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17 pages, 1494 KiB  
Article
Improved Genetic Algorithm for Solving Robot Path Planning Based on Grid Maps
by Jie Zhu and Dazhi Pan
Mathematics 2024, 12(24), 4017; https://doi.org/10.3390/math12244017 (registering DOI) - 21 Dec 2024
Viewed by 264
Abstract
Aiming at some shortcomings of the genetic algorithm to solve the path planning in a global static environment, such as a low efficiency of population initialization, slow convergence speed, and easy-to-fall-into the local optimum, an improved genetic algorithm is proposed to solve the [...] Read more.
Aiming at some shortcomings of the genetic algorithm to solve the path planning in a global static environment, such as a low efficiency of population initialization, slow convergence speed, and easy-to-fall-into the local optimum, an improved genetic algorithm is proposed to solve the path planning problem. Firstly, the environment model is established by using the grid method; secondly, in order to overcome the difficulty of a low efficiency of population initialization, a population initialization method with directional guidance is proposed; finally, in order to balance the global and local optimization searching and to speed up the solution speed, the proposed non-common point crossover operator, range mutation operator, and simplification operator are used in combination with the one-point crossover operator and one-point mutation operator in the traditional genetic algorithm to obtain an improved genetic algorithm. In the simulation experiment, Experiment 1 verifies the effectiveness of the population initialization method proposed in this paper. The success rates in Map 1, Map 2, Map 3, and Map 4 were 56.3854%, 55.851%, 34.1%, and 24.1514%, respectively, which were higher than the two initialization methods compared. Experiment 2 verifies the effectiveness of the genetic algorithm (IGA) improved in this paper for path planning. In four maps, the path planning is compared with the five algorithms and the shortest distance is achieved in all of them. The two experiments show that the improved genetic algorithm in this paper has advantages in path planning. Full article
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<p>Example of grid map.</p>
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<p>Examples of a feasible path.</p>
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<p>Example of gird selection.</p>
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<p>Example of one-point crossover operator.</p>
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<p>Example of the non-common point crossover operator.</p>
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<p>Example of one-point mutation operator.</p>
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<p>Example of range mutation operator.</p>
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<p>Example of simplification operator.</p>
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<p>Example of test maps.</p>
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<p>Map 4 of fitness curve.</p>
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<p>Example of path planning.</p>
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17 pages, 6724 KiB  
Article
Distributed Localization of Non-Cooperative Targets in Non-Coplanar Rendezvous Processes
by Zihan Zhen and Feng Yu
Aerospace 2024, 11(12), 1039; https://doi.org/10.3390/aerospace11121039 - 19 Dec 2024
Viewed by 252
Abstract
Precise positioning of non-cooperative targets is important for maintaining spacecraft operational environments in orbit. In order to address the challenges of non-cooperative target localization during non-coplanar rendezvous, this study develops a distributed cooperative localization scheme. First, a three-line-of-sight positioning method for long-range targets [...] Read more.
Precise positioning of non-cooperative targets is important for maintaining spacecraft operational environments in orbit. In order to address the challenges of non-cooperative target localization during non-coplanar rendezvous, this study develops a distributed cooperative localization scheme. First, a three-line-of-sight positioning method for long-range targets in non-coplanar orbits is proposed. Second, a distributed extended Kalman filter based on a consensus algorithm is designed, which reduces observation dimensions and increases system robustness. Subsequently, the rendezvous configuration optimization problem for long-range non-coplanar targets is transformed into a numerical optimization problem. Finally, an improved NSGA-III algorithm is proposed by introducing normal distribution crossover (NDX) and a cosine-like mutation distribution index to optimize the rendezvous configuration. A simulation shows that the methods proposed are effective, and the improved NSGA-III is superior to traditional algorithms in terms of search range and convergence speed. After configuration optimization, the performance of the system has been greatly improved, with better positioning accuracy and stronger robustness. Full article
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<p>Multi-LOS cooperative localization scheme.</p>
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<p>System observability. (<b>a</b>) System observability. (<b>b</b>) Distance between tracking satellites and target. (<b>c</b>) Observation angle between satellites 1 and 2 and target.</p>
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<p>Transferring configuration design.</p>
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<p>Cosine-like mutation distribution index.</p>
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<p>Improved NSGA-III algorithm.</p>
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<p>Comparation of two algorithms’ simulation results for DTLZ1. (<b>a</b>) Traditional NSGA-III. (<b>b</b>) Improved NSGA-III.</p>
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<p>Distribution of offspring.</p>
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<p>Convergence curve.</p>
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<p>Solution comparations for three algorithms. (<b>a</b>) Improved NSGA-III and NSGA-III. (<b>b</b>) Improved NSGA-III and NSGA-II.</p>
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<p>Position error of estimation in satellite 1, 2, 3. (<b>a</b>–<b>c</b>) Position error of <span class="html-italic">x</span>, <span class="html-italic">y</span>, <span class="html-italic">z</span> axis in satellite 1. (<b>d</b>–<b>f</b>) Position error of <span class="html-italic">x</span>, <span class="html-italic">y</span>, <span class="html-italic">z</span> axis in satellite 2. (<b>g</b>–<b>i</b>) Position error of <span class="html-italic">x</span>, <span class="html-italic">y</span>, <span class="html-italic">z</span> axis in satellite 3.</p>
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<p>Co-localization system position estimation error. (<b>a</b>) Estimation error of satellite 1; (<b>b</b>) Estimation error of satellite 2; (<b>c</b>) Estimation error of satellite 3.</p>
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21 pages, 2521 KiB  
Article
Crossover Operator Inspired by the Selection Operator for an Evolutionary Task Sequencing Algorithm
by Piotr Ciepliński and Sławomir Golak
Appl. Sci. 2024, 14(24), 11786; https://doi.org/10.3390/app142411786 - 17 Dec 2024
Viewed by 310
Abstract
This paper proposes a novel crossover operator for evolutionary algorithms in task sequencing and verifies its efficacy. Unlike the conventional blind and entirely stochastic selection of sequence fragments exchanged with the second individual, the proposed operator employs a method where the probability of [...] Read more.
This paper proposes a novel crossover operator for evolutionary algorithms in task sequencing and verifies its efficacy. Unlike the conventional blind and entirely stochastic selection of sequence fragments exchanged with the second individual, the proposed operator employs a method where the probability of fragment selection is influenced by the total cost of internal connections within the exchanged fragments. At the same time, the new operator retains its stochastic nature and is not a deterministic operator, which reduces the risk of the evolutionary algorithm getting stuck in a local minimum. The idea of the proposed crossover operator was based on the main mechanism of the evolutionary algorithm that determines the success of this type of algorithm selection. To assess its effectiveness, the new operator was compared against previously employed crossover operators using a traveling salesman problem (TSP) instance in a multidimensional space in order to map the problem of symmetric sequencing tasks described with multiparameters (e.g., a symmetric variant of production tasks sequencing). Full article
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<p>Flow diagram of the used evolutionary algorithm.</p>
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<p>The chromosome encodes the task sequence. Each task is described by a set of parameters, <math display="inline"><semantics> <mover> <mi mathvariant="bold">P</mi> <mo>¯</mo> </mover> </semantics></math>. Each node is connected to two neighbors by a connection, the length of which represents the cost <span class="html-italic">C</span> of the transition between tasks and is a function of the parameters of the adjacent tasks. During optimization, the chromosome forms a cyclic graph with no indication of the start of the sequence.</p>
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<p>Example of a chromosome in the form of a ring (cycle) graph for 12 tasks.</p>
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<p>The operation of selecting a sequence fragment to be transferred from the donor and a fragment to be removed from the recipient. Green items indicate selected sequence fragments. Yellow items are repeated in both fragments and do not require repair. Blue items are genes that will cause task duplication in the recipient. Red items represent tasks removed from the recipient and the lack of these tasks in the recipient’s chromosome.</p>
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<p>Creating offspring. Light blue items represent new genes inserted into the recipient chromosome. Dark red items are old recipient genes that cause erroneous duplication of tasks.</p>
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<p>Repairing the child. In place of each duplicate task in the recipient (green items), the task removed from the recipient chromosome at the stage of inserting the donor fragment is inserted (red items).</p>
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<p>Flow diagram of the proposed crossover operator. This crossover subalgorithm is implemented in each generation of the evolutionary algorithm.</p>
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<p>Preliminary impact analysis of metaparameter <span class="html-italic">a</span> on the effectiveness of the new crossover method (the criterion value of the best individual) for sequencing 100 tasks to determine its optimal value. The determined value (red dot) for the minimum was used in the main comparative analysis of the new operator and the existing operators.</p>
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<p>Preliminary impact analysis of exchanged sequence fragment length on the effectiveness of the new crossover method (the criterion value of the best individual) for sequencing 100 tasks to determine its optimal value for different cost definitions: Euclidean (<b>A</b>), Euclidean<sup>2</sup> (<b>B</b>), and Manhattan (<b>C</b>). The determined value (red dot) for the minimum was used in the main comparative analysis of the new operator and the existing operators.</p>
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<p>Influence of the number of sequencing tasks on the optimal exchanged sequence fragment length for different cost definitions: Euclidean (<b>A</b>), Euclidean<sup>2</sup> (<b>B</b>), and Manhattan (<b>C</b>). The red lines represent the mean values used as metaparameter values in further studies.</p>
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<p>Effectiveness of the crossover operator for the 250-task problem. The mean criterion value (three definitions of cost: Euclidean, Euclidean<sup>2</sup>, and Manhattan) of the best individual achieved after 1000 generations.</p>
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<p>Effectiveness of the crossover operator for the 500-task problem. The mean criterion value (three definitions of cost: Euclidean, Euclidean<sup>2</sup>, and Manhattan) of the best individual achieved after 1000 generations.</p>
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<p>Effectiveness of the crossover operator for the 1000-task problem. The mean criterion value (three definitions of cost: Euclidean, Euclidean<sup>2</sup>, and Manhattan) of the best individual achieved after 1000 generations.</p>
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<p>Effectiveness of the crossover operator for the 250-task problem with normally distributed parameters. The mean criterion value (three definitions of cost: Euclidean, Euclidean<sup>2</sup>, and Manhattan) of the best individual achieved after 1000 generations.</p>
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<p>Effectiveness of the crossover operator for the 250-task problem with discrete parameters (three levels of values). The mean criterion value (three definitions of cost: Euclidean, Euclidean<sup>2</sup>, and Manhattan) of the best individual achieved after 1000 generations.</p>
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<p>Effectiveness of the crossover operator for the 250-task problem with discrete parameters (four levels of values). The mean criterion value (three definitions of cost: Euclidean, Euclidean<sup>2</sup>, and Manhattan) of the best individual achieved after 1000 generations.</p>
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<p>Effectiveness of the crossover operator for the 250-task problem with discrete parameters (five levels of values). The mean criterion value (three definitions of cost: Euclidean, Euclidean<sup>2</sup>, and Manhattan) of the best individual achieved after 1000 generations.</p>
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<p>Comparison of execution time of 200 generations for the 500-task problem.</p>
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<p>Change in the criterion value over time for the 500-task problem (cost based on Euclidean distance) over 1000 generations.</p>
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<p>Change in the criterion value over time for the 500-task problem (cost based on Euclidean<sup>2</sup> distance) over 1000 generations.</p>
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<p>Change in the criterion value over time for the 500-task problem (cost based on Manhattan distance) over 1000 generations.</p>
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<p>Influence of the population size on the effectiveness of the crossover operators for the 500-task problem (cost based on Euclidean distance) over 1000 generations.</p>
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44 pages, 17816 KiB  
Article
An Improved Spider Wasp Optimizer for UAV Three-Dimensional Path Planning
by Haijun Liang, Wenhai Hu, Lifei Wang, Ke Gong, Yuxi Qian and Longchao Li
Biomimetics 2024, 9(12), 765; https://doi.org/10.3390/biomimetics9120765 - 16 Dec 2024
Viewed by 380
Abstract
This paper proposes an Improved Spider Wasp Optimizer (ISWO) to address inaccuracies in calculating the population (N) during iterations of the SWO algorithm. By innovating the population iteration formula and integrating the advantages of Differential Evolution and the Crayfish Optimization Algorithm, [...] Read more.
This paper proposes an Improved Spider Wasp Optimizer (ISWO) to address inaccuracies in calculating the population (N) during iterations of the SWO algorithm. By innovating the population iteration formula and integrating the advantages of Differential Evolution and the Crayfish Optimization Algorithm, along with introducing an opposition-based learning strategy, ISWO accelerates convergence. The adaptive parameters trade-off probability (TR) and crossover probability (Cr) are dynamically updated to balance the exploration and exploitation phases. In each generation, ISWO optimizes individual positions using Lévy flights, DE’s mutation, and crossover operations, and COA’s adaptive update mechanisms. The OBL strategy is applied every 10 generations to enhance population diversity. As the iterations progress, the population size gradually decreases, ultimately yielding the optimal solution and recording the convergence process. The algorithm’s performance is tested using the 2017 test set, modeling a mountainous environment with a Gaussian function model. Under constraint conditions, the objective function is updated to establish a mathematical model for UAV flight. The minimal cost for obstacle-avoiding flight within the specified airspace is obtained using the fitness function, and the flight path is smoothed through cubic spline interpolation. Overall, ISWO generates high-quality, smooth paths with fewer iterations, overcoming premature convergence and the insufficient local search capabilities of traditional genetic algorithms, adapting to complex terrains, and providing an efficient and reliable solution. Full article
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<p>Simplified diagram of UAV path planning.</p>
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<p>Flowchart of the SWO algorithm.</p>
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<p>Trade-off between the search phase and the subsequent tracking and evasion mechanisms.</p>
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<p>Flowchart of hunting and nesting behaviors in SWO.</p>
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<p>Flowchart of the ISWO algorithm.</p>
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<p>The improved Formula (25) accompanies the change in population size throughout the iterations of the ISWO algorithm.</p>
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<p>The adaptive adjustments of the TR and Cr parameters over 100 iterations illustrate their variations throughout the iterative process.</p>
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<p>Effect of temperature on crayfish intake.</p>
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<p>The adaptive adjustments of the TR and Cr parameters over 100 iterations illustrate their variation throughout the iterative process.</p>
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<p>Fitness curve based on inverse learning.</p>
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<p>Three-dimensional model of Gaussian mountains.</p>
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<p>Three times cubic spline interpolation optimizer effect diagram.</p>
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<p>Comparison chart of SWO algorithm curves with and without cubic spline interpolation.</p>
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<p>Six algorithms, ISWO, HO, BKA, SWO, CFOA, and COA, for planning routes.</p>
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<p>Convergence curves of the six algorithms: ISWO, HO, BKA, SWO, CFOA, and COA.</p>
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<p>Histogram of the path lengths of the six algorithms: ISWO, HO, BKA, SWO, CFOA, and COA.</p>
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<p>Seven algorithms, DBO, LO, SWO, COA, LSO, KOA, and ISWO, for planning routes.</p>
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<p>Convergence curves of the six algorithms: DBO, LO, SWO, COA, LSO, KOA, and ISWO.</p>
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<p>Histogram of the path lengths of the six algorithms: ISWO, HO, BKA, SWO, CFOA, and COA.</p>
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<p>F1–F6 (50 dims).</p>
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<p>F7–F12 (50 dims).</p>
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<p>F13–F18 (50 dims).</p>
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<p>F19–F24 (50 dims).</p>
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<p>F25–F30 (50 dims).</p>
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<p>F1–F6 (50 dims) box plot (math.).</p>
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<p>F7–F12 (50 dims) box plot (math.).</p>
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<p>F13–F18 (50 dims) box plot (math.).</p>
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<p>F19–F24 (50 dims) box plot (math.).</p>
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<p>F25–F30 (50 dims) box plot (math.).</p>
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<p>F1–F6 (100 dims).</p>
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<p>F7–F12 (100 dims).</p>
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<p>F13–F18 (100 dims).</p>
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<p>F19–F24 (100 dims).</p>
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<p>F25–F30 (100 dims).</p>
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<p>F1–F6 (100 dims) box plot (math.).</p>
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<p>F7–F12 (100 dims) box plot (math.).</p>
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<p>F13–F18 (100 dims) box plot (math.).</p>
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<p>F19–F24 (100 dims) box plot (math.).</p>
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<p>F25–F30 (100 dims) box plot (math.).</p>
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32 pages, 5806 KiB  
Article
Modeling and Solving the Multi-Objective Vehicle Routing Problem with Soft and Fuzzy Time Windows
by Ailing Chen and Tianao Li
Systems 2024, 12(12), 560; https://doi.org/10.3390/systems12120560 - 13 Dec 2024
Viewed by 536
Abstract
In the distribution field, distribution costs and customer service satisfaction are extremely important issues for enterprises. However, both the Vehicle Routing Problem with Soft Time Windows (VRPSTW) and the Vehicle Routing Problem with Fuzzy Time Windows (VRPFTW) have certain deficiencies in describing real-world [...] Read more.
In the distribution field, distribution costs and customer service satisfaction are extremely important issues for enterprises. However, both the Vehicle Routing Problem with Soft Time Windows (VRPSTW) and the Vehicle Routing Problem with Fuzzy Time Windows (VRPFTW) have certain deficiencies in describing real-world scenarios. Therefore, this paper considers both soft time windows and fuzzy time windows, improving upon the traditional VRPSTW and VRPFTW models to establish a more comprehensive and realistic model called the Vehicle Routing Problem with Soft Time Windows and Fuzzy Time Windows (VRPSFTW). Secondly, to solve the relevant problems, this paper proposes a Directed Mutation Genetic Algorithm integrated with Large Neighborhood Search (LDGA), which fully utilizes the advantages of the Genetic Algorithm (GA) in the early stages and appropriately adopts removal and re-insertion operators from the Large Neighborhood Search (LNS). This approach not only makes efficient use of computational resources but also compensates for the weaknesses of crossover and mutation operators in the later stages of the genetic algorithm. Thereby, it improves the overall efficiency and accuracy of the algorithm and achieves better solution results. In addition, in order to solve multi-objective problems, this paper employs a two-stage solution approach and designs two sets of algorithms based on the principles of “cost priority” and “service-level priority”. Simulation experiments demonstrated that the algorithms designed in this study achieved a more competitive solving performance. Full article
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<p>Framework diagram of the algorithm designed in this paper.</p>
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<p>The idea behind the operator for determining the start service time in the “cost priority” algorithm.</p>
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<p>The idea behind the operator for determining the start service time in the “service-level priority” algorithm.</p>
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<p>Framework of two-stage algorithm (i indicates the current generation number, n is a positive integer, and the meaning of the other letters is the same as in <a href="#sec3dot3-systems-12-00560" class="html-sec">Section 3.3</a>).</p>
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<p>C208 and RC208 convergence curves. (<b>a</b>) Convergence curve of C208; (<b>b</b>) convergence curve of RC208.</p>
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<p>Charts of the vehicle transport route schemes of six instances (Different colored lines represent the paths of different vehicles). (<b>a</b>) Chart for instance C101; (<b>b</b>) chart for instance R101; (<b>c</b>) chart for instance RC101; (<b>d</b>) chart for instance C208; (<b>e</b>) chart for instance R208; (<b>f</b>) chart for instance RC208.</p>
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<p>The transportation route schemes derived from the two-stage algorithm (Different colored lines represent the paths of different vehicles): (<b>a</b>) the cost-priority scheme; (<b>b</b>) the satisfaction-priority scheme.</p>
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<p>Transportation route schemes obtained from the two-stage algorithm for solving the VRPSFTW (Different colored lines represent the paths of different vehicles). (<b>a</b>) Instance Extended C101 (cost priority); (<b>b</b>) Instance Extended C101 (Service-level priority); (<b>c</b>) Instance Extended R101 (cost priority); (<b>d</b>) Instance Extended R101 (Service-level priority); (<b>e</b>) Instance Extended RC101 (cost priority); (<b>f</b>) Instance Extended RC101 (Service-level priority).</p>
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<p>Taking the Extended C101 as an example: (<b>a</b>) the evolution of the historical minimum cost and (<b>b</b>) the corresponding maximum service level.</p>
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<p>Scatter plot of cost and service level using the Extended C101 as an example.</p>
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19 pages, 1007 KiB  
Article
Acute Alpha-Glycerylphosphorylcholine Supplementation Enhances Cognitive Performance in Healthy Men
by Chad M. Kerksick
Nutrients 2024, 16(23), 4240; https://doi.org/10.3390/nu16234240 - 9 Dec 2024
Viewed by 834
Abstract
Background: Choline is an essential nutrient required for proper cell functioning. Due to its status as a precursor to acetylcholine, an important neurotransmitter connected to cognition and neuromuscular function, maintaining or enhancing choline levels is of interest. Supplementation with alpha-glycerylphosphorycholine (A-GPC) can maintain [...] Read more.
Background: Choline is an essential nutrient required for proper cell functioning. Due to its status as a precursor to acetylcholine, an important neurotransmitter connected to cognition and neuromuscular function, maintaining or enhancing choline levels is of interest. Supplementation with alpha-glycerylphosphorycholine (A-GPC) can maintain choline levels, but its ability to offer support towards cognition remains an area of ongoing research. Methods: Using a randomized, double-blind, placebo-controlled, crossover approach, 20 resistance-trained males (31.3 ± 11.0 years, 178.6 ± 7.3 cm, 84.6 ± 11.4 kg, 15.4 ± 5.6% body fat) consumed either a placebo (PL), 630 mg A-GPC (HD), or 315 mg (LD) A-GPC (GeniusPure®, NNB Nutrition, Nanjing, China). After resting hemodynamic assessments, participants took their assigned dose and had cognitive assessments (Stroop, N-Back, and Flanker), visual analog scales, and hemodynamics evaluated 60 min after ingestion. All participants then warmed up and completed vertical jumps and bench press throws before completing a bout of lower-body resistance exercise (6 × 10 repetitions using the Smith squat at a load of 70% 1RM). Venous blood was collected 5, 15, 30, and 60 min after completion of the squat protocol to evaluate changes in growth hormones, and follow-up visual analog scales and cognitive measurements were evaluated 30 min after completing the exercise bout. Results: When compared to PL, changes in Stroop total score were statistically greater after HD (13.0 ± 8.2 vs. 5.2 ± 9.0, p = 0.013, d = 0.61) and LD (10.8 ± 7.7 vs. 5.2 ± 9.0, p = 0.046, d = 0.48) administration, in addition to significantly faster times to complete the Stroop test in the HD group when compared to PL (−0.12 ± 0.09 s vs. −0.05 ± 0.09 s, p = 0.021, d = 0.56). No significant differences between groups were found for the Flanker and N-Back assessments, while a tendency was observed for HD to have faster reaction times when compared to PL during the Flanker test. No group differences were realized for visual analog scales, physical performance, or growth hormone. Statistically significant changes in heart rate and blood pressure were observed in all groups, with all recorded values aligning with clinically accepted normative values. Conclusions: HD and LD A-GPC supplementation significantly increased cognitive performance in a group of young, healthy males as measured by changes in the Stroop Total Score and completion time of the Stroop test. These results offer unique insight into the potential for A-GPC to acutely increase cognition in a group of young, healthy males. While previous research has indicated potential for A-GPC to acutely improve cognition in clinical populations, extending these outcomes to healthy individuals can be potentially meaningful for a wide variety of populations such as athletes, race car drivers, military operators, and other non-athletic populations who desire and have a need to improve their mental performance. This study was retrospectively registered as NCT06690619 on clinicaltrials.gov. Full article
(This article belongs to the Special Issue Dietary Supplements in Exercise and Sports Activities)
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<p>Timeline schematic of study design and procedures.</p>
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<p>Consolidated Standards of Reporting Trials (CONSORT) diagram.</p>
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<p>Delta Stroop total score. * = Different than PL (<span class="html-italic">p</span> &lt; 0.05).</p>
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<p>Delta time per score. * = Different than PL (<span class="html-italic">p</span> &lt; 0.05).</p>
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15 pages, 1009 KiB  
Article
An Enhanced Crowned Porcupine Optimization Algorithm Based on Multiple Improvement Strategies
by Wenli Lei, Yifan Gu and Jianyu Huang
Appl. Sci. 2024, 14(23), 11414; https://doi.org/10.3390/app142311414 - 8 Dec 2024
Viewed by 433
Abstract
The Crowned Porcupine Optimization (CPO) algorithm exhibits certain deficiencies in initialization efficiency, convergence speed, and adaptability. To address these issues, this paper proposes an enhanced Crowned Porcupine Optimization algorithm (ICPO) based on multiple improvement strategies. ICPO optimizes the initialization process by introducing Logistic [...] Read more.
The Crowned Porcupine Optimization (CPO) algorithm exhibits certain deficiencies in initialization efficiency, convergence speed, and adaptability. To address these issues, this paper proposes an enhanced Crowned Porcupine Optimization algorithm (ICPO) based on multiple improvement strategies. ICPO optimizes the initialization process by introducing Logistic chaotic mapping, thereby expanding the search space. It accelerates convergence through an elite retention strategy and enhances global search capability by integrating stochastic operations, mutation-like operations, and crossover-like operations to increase population diversity. Additionally, adaptive step tuning based on fitness values is employed to comprehensively improve the algorithm’s performance. To verify the effectiveness of ICPO, 23 standard functions were used for a comprehensive evaluation, and its practicality was further validated through optimization of actual engineering design problems. The experimental results demonstrate significant improvements in convergence speed, solution quality, and adaptability with ICPO. Full article
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<p>Convergence curves for standard functions.</p>
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<p>Convergence curves for standard functions.</p>
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<p>Convergence curves for standard functions.</p>
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25 pages, 5956 KiB  
Article
Optimization of Adaptive Sliding Mode Controllers Using Customized Metaheuristics in DC-DC Buck-Boost Converters
by Daniel F. Zambrano-Gutierrez, Jorge M. Cruz-Duarte, Herman Castañeda and Juan Gabriel Avina-Cervantes
Mathematics 2024, 12(23), 3709; https://doi.org/10.3390/math12233709 - 26 Nov 2024
Viewed by 496
Abstract
Metaheuristics have become popular tools for solving complex optimization problems; however, the overwhelming number of tools and the fact that many are based on metaphors rather than mathematical foundations make it difficult to choose and apply them to real engineering problems. This paper [...] Read more.
Metaheuristics have become popular tools for solving complex optimization problems; however, the overwhelming number of tools and the fact that many are based on metaphors rather than mathematical foundations make it difficult to choose and apply them to real engineering problems. This paper addresses this challenge by automatically designing optimization algorithms using hyper-heuristics as a master tool. Hyper-heuristics produce customized metaheuristics by combining simple heuristics, guiding a population of initially random individuals to a solution that satisfies the design criteria. As a case study, the obtained metaheuristic tunes an Adaptive Sliding Mode Controller to improve the dynamic response of a DC-DC Buck–Boost converter under various operating conditions (such as overshoot and settling time), including nonlinear disturbances. Specifically, our hyper-heuristic obtained a tailored metaheuristic composed of Genetic Crossover- and Swarm Dynamics-type operators. The goal is to build the metaheuristic solver that best fits the problem and thus find the control parameters that satisfy a predefined performance. The numerical results reveal the reliability and potential of the proposed methodology in finding suitable solutions for power converter control design. The system overshoot was reduced from 87.78% to 0.98%, and the settling time was reduced from 31.90 ms to 0.4508 ms. Furthermore, statistical analyses support our conclusions by comparing the custom metaheuristic with recognized methods such as MadDE, L-SHADE, and emerging metaheuristics. The results highlight the generated optimizer’s competitiveness, evidencing the potential of Automated Algorithm Design to develop high-performance solutions without manual intervention. Full article
(This article belongs to the Section Computational and Applied Mathematics)
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<p>Metaheuristic model represented through simple heuristics. It comprises an initializer (<math display="inline"><semantics> <msub> <mi>h</mi> <mi>i</mi> </msub> </semantics></math>), one or many search operators (<math display="inline"><semantics> <msub> <mi>h</mi> <mi>o</mi> </msub> </semantics></math>) under the composition operation (∘), and a finalizer (<math display="inline"><semantics> <msub> <mi>h</mi> <mi>f</mi> </msub> </semantics></math>).</p>
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<p>Basic circuit diagram of a DC-DC Buck–Boost converter.</p>
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<p>Open-loop response of the Buck–Boost converter for a pulse-shape input. The main signal features, including the overshoot (M<sub>p</sub>), which represents how much of the reference voltage (Ref) has been exceeded, and the settling time (T<sub>s</sub>), which indicates the amount of time required for the system to be stable, are presented.</p>
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<p>DC-DC Buck–Boost converter driven by an Adaptive Sliding Mode Controller.</p>
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<p>Overview of the proposed framework. A hyper-heuristic approach is employed in the high-level domain to automatically obtain tailored metaheuristics using a collection of 205 search operators. In the low-level domain, an Adaptive Sliding Mode Controller is tuned, optimizing the performance of a DC-DC Buck–Boost converter.</p>
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<p>(<b>a</b>) The tendency of the performance metric <span class="html-italic">Q</span> along the hyper-heuristic process (High-level problem), where the dashed line represents the performance evolution. (<b>b</b>) The behavior of the custom MH in step 8 (<math display="inline"><semantics> <mrow> <msub> <mi>MH</mi> <mn>8</mn> </msub> <mo>≡</mo> <msub> <mi>MH</mi> <mo>*</mo> </msub> </mrow> </semantics></math>) generated to solve the low-level problem.</p>
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<p>Fitness values correspond to 20 controller designs achieved by the tailored (MH<sub>*</sub>) and two classical (PSO and GA) metaheuristics.</p>
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<p>Step response of the DC-DC Buck–Boost converter in a closed-loop configuration with an Adaptive Sliding Mode Controller (ASMC) tuned using MH<sub>*</sub>, PSO, and GA. The ASMC parameters were set to the average values in <a href="#mathematics-12-03709-t005" class="html-table">Table 5</a>, obtained from 20 independent runs.</p>
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<p>(<b>a</b>) Overshoot (<math display="inline"><semantics> <msub> <mi mathvariant="normal">M</mi> <mi mathvariant="normal">p</mi> </msub> </semantics></math> [%]) and (<b>b</b>) Settling Time (T<span class="html-italic">s</span> [s]) values for the Adaptive Sliding Mode Controller tuned by the tailored (MH<sub>*</sub>) and two classical (PSO and GA) metaheuristics, corresponding to 20 controller designs.</p>
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<p>The output voltage of the Buck–Boost DC-DC converter, controlled by an ASMC tuned with MH<sub>*</sub>, is shown for different input voltage profiles, including step and ramp functions.</p>
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<p>(<b>a</b>) Disturbance signal representing a nonlinear load profile connected to the controlled system. (<b>b</b>) Response to nonlinear perturbations achieved by the DC-DC Buck–Boost converter controlled by the Adaptive Sliding Mode Controller tuned with the tailored metaheuristic (MH<sub>*</sub>).</p>
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<p>Analysis of the Adaptive Sliding Mode Controller performance under nonlinear perturbations: (<b>a</b>) Control action signal and adaptive gain variation and (<b>b</b>) behavior of the sliding surface function.</p>
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16 pages, 2814 KiB  
Article
A Study of Flexible Job-Shop Scheduling with Dual Constraints
by Zhenhua Gao and Hengyun Qiao
Processes 2024, 12(12), 2649; https://doi.org/10.3390/pr12122649 - 24 Nov 2024
Viewed by 444
Abstract
The flexible production job shop was selected as the research object, with the goal of minimizing the maximum completion time. A novel production scheduling model was devised by taking into account the sequence of occurrence of two distinct perturbations, namely preventive maintenance and [...] Read more.
The flexible production job shop was selected as the research object, with the goal of minimizing the maximum completion time. A novel production scheduling model was devised by taking into account the sequence of occurrence of two distinct perturbations, namely preventive maintenance and emergency order insertion, within the same production scheduling plan. This was solved by an improved three-body crossover operator genetic algorithm. Finally, the superiority and effectiveness of the new production scheduling were demonstrated through an illustrative analysis. Full article
(This article belongs to the Section Automation Control Systems)
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<p>Genetic algorithm flowchart.</p>
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<p>Genetic algorithm flowchart.</p>
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<p>Genetic algorithm flowchart.</p>
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<p>Flowchart of three-body crossover algorithm.</p>
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<p>Schematic diagram of a three-body crossover operation.</p>
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<p>Immediate preventive maintenance Gantt chart.</p>
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<p>Right-shift strategy preventive maintenance Gantt chart.</p>
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<p>Periodic maintenance Gantt chart.</p>
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<p>Gantt chart based on full rescheduling strategy for only urgent insertion orders after the insertion moment.</p>
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<p>Gantt chart based on full rescheduling policy after the insertion moment.</p>
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11 pages, 284 KiB  
Article
Single-Machine Rescheduling with Rejection and an Operator No-Availability Period
by Guanghua Wu and Hongli Zhu
Mathematics 2024, 12(23), 3678; https://doi.org/10.3390/math12233678 - 24 Nov 2024
Viewed by 354
Abstract
In this paper, we investigate a rescheduling problem with rejection and an operator non-availability period on a single machine. An optimal original schedule with the objective of minimizing the total weighted completion time has been made in a deterministic production scheduling system without [...] Read more.
In this paper, we investigate a rescheduling problem with rejection and an operator non-availability period on a single machine. An optimal original schedule with the objective of minimizing the total weighted completion time has been made in a deterministic production scheduling system without an unavailable interval. However, prior to the start of formal job processing, a time interval becomes unavailable due to the operator. No jobs can start or complete in the interval; nonetheless, a job that begins prior to this interval and finishes afterward is possible (if there is such a job, we call it a crossover job). In order to deal with the operator non-availability period, job rejection is allowed. Each job is either accepted for processing or rejected by paying a rejection cost. The planned original schedule is required to be rescheduled. The objective is to minimize the total weighted completion time of the accepted jobs plus the total penalty of the rejected jobs plus the weighted maximum tardiness penalty between the original schedule and the new reschedule. We present a pseudo-polynomial time dynamic programming exact algorithm and subsequently develop it into a fully polynomial time approximation scheme. Full article
25 pages, 1758 KiB  
Article
Collision Avoidance for Unmanned Surface Vehicles in Multi-Ship Encounters Based on Analytic Hierarchy Process–Adaptive Differential Evolution Algorithm
by Zhongming Xiao, Baoyi Hou, Jun Ning, Bin Lin and Zhengjiang Liu
J. Mar. Sci. Eng. 2024, 12(12), 2123; https://doi.org/10.3390/jmse12122123 - 21 Nov 2024
Viewed by 655
Abstract
Path planning and collision avoidance issues are key to the autonomous navigation of unmanned surface vehicles (USVs). This study proposes an adaptive differential evolution algorithm model integrated with the analytic hierarchy process (AHP-ADE). The traditional differential evolution algorithm is enhanced by introducing an [...] Read more.
Path planning and collision avoidance issues are key to the autonomous navigation of unmanned surface vehicles (USVs). This study proposes an adaptive differential evolution algorithm model integrated with the analytic hierarchy process (AHP-ADE). The traditional differential evolution algorithm is enhanced by introducing an elite archive strategy and adaptively adjusting the scale factor F and the crossover factor CR to balance global and local search capabilities, preventing premature convergence and improving the search accuracy. Additionally, the collision risk index (CRI) model is optimized and combined with the quaternion ship domain, enhancing the precision of CRI calculations and USV autonomous collision avoidance capabilities. The improved CRI model, the International Regulations for Preventing Collisions at Sea, and the optimal collision avoidance distance were incorporated as evaluation factors in a fitness function assessment, with weights determined through the AHP to enhance the rationality and accuracy of the fitness function. The proposed AHP-ADE algorithm was compared with the improved particle swarm algorithm, and the performance of the algorithm was comprehensively evaluated using safety, economy, and operational efficiency. Simulation experiments on the MATLAB platform demonstrated that the proposed AHP-ADE algorithm exhibited better performance in scenarios involving multiple ship encounters, thus proving its effectiveness. Full article
(This article belongs to the Special Issue Unmanned Marine Vehicles: Perception, Planning, Control and Swarm)
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<p>Crossover operation.</p>
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<p>Quaternion ship domain model.</p>
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<p>Various situations of OS and the TS domains being intruded upon: (<b>a</b>) the TS does not intrude into the OS’s domain, but the OS intrudes into the TS’s domain; (<b>b</b>) the OS does not intrude into the TS’s domain, but the TS intrudes into the OS’s domain; (<b>c</b>) both ships intrude into each other’s domains.</p>
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<p>The relative motion lines intersect at the boundary of the ship domain.</p>
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<p>Weights of evaluation factors.</p>
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<p>Algorithmic process.</p>
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<p>Simulation results of the two-ship encounter.</p>
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<p>The state of the two-ship encounter ship at specific time intervals.</p>
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<p>Real-time distance of the OS from the TS and static obstacles.</p>
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<p>Simulation results of the four-ship encounter.</p>
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<p>The state of a four-ship encounter ship at specific time intervals.</p>
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<p>Real-time distance of the OS from the TSs.</p>
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21 pages, 4021 KiB  
Article
System-Level Dynamic Model of Redox Flow Batteries (RFBs) for Energy Losses Analysis
by Ikechukwu S. Anyanwu, Fulvio Buzzi, Pekka Peljo, Aldo Bischi and Antonio Bertei
Energies 2024, 17(21), 5324; https://doi.org/10.3390/en17215324 - 25 Oct 2024
Viewed by 605
Abstract
This paper presents a zero-dimensional dynamic model of redox flow batteries (RFBs) for the system-level analysis of energy loss. The model is used to simulate multi-cell systems considering the effect of design and operational parameters on energy loss and overall performance. The effect [...] Read more.
This paper presents a zero-dimensional dynamic model of redox flow batteries (RFBs) for the system-level analysis of energy loss. The model is used to simulate multi-cell systems considering the effect of design and operational parameters on energy loss and overall performance. The effect and contribution of stack losses (e.g., overpotential and crossover losses) and system losses (e.g., shunt currents and pumps) to total energy loss are examined. The model is tested by using literature data from a vanadium RFB energy storage. The results show that four parameters mainly affect RFB system performance: manifold diameter, stack current, cell standard potential, and internal resistance. A reduction in manifold diameter from 60 mm to 20 mm reduced shunt current loss by a factor of four without significantly increasing pumping loss, thus boosting round-trip efficiency (RTE) by 10%. The increase in stack current at a low flow rate increases power, while the cell standard potential and internal resistance play a crucial role in influencing both power and energy output. In summary, the modeling activities enabled the understanding of critical aspects of RFB systems, thereby serving as tools for system design and operation awareness. Full article
(This article belongs to the Special Issue Advances in Battery Energy Storage Systems)
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<p>Schematic diagram of a typical RFB system. While the current direction within the cells is displayed in discharge mode only, the movement of electrons in the external circuit is depicted with solid black lines during charge and grey arrows during discharge.</p>
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<p>Comparison of the breakdown of energy loss between (<b>a</b>) experimental data and (<b>b</b>) simulated results for a charge/discharge cycle at 50 A for the 40-cell VRFB system investigated by Trovò et al. [<a href="#B18-energies-17-05324" class="html-bibr">18</a>].</p>
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<p>RTE, energy, and breakdown of energy losses during charge and discharge at (<b>a</b>–<b>c</b>) 60 mm and (<b>d</b>–<b>f</b>) 20 mm manifold diameters, at <span class="html-italic">I</span> = 50 A and <span class="html-italic">Q</span> = 25 L/min.</p>
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<p>Sankey diagram of energy flows and loss terms of a characteristic RFB.</p>
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<p>(<b>a</b>) RTE and power discharged for different values of current and flow rates. (<b>b</b>–<b>d</b>) RTE, energy, and breakdown of energy losses during charge and discharge at the nominal operating point of 2.5 kW discharge power (i.e., <span class="html-italic">I</span> = 51.5 A, <span class="html-italic">Q</span> = 20.5 L/min).</p>
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<p>RTE as a function of the energy-to-power ratio (i.e., tank size) at the nominal operating conditions of 51.5 A and 20.5 L/min.</p>
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<p>RTE, energy, and breakdown of energy losses during charge and discharge for three couplings of electrolyte viscosity and density (<b>a</b>–<b>c</b>) <span class="html-italic">µ</span><sub>p</sub> = 0.007 Pa.s, <span class="html-italic">µ</span><sub>n</sub> = 0.0055 Pa.s, <span class="html-italic">ρ</span> = 1350 kg/m<sup>3</sup> (<b>d</b>–<b>f</b>) <span class="html-italic">µ</span><sub>p</sub> = 0.014 Pa.s, <span class="html-italic">µ</span><sub>n</sub> = 0.011 Pa.s, <span class="html-italic">ρ</span> = 1350 kg/m<sup>3</sup> (<b>g</b>–<b>i</b>) <span class="html-italic">µ</span><sub>p</sub> = <span class="html-italic">µ</span><sub>n</sub> = 0.001 Pa.s, <span class="html-italic">ρ</span> = 1000 kg/m<sup>3</sup> at E–P ratio of 6 h for a 2.5 kW power discharge.</p>
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<p>RTE, energy, and breakdown of energy losses during charge and discharge for three couplings of electrolyte viscosity and density (<b>a</b>–<b>c</b>) <span class="html-italic">µ</span><sub>p</sub> = 0.007 Pa.s, <span class="html-italic">µ</span><sub>n</sub> = 0.0055 Pa.s, <span class="html-italic">ρ</span> = 1350 kg/m<sup>3</sup> (<b>d</b>–<b>f</b>) <span class="html-italic">µ</span><sub>p</sub> = 0.014 Pa.s, <span class="html-italic">µ</span><sub>n</sub> = 0.011 Pa.s, <span class="html-italic">ρ</span> = 1350 kg/m<sup>3</sup> (<b>g</b>–<b>i</b>) <span class="html-italic">µ</span><sub>p</sub> = <span class="html-italic">µ</span><sub>n</sub> = 0.001 Pa.s, <span class="html-italic">ρ</span> = 1000 kg/m<sup>3</sup> at E–P ratio of 6 h for a 2.5 kW power discharge.</p>
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<p>RTE, energy, and breakdown of energy losses during charge and discharge at different internal resistances (<b>a</b>–<b>c</b>) default <span class="html-italic">r<sub>in</sub></span> and (<b>d</b>–<b>f</b>) half <span class="html-italic">r<sub>in</sub></span> at current, flow rate and E–P ratio of 51.5 A, 20.5 L/min and 6 h.</p>
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<p>RTE, energy, and breakdown of energy losses during charge and discharge for limiting the current window of <span class="html-italic">i</span><sub>lim</sub> × 10<sup>2/3</sup> at current (<b>a</b>–<b>c</b>) 51.5 A and (<b>d</b>–<b>f</b>) 62.5 A based on flow rate and tank volume of 20.5 L/min and 516 L, respectively.</p>
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24 pages, 6142 KiB  
Article
A Study on the Evolution Laws of Entrainment Performances Using Different Mixer Structures of Ejectors
by Hongjie Chen, Jing Ge and Zhizhou Xu
Entropy 2024, 26(11), 891; https://doi.org/10.3390/e26110891 - 22 Oct 2024
Viewed by 651
Abstract
Being the core of the ejector refrigeration system, an ejector with a suitable mixer, conical–cylindrical or cylindrical, is key to high-energy-efficiency and low-carbon systems. To promote the scientific selection of mixers for ejectors based on the theoretical models that have been validated by [...] Read more.
Being the core of the ejector refrigeration system, an ejector with a suitable mixer, conical–cylindrical or cylindrical, is key to high-energy-efficiency and low-carbon systems. To promote the scientific selection of mixers for ejectors based on the theoretical models that have been validated by experiments, the evolution laws of the entrainment ratios in the two types of ejectors are studied under various operating conditions. Furthermore, the influence mechanism of the mixer structures on the entrainment ratio of the ejector is elucidated by comparing the distribution characteristics of the entropy generation rate, pressure lift proportion, and entropy generation rate of the per-unit pressure lift in the two types of ejectors. The efficiencies of the conical-cylindrical mixer ejector and cylindrical mixer ejector exist a crossover, which makes the entrainment ratio of the conical–cylindrical mixer ejector smaller under small compression ratios but larger under large compression ratios. By changing the cylindrical mixer into a conical one, on the one hand, more pressure rise will be distributed in the diffuser, which helps to reduce the entropy increase rate in the pressurization process; on the other hand, the wall impulse effect of the conical mixer will lead to an increase in entropy generation rate of per-unit pressure lift, resulting in a growing entropy generation rate of boosting. The dominant roles are not the same with changing compression ratios, which leads to different relationships of entrainment ratio between the cylindrical and conical mixer ejectors. Full article
(This article belongs to the Section Thermodynamics)
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<p>Structure of ejectors with cylindrical (<b>a</b>) and conical–cylindrical (<b>b</b>) mixers.</p>
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<p>Structure of the cylindrical mixer ejector.</p>
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<p>A structure of the conical–cylindrical mixer ejector.</p>
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<p>The flow in the inlet region of the conical–cylindrical mixer.</p>
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<p>A calculation flow chart of the ejector with the cylindrical mixer.</p>
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<p>A calculation flow chart of the ejector with the conical–cylindrical mixer.</p>
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<p>A schematic diagram of ejector performance experiment.</p>
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<p>A device for the ejector performance test.</p>
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<p>The detachable ejector for experiments: (<b>a</b>) Ejector body; (<b>b</b>) Screw thread structure; (<b>c</b>) Ejector structure design drawing; (<b>d</b>) Nozzles; (<b>e</b>) Mixing–diffusing chambers.</p>
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<p>A structure of the nozzle.</p>
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<p>A structure of the mixing–diffusing chamber with cylindrical (<b>a</b>) and conical–cylindrical (<b>b</b>) mixer.</p>
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<p>Performance comparison of the CME and CCME.</p>
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<p>Entropy generation ratios in each part of the CME and CCME with <span class="html-italic">E</span> = 50.</p>
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<p>The pressure lift proportion as a function of the compression ratio in the mixer and diffuser.</p>
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<p>The EGRPs in the mixer and diffuser of the two types of ejectors under different compression ratios.</p>
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<p>The entropy generation ratio as a function of the compression ratio in the mixer and diffuser of the two types of ejectors.</p>
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<p>The total entropy generation ratio as a function of the compression ratio in the CME and CCME.</p>
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<p>The influence of the compression ratio on <span class="html-italic">Mr</span>.</p>
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14 pages, 1900 KiB  
Article
Combining Genetic Algorithm with Local Search Method in Solving Optimization Problems
by Velin Kralev and Radoslava Kraleva
Electronics 2024, 13(20), 4126; https://doi.org/10.3390/electronics13204126 - 20 Oct 2024
Viewed by 1003
Abstract
This research is focused on evolutionary algorithms, with genetic and memetic algorithms discussed in more detail. A graph theory problem related to finding a minimal Hamiltonian cycle in a complete undirected graph (Travelling Salesman Problem—TSP) is considered. The implementations of two approximate algorithms [...] Read more.
This research is focused on evolutionary algorithms, with genetic and memetic algorithms discussed in more detail. A graph theory problem related to finding a minimal Hamiltonian cycle in a complete undirected graph (Travelling Salesman Problem—TSP) is considered. The implementations of two approximate algorithms for solving this problem, genetic and memetic, are presented. The main objective of this study is to determine the influence of the local search method versus the influence of the genetic crossover operator on the quality of the solutions generated by the memetic algorithm for the same input data. The results show that when the number of possible Hamiltonian cycles in a graph is increased, the memetic algorithm finds better solutions. The execution time of both algorithms is comparable. Also, the number of solutions that mutated during the execution of the genetic algorithm exceeds 50% of the total number of all solutions generated by the crossover operator. In the memetic algorithm, the number of solutions that mutate does not exceed 10% of the total number of all solutions generated by the crossover operator, summed with those of the local search method. Full article
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<p>Complete undirected graph G (|V| = 12, |E| = 66).</p>
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<p>Minimal Hamiltonian cycle in graph G (|V| = 12, |E| = 66).</p>
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<p>The best-found solution by the genetic algorithm after 100 iterations.</p>
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<p>The best-found solution by the memetic algorithm after 100 iterations.</p>
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<p>Comparison between execution times for genetic algorithm and memetic algorithm.</p>
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<p>Differences between results found by the genetic algorithm and memetic algorithm.</p>
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23 pages, 3858 KiB  
Article
Sequential Task Allocation of More Scalable Artificial Dragonfly Swarms Considering Dubins Trajectory
by Yonggang Li, Dan Wen, Siyuan Zhang and Longjiang Li
Drones 2024, 8(10), 596; https://doi.org/10.3390/drones8100596 - 18 Oct 2024
Viewed by 617
Abstract
With the rapid advancement of UAV technology and the increasing complexity of tasks, multi-UAV systems face growing challenges in task execution. Traditional task allocation algorithms often perform poorly when dealing with issues such as local optima, slow convergence speed, and low convergence accuracy, [...] Read more.
With the rapid advancement of UAV technology and the increasing complexity of tasks, multi-UAV systems face growing challenges in task execution. Traditional task allocation algorithms often perform poorly when dealing with issues such as local optima, slow convergence speed, and low convergence accuracy, making it difficult to meet the demands for efficiency and practicality in real-world applications. To address these problems, this paper focuses on collaborative task allocation technology for multi-UAV. It proposes a collaborative task allocation strategy for multi-UAV in a multi-target environment, which comprehensively considers various complex constraints in practical application scenarios. The strategy utilizes Dubins curves for trajectory planning and constructs a multi-UAV collaborative task allocation model, with targets including the shortest total distance index, the minimum time index, and the trajectory coordination index. Each UAV is set as an artificial dragonfly by modifying the traditional dragonfly algorithm, incorporating differential evolution algorithms and their crossover, mutation, and selection operations to bring UAV swarms closer to the characteristics of biological dragonflies. The modifications can enhance the global scalability of artificial dragonfly swarms (ADSs), including wider search capacity, wider speed range, and more diverse search accuracy. Meanwhile, potential solutions with global convergence properties are stored to better support real-time adjustments to task allocation. The simulation results show that the proposed strategy can generate a conflict-free task execution scheme and plan the trajectory, which has advantages in changing the data scale of the UAV and the target and improves the reliability of the system to a certain extent. Full article
(This article belongs to the Collection Drones for Security and Defense Applications)
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<p>Dubins curve type.</p>
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<p>Inscribed Dubins curve.</p>
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<p>Distribution map of initial combat area.</p>
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<p>Average convergence curve.</p>
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<p>Specific time allocation of each UAV.</p>
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<p>Dubins fight planning based on collaborative task allocation.</p>
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<p>The convergence of the four different algorithms.</p>
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<p>Fitness values of target sequences for different algorithms.</p>
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<p>Comparison chart of adaptability changes in the HDEHA for different UAV numbers.</p>
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<p>Comparison of fitness values for changes in the number of UAVs.</p>
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<p>Specific time allocation of each UAV after dynamic task adjustment.</p>
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<p>Dubins flight path planning based on dynamic task adjustment scheme.</p>
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