-ideal solution—that are familiar from everyday experiences and provide valuable insights from a behavioral perspective. Moreover, the proposed method can be seen as an extension of Hellwig’s approach, designed to facilitate the ranking of alternatives based on two reference points: the ideal point and the anti-ideal point, measuring the distance between the alternative and the ideal point and the distance between the ideal and anti-ideal points. The MIDIA method integrates elements from both TOPSIS and VIKOR, by incorporating the structure of TOPSIS and the compromise perspective of VIKOR, offering a balanced approach to multi-criteria decision-making by focusing on the distances from ideal and anti-ideal points. Illustrative examples are given to demonstrate the usability of the proposed tool in situations where the decision-maker has asymmetrical preferences concerning the importance of ideal and anti-ideal points in ranking alternatives. Moreover, the MIDIA method is applied to one of the Sustainable Development Goals, in the area of education (SDG4), to obtain the rankings of EU member countries in 2022. The results obtained using the MIDIA method were compared with those obtained using the TOPSIS and VIKOR approaches. The study concludes that the ranking of alternatives depends on the coefficients of the importance of the distances to reference points and the data setup.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141947549","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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