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Keywords = symmetrical optimum principle

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31 pages, 2868 KB  
Article
Optimized Scheduling for Multi-Drop Vehicle–Drone Collaboration with Delivery Constraints Using Large Language Models and Genetic Algorithms with Symmetry Principles
by Mingyang Geng and Anping Chen
Symmetry 2025, 17(6), 934; https://doi.org/10.3390/sym17060934 - 12 Jun 2025
Cited by 3 | Viewed by 2107
Abstract
With the rapid development of e-commerce and globalization, logistics distribution systems have become integral to modern economies, directly impacting transportation efficiency, resource utilization, and supply chain flexibility. However, solving the Vehicle and Multi-Drone Cooperative Delivery Problem with Delivery Restrictions is challenging due to [...] Read more.
With the rapid development of e-commerce and globalization, logistics distribution systems have become integral to modern economies, directly impacting transportation efficiency, resource utilization, and supply chain flexibility. However, solving the Vehicle and Multi-Drone Cooperative Delivery Problem with Delivery Restrictions is challenging due to complex constraints, including limited payloads, short endurance, regional restrictions, and multi-objective optimization. Traditional optimization methods, particularly genetic algorithms, struggle to address these complexities, often relying on static rules or single-objective optimization that fails to balance exploration and exploitation, resulting in local optima and slow convergence. The concept of symmetry plays a crucial role in optimizing the scheduling process, as many logistics problems inherently possess symmetrical properties. By exploiting these symmetries, we can reduce the problem’s complexity and improve solution efficiency. This study proposes a novel and scalable scheduling approach to address the Vehicle and Multi-Drone Cooperative Delivery Problem with Delivery Restrictions, tackling its high complexity, constraint handling, and real-world applicability. Specifically, we propose a logistics scheduling method called Loegised, which integrates large language models with genetic algorithms while incorporating symmetry principles to enhance the optimization process. Loegised includes three innovative modules: a cognitive initialization module to accelerate convergence by generating high-quality initial solutions, a dynamic operator parameter adjustment module to optimize crossover and mutation rates in real-time for better global search, and a local optimum escape mechanism to prevent stagnation and improve solution diversity. The experimental results on benchmark datasets show that Loegised achieves an average delivery time of 14.80, significantly outperforming six state-of-the-art baseline methods, with improvements confirmed by Wilcoxon signed-rank tests (p<0.001). In large-scale scenarios, Loegised reduces delivery time by over 20% compared to conventional methods, demonstrating strong scalability and practical applicability. These findings validate the effectiveness and real-world potential of symmetry-enhanced, language model-guided optimization for advanced logistics scheduling. Full article
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25 pages, 8376 KB  
Review
A Review of the Development and Research Status of Symmetrical Diaphragm Pumps
by Kai Zhao, Yuan Lou, Guangjie Peng, Chengqiang Liu and Hao Chang
Symmetry 2023, 15(11), 2091; https://doi.org/10.3390/sym15112091 - 20 Nov 2023
Cited by 13 | Viewed by 5001
Abstract
With the continuous improvement in human awareness of environmental protection, energy savings, and emission reduction, as well as the vigorous development of precision machinery and process technology, energy-saving and efficient diaphragm pumps have become a hot research topic at home and abroad. The [...] Read more.
With the continuous improvement in human awareness of environmental protection, energy savings, and emission reduction, as well as the vigorous development of precision machinery and process technology, energy-saving and efficient diaphragm pumps have become a hot research topic at home and abroad. The diaphragm pump is a membrane-isolated reciprocating transport pump that isolates the transport medium from the piston through the diaphragm and can be used to transport high-viscosity, volatile, and corrosive media, and the symmetrical structure can make it easier for the diaphragm pump to achieve stable operation, reduce vibration and noise, and extend the life of the pump. This paper summarizes the development and research status of diaphragm pumps in recent years, including diaphragm pump structure, working principle, category, cavitation research, wear research, fault diagnosis research, vibration and noise research, fluid–solid-interaction research, and optimum research on one-way valves and diaphragms. It also puts forward some reasonable and novel viewpoints, such as applying the theory of entropy production to explore the motion mechanism of diaphragm pumps, optimizing the performance of diaphragm pumps, using new technologies to study new materials for diaphragm pumps, and designing diaphragm protection devices. This review provides valuable references and suggestions for the future development and research of diaphragm pumps. Full article
(This article belongs to the Special Issue Symmetry in Micro/Nanofluid and Fluid Flow)
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25 pages, 2611 KB  
Article
A Hybrid Multi-Step Probability Selection Particle Swarm Optimization with Dynamic Chaotic Inertial Weight and Acceleration Coefficients for Numerical Function Optimization
by Yuji Du and Fanfan Xu
Symmetry 2020, 12(6), 922; https://doi.org/10.3390/sym12060922 - 2 Jun 2020
Cited by 27 | Viewed by 3594
Abstract
As a meta-heuristic algoriTthm, particle swarm optimization (PSO) has the advantages of having a simple principle, few required parameters, easy realization and strong adaptability. However, it is easy to fall into a local optimum in the early stage of iteration. Aiming at this [...] Read more.
As a meta-heuristic algoriTthm, particle swarm optimization (PSO) has the advantages of having a simple principle, few required parameters, easy realization and strong adaptability. However, it is easy to fall into a local optimum in the early stage of iteration. Aiming at this shortcoming, this paper presents a hybrid multi-step probability selection particle swarm optimization with sine chaotic inertial weight and symmetric tangent chaotic acceleration coefficients (MPSPSO-ST), which can strengthen the overall performance of PSO to a large extent. Firstly, we propose a hybrid multi-step probability selection update mechanism (MPSPSO), which skillfully uses a multi-step process and roulette wheel selection to improve the performance. In order to achieve a good balance between global search capability and local search capability to further enhance the performance of the method, we also design sine chaotic inertial weight and symmetric tangent chaotic acceleration coefficients inspired by chaos mechanism and trigonometric functions, which are integrated into the MPSPSO-ST algorithm. This strategy enables the diversity of the swarm to be preserved to discourage premature convergence. To evaluate the effectiveness of the MPSPSO-ST algorithm, we conducted extensive experiments with 20 classic benchmark functions. The experimental results show that the MPSPSO-ST algorithm has faster convergence speed, higher optimization accuracy and better robustness, which is competitive in solving numerical optimization problems and outperforms a lot of classical PSO variants and well-known optimization algorithms. Full article
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21 pages, 7555 KB  
Article
Simplified Fractional Order Controller Design Algorithm
by Eva-Henrietta Dulf
Mathematics 2019, 7(12), 1166; https://doi.org/10.3390/math7121166 - 2 Dec 2019
Cited by 46 | Viewed by 4551
Abstract
Classical fractional order controller tuning techniques usually establish the parameters of the controller by solving a system of nonlinear equations resulted from the frequency domain specifications like phase margin, gain crossover frequency, iso-damping property, robustness to uncertainty, etc. In the present paper a [...] Read more.
Classical fractional order controller tuning techniques usually establish the parameters of the controller by solving a system of nonlinear equations resulted from the frequency domain specifications like phase margin, gain crossover frequency, iso-damping property, robustness to uncertainty, etc. In the present paper a novel fractional order generalized optimum method for controller design using frequency domain is presented. The tuning rules are inspired from the symmetrical optimum principles of Kessler. In the first part of the paper are presented the generalized tuning rules of this method. Introducing the fractional order, one more degree of freedom is obtained in design, offering solution for practically any desired closed-loop performance measures. The proposed method has the advantage that takes into account both robustness aspects and desired closed-loop characteristics, using simple tuning-friendly equations. It can be applied to a wide range of process models, from integer order models to fractional order models. Simulation results are given to highlight these advantages. Full article
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