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Search Results (219)

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22 pages, 3272 KiB  
Article
Stochastic Multi-Objective Multi-Trip AMR Routing Problem with Time Windows
by Lulu Cheng, Ning Zhao and Kan Wu
Mathematics 2024, 12(15), 2394; https://doi.org/10.3390/math12152394 - 31 Jul 2024
Viewed by 366
Abstract
In recent years, with the rapidly aging population, alleviating the pressure on medical staff has become a critical issue. To improve the work efficiency of medical staff and reduce the risk of infection, we consider the multi-trip autonomous mobile robot (AMR) routing problem [...] Read more.
In recent years, with the rapidly aging population, alleviating the pressure on medical staff has become a critical issue. To improve the work efficiency of medical staff and reduce the risk of infection, we consider the multi-trip autonomous mobile robot (AMR) routing problem in a stochastic environment. Our goal is to minimize the total expected operating cost and maximize the total service quality for patients, ensuring that each route violates the vehicle capacity and the time window with only a minimal probability. The travel time of AMRs is stochastically affected by the surrounding environment; the demand for each ward is unknown until the AMR reaches the ward, and the service time is linearly related to the actual demand. We developed a population-based tabu search algorithm (PTS) that combines the genetic algorithm with the tabu search algorithm to solve this problem. Extensive numerical experiments were conducted on the modified Solomon instances to demonstrate the efficiency of the PTS algorithm and reveal the impacts of the confidence level on the optimal solution, providing insights for decision-makers to devise delivery schemes that balance operating costs with patient satisfaction. Full article
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<p>The 2-opt operator: (<b>a</b>) before using the 2-opt operator; (<b>b</b>) after using the 2-opt operator.</p>
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<p>Relocation operator: (<b>a</b>) before using the relocation operator; (<b>b</b>) after using the relocation operator.</p>
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<p>Depot insertion operator: (<b>a</b>) the current route is infeasible; (<b>b</b>) feasible route after repair.</p>
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<p>Crossover operator.</p>
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<p>Swap operator.</p>
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<p>The mean S/N ratio plot for the PTS algorithm.</p>
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<p>Experiment to determine the population setting of the PTS algorithm: (<b>a</b>) C101 instance; (<b>b</b>) C201 instance; (<b>c</b>) R101 instance; (<b>d</b>) R201 instance; (<b>e</b>) RC101 instance; (<b>f</b>) RC201 instance.</p>
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<p>Experiment to determine the population setting of the PTS algorithm: (<b>a</b>) C101 instance; (<b>b</b>) C201 instance; (<b>c</b>) R101 instance; (<b>d</b>) R201 instance; (<b>e</b>) RC101 instance; (<b>f</b>) RC201 instance.</p>
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<p>The impact of changing confidence levels: (<b>a</b>) the impact of confidence levels of types C1, R1, and RC1 instances on TDS; (<b>b</b>) the impact of confidence levels of types C2, R2, and RC2 instances on TDS; (<b>c</b>) the impact of confidence levels of types C1, R1, and RC1 instances on the number of AMR; (<b>d</b>) the impact of confidence levels of types C2, R2, and RC2 instances on the number of AMR.</p>
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27 pages, 648 KiB  
Article
Dual-Neighborhood Tabu Search for Computing Stable Extensions in Abstract Argumentation Frameworks
by Yuanzhi Ke, Xiaogang Hu, Junjie Sun, Xinyun Wu, Caiquan Xiong and Mao Luo
Appl. Sci. 2024, 14(15), 6428; https://doi.org/10.3390/app14156428 - 23 Jul 2024
Viewed by 465
Abstract
Abstract argumentation has become one of the important fields of artificial intelligence. This paper proposes a dual-neighborhood tabu search (DNTS) method specifically designed to find a single stable extension in abstract argumentation frameworks. The proposed algorithm implements an improved dual-neighborhood strategy incorporating a [...] Read more.
Abstract argumentation has become one of the important fields of artificial intelligence. This paper proposes a dual-neighborhood tabu search (DNTS) method specifically designed to find a single stable extension in abstract argumentation frameworks. The proposed algorithm implements an improved dual-neighborhood strategy incorporating a fast neighborhood evaluation method. In addition, by introducing techniques such as tabu and perturbation, this algorithm is able to jump out of the local optimum, which significantly improves the performance of the algorithm. In order to evaluate the effectiveness of the method, the performance of the algorithm on more than 300 randomly generated benchmark datasets was studied and compared with the algorithm in the literature. In the experiment, DNTS outperforms the other method regarding time consumption in more than 50 instances and surpasses the other meta-heuristic method in the number of solved cases. Further analysis shows that the initialization method, the tabu strategy, and the perturbation technique help guarantee the efficiency of the proposed DNTS. Full article
(This article belongs to the Special Issue Heuristic and Evolutionary Algorithms for Engineering Optimization)
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<p>Example of a stable extension, with the stable extension marked in red.</p>
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<p>Example of abstract argumentation frameworks.</p>
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<p>Example of grounded extension. Directed edges represent attack relations. (<b>a</b>) there is a relationship of defense, with <span class="html-italic">a</span> defending against <span class="html-italic">c</span>; (<b>b</b>) there is a relationship of self-attack; (<b>c</b>) there is a relationship of mutual attack.</p>
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<p>Stable labeling.</p>
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<p>Example of a neighborhood move.</p>
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<p>Example of abstract argumentation frameworks.</p>
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<p>The evaluation of iterations per second with the growth of the problem size. The x-axis represents the increasing size of instances from left to right. (<b>a</b>) Experimental results for sparse graphs; (<b>b</b>) experimental results for dense graphs.</p>
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19 pages, 1296 KiB  
Article
A Local Search Algorithm with Vertex Weighting Strategy and Two-Level Configuration Checking for the Minimum Connected Dominating Set Problem
by Ruizhi Li, Jintao He, Shangqiong Liu, Shuli Hu and Minghao Yin
Biomimetics 2024, 9(7), 429; https://doi.org/10.3390/biomimetics9070429 - 15 Jul 2024
Viewed by 489
Abstract
The minimum connected dominating set problem is a combinatorial optimization problem with a wide range of applications in many fields. We propose an efficient local search algorithm to solve this problem. In this work, first, we adopt a new initial solution construction method [...] Read more.
The minimum connected dominating set problem is a combinatorial optimization problem with a wide range of applications in many fields. We propose an efficient local search algorithm to solve this problem. In this work, first, we adopt a new initial solution construction method based on three simplification rules. This method can reduce the size of the original graph and thus obtain a high-quality initial solution. Second, we propose an approach based on a two-level configuration checking strategy and a tabu strategy to reduce the cycling problem. Third, we introduce a perturbation strategy and a vertex weighting strategy to help the algorithm be able to jump out of the local optimum effectively. Fourth, we combine the scoring functions Cscore and Mscore with the aforementioned strategies to propose effective methods for selecting vertices. These methods assist the algorithm in selecting vertices that are suitable for addition to or removal from the current candidate solution. Finally, we verify the performance advantages of the local search algorithm by comparing it with existing optimal heuristic algorithms on two sets of instances. The experimental results show that the algorithm exhibits better performance on two sets of classical instances. Full article
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<p>An example of applying simplification rules.</p>
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<p>The comparison of ‘<span class="html-italic">BEST</span>’ values of greedy, ACO, ACO + PCS, GRASP, VDNS, MSLS, and PCC<sup>2</sup>LS on common UDG instances.</p>
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<p>The comparison of ‘<span class="html-italic">Average</span>’ values of greedy, ACO, ACO + PCS, GRASP, VDNS, MSLS, and PCC<sup>2</sup>LS on common UDG instances.</p>
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<p>The run time of PCC<sup>2</sup>LS on common UDG benchmark instances.</p>
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<p>Comparing the time needed to find the best solution between PCC<sup>2</sup>LS and other algorithms on common UDG instances.</p>
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20 pages, 3137 KiB  
Article
Container Yard Layout Design Problem with an Underground Logistics System
by Bin Lu, Mengxia Zhang, Xiaojie Xu, Chengji Liang, Yu Wang and Hongchen Liu
J. Mar. Sci. Eng. 2024, 12(7), 1103; https://doi.org/10.3390/jmse12071103 - 28 Jun 2024
Viewed by 628
Abstract
In recent years, underground logistics systems have attracted more and more attention from scholars and are considered to be a promising new green and intelligent transportation mode. This paper proposes a yard design problem considering an underground container logistics system. The structure and [...] Read more.
In recent years, underground logistics systems have attracted more and more attention from scholars and are considered to be a promising new green and intelligent transportation mode. This paper proposes a yard design problem considering an underground container logistics system. The structure and workflow of the underground container logistics system are analyzed, and key features are recognized for the yard design problem, such as the container block layout direction, the lane configuration in the yard, and the number of container blocks. We formulate the problem into mathematical models under different scenarios of the key features with the comprehensive objective of maximizing the total throughput and minimizing the total operation cost simultaneously. An improved tabu search algorithm is designed to solve the problem. Experimental results show that the proposed algorithm can generate a satisfactory layout design solution for a real-size instance. Our research studies different container yard design options for introducing the underground logistics system into port terminals, which provides an important scientific foundation for promoting the application of underground container logistics systems. Full article
(This article belongs to the Section Ocean Engineering)
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<p>Schematic diagram of the underground container logistics system.</p>
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<p>Workflow of underground container logistics system.</p>
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<p>Schematic diagram of the container yard layout with underground system. (<b>a</b>) Top view of container yard layout with underground system. (<b>b</b>) Example layout of the container yard with multiple blocks.</p>
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<p>Front view of two container blocks in a yard.</p>
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<p>Container truck transportation routes in single-lane and dual-lane modes. (<b>a</b>) Container truck transportation routes in single-lane layout; (<b>b</b>) Container truck transportation routes in dual-lane layout.</p>
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<p>Improved Tabu Search Algorithm.</p>
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<p>Algorithm iteration diagram.</p>
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25 pages, 821 KiB  
Article
Enhancing Service Quality of On-Demand Transportation Systems Using a Hybrid Approach with Customized Heuristics
by Sonia Nasri, Hend Bouziri and Wassila Aggoune Mtalaa
Smart Cities 2024, 7(4), 1551-1575; https://doi.org/10.3390/smartcities7040063 - 26 Jun 2024
Viewed by 935
Abstract
As customers’ expectations continue to rise, advanced on-demand transport services face the challenge of meeting new requirements. This study addresses a specific transportation issue belonging to dial-a-ride problems, including constraints aimed at fulfilling customer needs. In order to provide more efficient on-demand transportation [...] Read more.
As customers’ expectations continue to rise, advanced on-demand transport services face the challenge of meeting new requirements. This study addresses a specific transportation issue belonging to dial-a-ride problems, including constraints aimed at fulfilling customer needs. In order to provide more efficient on-demand transportation solutions, we propose a new hybrid evolutionary computation method. This method combines customized heuristics including two exchanged mutation operators, a crossover, and a tabu search. These optimization techniques have been empirically proven to support advanced designs and reduce operational costs, while significantly enhancing service quality. A comparative analysis with an evolutionary local search method from the literature has demonstrated the effectiveness of our approach across small-to-large-scale problems. The main results show that service providers can optimize their scheduling operations, reduce travel costs, and ensure a high level of service quality from the customer’s perspective. Full article
(This article belongs to the Section Smart Transportation)
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<p>An on-demand transport network with two requests having time windows, maximal ride times, and loads.</p>
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<p>The vehicle tour schedule before the time windows calculation.</p>
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<p>The vehicle tour schedule after the time windows calculation.</p>
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<p>Flow chart of the ETS algorithm.</p>
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<p>Construction of a new solution with the interruption operator.</p>
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<p>Construction of a new solution with the swap operator.</p>
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<p>An illustrative example of the SXO.</p>
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<p>An illustrative example of the neighborhood strategy of the TS.</p>
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<p>The solution of the <math display="inline"><semantics> <mrow> <mi>d</mi> <mn>75</mn> </mrow> </semantics></math> instance obtained with the ELS.</p>
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<p>The schedule time for request 9 in the vehicle (<math display="inline"><semantics> <mrow> <mi>v</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>) obtained with the ELS.</p>
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<p>The solution of the <math display="inline"><semantics> <mrow> <mi>d</mi> <mn>75</mn> </mrow> </semantics></math> instance obtained with the ETS.</p>
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<p>The details related to requests 7 and 9 in <math display="inline"><semantics> <mrow> <mo>(</mo> <mi>v</mi> <mo>=</mo> <mn>1</mn> <mo>)</mo> </mrow> </semantics></math> in the solution obtained with the ETS.</p>
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<p>Number of solutions obtained with the ETS that are better or worse than the solutions of the ELS.</p>
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18 pages, 2925 KiB  
Article
Variable Neighborhood Search for Minimizing the Makespan in a Uniform Parallel Machine Scheduling
by Khaled Bamatraf and Anis Gharbi
Systems 2024, 12(6), 221; https://doi.org/10.3390/systems12060221 - 20 Jun 2024
Viewed by 767
Abstract
This paper investigates a uniform parallel machine scheduling problem for makespan minimization. Due to the problem’s NP-hardness, much effort from researchers has been directed toward proposing heuristic and metaheuristic algorithms that can find an optimal or a near-optimal solution in a reasonable amount [...] Read more.
This paper investigates a uniform parallel machine scheduling problem for makespan minimization. Due to the problem’s NP-hardness, much effort from researchers has been directed toward proposing heuristic and metaheuristic algorithms that can find an optimal or a near-optimal solution in a reasonable amount of time. This work proposes two versions of a variable neighborhood search (VNS) algorithm with five neighborhood structures, differing in their initial solution generation strategy. The first uses the longest processing time (LPT) rule, while the second introduces a novel element by utilizing a randomized longest processing time (RLPT) rule. The neighborhood structures for both versions were modified from the literature to account for the variable processing times in uniform parallel machines. We evaluated the performance of both VNS versions using a numerical example, comparing them against a genetic algorithm and a tabu search from existing literature. Results showed that the proposed VNS algorithms were competitive and obtained the optimal solution with much less effort. Additionally, we assessed the performance of the VNS algorithms on randomly generated instances. For small-sized instances, we compared their performance against the optimal solution obtained from a mathematical formulation, and against lower bounds derived from the literature for larger instances. Computational results showed that the VNS version with the randomized LPT rule (RLPT) as the initial solution (RVNS) outperformed that with the LPT rule as the initial solution (LVNS). Moreover, RVNS found the optimal solution in 90.19% of the small instances and yielded an average relative gap of about 0.15% for all cases. Full article
(This article belongs to the Special Issue Management and Simulation of Digitalized Smart Manufacturing Systems)
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<p>Flowchart of the proposed VNS algorithms.</p>
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<p>Gantt chart schedule for <span class="html-italic">LPT</span>.</p>
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<p>Gantt chart schedule for <span class="html-italic">LVNS</span>.</p>
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<p>Average RPD for the LPT and RLPT heuristics.</p>
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<p>Bar chart for the outperformance comparison between LPT and RLPT algorithms.</p>
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<p>Average RPD for the LVNS and RVNS algorithms.</p>
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<p>Bar chart for the outperformance comparison of LVNS and RVNS algorithms.</p>
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<p>Average CPU time reduction with the LVNS upper bound.</p>
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26 pages, 2715 KiB  
Article
Hybrid Genetic Algorithm and Tabu Search for Solving Preventive Maintenance Scheduling Problem for Cogeneration Plants
by Khaled Alhamad and Yousuf Alkhezi
Mathematics 2024, 12(12), 1881; https://doi.org/10.3390/math12121881 - 17 Jun 2024
Viewed by 449
Abstract
Preventive Maintenance (PM) is a periodic maintenance strategy that has great results for devices in extending their lives, increasing productivity, and, most importantly, helping to avoid unexpected breakdowns and their costly consequences. Preventive maintenance scheduling (PMS) is determining the time for carrying out [...] Read more.
Preventive Maintenance (PM) is a periodic maintenance strategy that has great results for devices in extending their lives, increasing productivity, and, most importantly, helping to avoid unexpected breakdowns and their costly consequences. Preventive maintenance scheduling (PMS) is determining the time for carrying out PM, and it represents a sensitive issue in terms of impact on production if the time for the PM process is not optimally distributed. This study employs hybrid heuristic methods, integrating Genetic Algorithm (GA) and Tabu Search (TS), to address the PMS problem. Notably, the search for an optimal solution remained elusive with GA alone until the inclusion of TS. The resultant optimal solution is achieved swiftly, surpassing the time benchmarks set by conventional methods like integer programming and nonlinear integer programming. A comparison with a published article that used metaheuristics was also applied in order to evaluate the effectiveness of the proposed hybrid approach in terms of solution quality and convergence speed. Moreover, sensitivity analysis underscores the robustness and efficacy of the hybrid approach, consistently yielding optimal solutions across diverse scenarios. The schedule created exceeds standards set by waterworks experts, yielding significant water and electricity surpluses—16.6% and 12.1%, respectively—while simultaneously matching or surpassing total production levels. This method can be used for power plants in private or public sectors to generate an optimal PMS, save money, and avoid water or electricity cuts. In summary, this hybrid approach offers an efficient and effective solution for optimizing PMS, presenting opportunities for enhancement across various industries. Full article
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<p>The preventive maintenance workflow.</p>
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<p>A population (chromosomes) represents PMS, and each gene represents a week in the time horizon.</p>
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<p>Representation of chromosomes, where the number in the gene represents equipment under maintenance.</p>
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<p>Crossover operation.</p>
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<p>Mutation operation.</p>
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<p>PMS generation process for all equipment. (<span class="html-italic">tn</span> means tenure).</p>
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<p>(<b>a</b>) Total demand for water for 52 weeks. (<b>b</b>) Total demand for power for 52 weeks.</p>
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<p>(<b>a</b>) Turbine equipment system output for the proposed method. (<b>b</b>) Distiller equipment system output for the proposed method.</p>
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<p>(<b>a</b>) Turbine equipment system output for the proposed method. (<b>b</b>) Distiller equipment system output for the proposed method.</p>
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<p>(<b>a</b>) Turbine equipment system output for MEW. (<b>b</b>) Distiller equipment system output for MEW.</p>
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<p>Comparison between the three methods in terms of CPU time (Water and Electricity surplus production).</p>
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20 pages, 2890 KiB  
Article
A Hybrid Genetic Algorithm for Ground Station Scheduling Problems
by Longzeng Xu, Changhong Yu, Bin Wu and Ming Gao
Appl. Sci. 2024, 14(12), 5045; https://doi.org/10.3390/app14125045 - 10 Jun 2024
Viewed by 557
Abstract
In recent years, the substantial growth in satellite data transmission tasks and volume, coupled with the limited availability of ground station hardware resources, has exacerbated conflicts among missions and rendered traditional scheduling algorithms inadequate. To address this challenge, this paper introduces an improved [...] Read more.
In recent years, the substantial growth in satellite data transmission tasks and volume, coupled with the limited availability of ground station hardware resources, has exacerbated conflicts among missions and rendered traditional scheduling algorithms inadequate. To address this challenge, this paper introduces an improved tabu genetic hybrid algorithm (ITGA) integrated with heuristic rules for the first time. Firstly, a constraint satisfaction model for satellite data transmission tasks is established, considering multiple factors such as task execution windows, satellite–ground visibility, and ground station capabilities. Leveraging heuristic rules, an initial population of high-fitness chromosomes is selected for iterative refinement. Secondly, the proposed hybrid algorithm iteratively evolves this population towards optimal solutions. Finally, the scheduling plan with the highest fitness value is selected as the best strategy. Comparative simulation experimental results demonstrate that, across four distinct scenarios, our algorithm achieves improvements in the average task success rate ranging from 1.5% to 19.8% compared to alternative methods. Moreover, it reduces the average algorithm execution time by 0.5 s to 28.46 s and enhances algorithm stability by 0.8% to 27.7%. This research contributes a novel approach to the efficient scheduling of satellite data transmission tasks. Full article
(This article belongs to the Section Aerospace Science and Engineering)
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<p>Structure of ground receiving system.</p>
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<p>Satellite visible time conflict diagram.</p>
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<p>Resource usage conflict diagram.</p>
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<p>Flow chart of ITGA.</p>
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<p>Chromosome: the number indicates the task number, and the location sequence indicates the execution sequence.</p>
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<p>Flow chart of the initial population generation.</p>
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<p>Crossover operation. Different colors indicate chromosomal position changes.</p>
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<p>Mutation operation. P1, P2, and different colors indicate chromosomal position changes.</p>
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<p>Ground resource allocation results solved by the ITGA in case 2.</p>
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<p>ITGA antenna usage time distribution diagram.</p>
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<p>Comparison of convergence speeds of various algorithms in a specific experiment.</p>
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<p>Comparison of algorithm stability.</p>
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18 pages, 1008 KiB  
Article
Network Reconfiguration for Loss Reduction Using Tabu Search and a Voltage Drop
by Dionicio Zocimo Ñaupari Huatuco, Luiz Otávio Pinheiro Filho, Franklin Jesus Simeon Pucuhuayla and Yuri Percy Molina Rodriguez
Energies 2024, 17(11), 2744; https://doi.org/10.3390/en17112744 - 4 Jun 2024
Viewed by 456
Abstract
This paper introduces a new algorithm designed to address the challenge of distribution network reconfiguration, employing the tabu search metaheuristic in conjunction with the voltage drop concept. Distinguishing itself from existing methods, our proposed approach not only utilizes voltage drop for obtaining the [...] Read more.
This paper introduces a new algorithm designed to address the challenge of distribution network reconfiguration, employing the tabu search metaheuristic in conjunction with the voltage drop concept. Distinguishing itself from existing methods, our proposed approach not only utilizes voltage drop for obtaining the initial solution but also introduces a novel technique for generating a candidate solution neighborhood. This method leverages both randomness and voltage drop, ensuring a smooth and steady descent during algorithm execution. The primary goal of our algorithm is to minimize active power losses within distribution networks. To validate its effectiveness, the proposed method underwent testing on three commonly referenced distribution systems: the 33-Bus, 69-Bus, and 94-Bus systems, widely acknowledged in the literature. A pivotal aspect of our work involves the synergy of the tabu search algorithm with a combination of both random and deterministic methods for generating neighbors. This strategic amalgamation plays a crucial role, enabling rapid execution while consistently yielding high-quality solutions. Additionally, the adoption of the electric distance method for generating the initial solution adds significant value, offering a commendable solution with minimal computational effort. Comparative assessments against other algorithms documented in the literature underscore the superior efficiency of our proposed algorithm. Full article
(This article belongs to the Section F: Electrical Engineering)
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<p>Two-bus example system.</p>
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<p>The initial solution flowchart.</p>
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<p>Example of one iteration for the hybrid neighborhood algorithm. (<b>a</b>) The random algorithm for even iterations. (<b>b</b>) The <math display="inline"><semantics> <mo>Δ</mo> </semantics></math>V algorithm for odd iterations.</p>
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<p>Single line diagram of IEEE-33 bus distribution system. Adapted from [<a href="#B25-energies-17-02744" class="html-bibr">25</a>].</p>
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<p>Voltages before and after reconfiguration for 33-Bus system.</p>
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<p>Single line diagram of 69-Bus distribution system. Adapted from [<a href="#B27-energies-17-02744" class="html-bibr">27</a>].</p>
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<p>Voltages before and after reconfiguration for 69-Bus system.</p>
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<p>Single-line diagram of 94-Bus distribution system. Adapted from [<a href="#B26-energies-17-02744" class="html-bibr">26</a>].</p>
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<p>Voltages before and after reconfiguration for 94-Bus system.</p>
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28 pages, 1809 KiB  
Article
An Adaptive Search Algorithm for Multiplicity Dynamic Flexible Job Shop Scheduling with New Order Arrivals
by Linshan Ding, Zailin Guan, Dan Luo, Mudassar Rauf and Weikang Fang
Symmetry 2024, 16(6), 641; https://doi.org/10.3390/sym16060641 - 22 May 2024
Viewed by 913
Abstract
In today’s customer-centric economy, the demand for personalized products has compelled corporations to develop manufacturing processes that are more flexible, efficient, and cost-effective. Flexible job shops offer organizations the agility and cost-efficiency that traditional manufacturing processes lack. However, the dynamics of modern manufacturing, [...] Read more.
In today’s customer-centric economy, the demand for personalized products has compelled corporations to develop manufacturing processes that are more flexible, efficient, and cost-effective. Flexible job shops offer organizations the agility and cost-efficiency that traditional manufacturing processes lack. However, the dynamics of modern manufacturing, including machine breakdown and new order arrivals, introduce unpredictability and complexity. This study investigates the multiplicity dynamic flexible job shop scheduling problem (MDFJSP) with new order arrivals. To address this problem, we incorporate the fluid model to propose a fluid randomized adaptive search (FRAS) algorithm, comprising a construction phase and a local search phase. Firstly, in the construction phase, a fluid construction heuristic with an online fluid dynamic tracking policy generates high-quality initial solutions. Secondly, in the local search phase, we employ an improved tabu search procedure to enhance search efficiency in the solution space, incorporating symmetry considerations. The results of the numerical experiments demonstrate the superior effectiveness of the FRAS algorithm in solving the MDFJSP when compared to other algorithms. Specifically, the proposed algorithm demonstrates a superior quality of solution relative to existing algorithms, with an average improvement of 29.90%; and exhibits an acceleration in solution speed, with an average increase of 1.95%. Full article
(This article belongs to the Special Issue Symmetry in Computing Algorithms and Applications)
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<p>An example of the MDFJSP with new order arrivals.</p>
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<p>(<b>a</b>) A flow diagram of the dynamic scheduling system. (<b>b</b>) A basic flow of the FRAS algorithm.</p>
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<p>An example of public critical operations.</p>
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<p>The trend of the factor level.</p>
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<p>(<b>a</b>) The average makespan of different cases. (<b>b</b>) The interval plot for <math display="inline"><semantics> <mrow> <mi>R</mi> <mi>P</mi> <mi>D</mi> </mrow> </semantics></math> of the five algorithms. (<b>c</b>) The total computation time. (<b>d</b>) The total response time.</p>
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<p>The mean response time of the four algorithms at each rescheduling point on four represent instances.</p>
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<p>The production process of the motorcycle parts manufacturing factory.</p>
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<p>The initial scheduling scheme and rescheduling scheme of Data01 obtained by the FRAS algorithm.</p>
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<p>The average makespan of different static cases and interval plot for <math display="inline"><semantics> <mrow> <mi>R</mi> <mi>P</mi> <mi>D</mi> </mrow> </semantics></math> of the five algorithms.</p>
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<p>The mean convergence curve of LSM-Mk01-LSM-Mk10.</p>
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<p>The impact of the time interval between new orders’ arrival on the objective and the mean total response time (TR).</p>
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31 pages, 3858 KiB  
Article
A Decision Support Framework for Aircraft Arrival Scheduling and Trajectory Optimization in Terminal Maneuvering Areas
by Dongdong Gui, Meilong Le, Zhouchun Huang and Andrea D’Ariano
Aerospace 2024, 11(5), 405; https://doi.org/10.3390/aerospace11050405 - 16 May 2024
Viewed by 781
Abstract
This study introduces a decision support framework that integrates aircraft trajectory optimization and arrival scheduling to facilitate efficient management of descent operations for arriving aircraft within terminal maneuvering areas. The framework comprises three modules designed to tackle specific challenges in the descent process. [...] Read more.
This study introduces a decision support framework that integrates aircraft trajectory optimization and arrival scheduling to facilitate efficient management of descent operations for arriving aircraft within terminal maneuvering areas. The framework comprises three modules designed to tackle specific challenges in the descent process. The first module formulates and solves a trajectory optimization problem, generating a range of candidate descent trajectories for each arriving aircraft. The options for descent operations include step-down descent operation, Continuous Descent Operation (CDO), and CDO with a lateral path stretching strategy. The second module addresses the assignment of conflict-free trajectories to aircraft, determining precise arrival times at each waypoint. This is achieved by solving an aircraft arrival scheduling problem. To overcome computational complexities, a novel variable neighborhood search algorithm is proposed as the solution approach. This algorithm utilizes three neighborhood structures within an extended relaxing and solving framework, and incorporates a tabu search algorithm to enhance the efficiency of the search process in the solution space. The third module focuses on comparing the total cost incurred from flight delays and fuel consumption across the three descent operations, enabling the selection of the most suitable operation for the descent process. The decision support framework is evaluated using real air traffic data from Guangzhou Baiyun International Airport. Experimental results demonstrate that the framework effectively supports air traffic controllers by scheduling more cost-efficient descent operations for arrival aircraft. Full article
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<p>A simplified scenario for our studied problem.</p>
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<p>A schematic diagram of the earliest and latest trajectories for three descent operations: (<b>a</b>) Vertical profile of descent trajectories. (<b>b</b>) Travel time window in an air segment.</p>
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<p>An overview of the proposed decision support framework.</p>
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<p>The process for the neighborhood structure <math display="inline"><semantics> <msub> <mi mathvariant="script">N</mi> <mn>1</mn> </msub> </semantics></math>.</p>
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<p>An example of the relaxing neighborhood.</p>
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<p>An example of a swap operation in neighborhood structure <math display="inline"><semantics> <msub> <mi mathvariant="script">N</mi> <mn>2</mn> </msub> </semantics></math>.</p>
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<p>An example of a change operation within neighborhood structure <math display="inline"><semantics> <msub> <mi mathvariant="script">N</mi> <mn>3</mn> </msub> </semantics></math>.</p>
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<p>The rolling horizon approach.</p>
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<p>GBIA E-TMA configurations: (<b>a</b>) E-TMA of GBIA. (<b>b</b>) Path stretching design. (<b>c</b>) Parallel runway operation pattern.</p>
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<p>Hourly movements at GBIA.</p>
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<p>Effect on the total delay and fuel consumption for the SDO (solid lines) and the ps-CDO (dashed lines) to weight parameter <math display="inline"><semantics> <mi>λ</mi> </semantics></math>.</p>
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<p>Costs results for the SDO (solid lines) and the ps-CDO (dashed lines) to weight parameter <math display="inline"><semantics> <mi>λ</mi> </semantics></math>.</p>
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<p>Optimal descent operation solutions for arriving aircraft hourly throughout the day: (<b>a</b>) Case (i): arrival traffic only. (<b>b</b>) Case (ii): both arrival and departure traffic.</p>
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18 pages, 4003 KiB  
Article
Research on Genetic Algorithm Optimization with Fusion Tabu Search Strategy and Its Application in Solving Three-Dimensional Packing Problems
by Zhenjia Kang, Yong Guan, Jiake Wang and Pengzhan Chen
Symmetry 2024, 16(4), 449; https://doi.org/10.3390/sym16040449 - 7 Apr 2024
Viewed by 1047
Abstract
Symmetry is an important principle and characteristic that is prevalent in nature and artificial environments. In the three-dimensional packing problem, leveraging the inherent symmetry of goods and the symmetry of the packing space can enhance packing efficiency and utilization.The three-dimensional packing problem is [...] Read more.
Symmetry is an important principle and characteristic that is prevalent in nature and artificial environments. In the three-dimensional packing problem, leveraging the inherent symmetry of goods and the symmetry of the packing space can enhance packing efficiency and utilization.The three-dimensional packing problem is an NP-hard combinatorial optimization problem in the field of modern logistics, with high computational complexity. This paper proposes an improved genetic algorithm by incorporating a fusion tabu search strategy to address this problem. The algorithm employs a three-dimensional loading mathematical model and utilizes a wall-building method under residual space constraints for stacking goods. Furthermore, adaptation of fitness variation strategy, chromosome adjustment, and tabu search algorithm are introduced to balance the algorithm’s global and local search capabilities, as well as to enhance population diversity and convergence speed. Through testing on benchmark cases such as Bischoff and Ratcliff, the improved algorithm demonstrates an average increase of over 3% in packing space utilization compared to traditional genetic algorithms and other heuristic algorithms, validating its feasibility and effectiveness. The proposed improved genetic algorithm provides new insights for solving three-dimensional packing problems and optimizing logistics loading schedules, offering promising prospects for various applications. Full article
(This article belongs to the Section Computer)
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<p>The schematic diagram of container and item placement.</p>
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<p>The schematic diagram of the item wall.</p>
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<p>The schematic diagram of the remaining space.</p>
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<p>The schematic diagram of the sequence of item wall placement.Roman numerals <span class="html-italic">I</span> to <span class="html-italic">X</span> denote the sequence of filling the item wall.</p>
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<p>The schematic diagram of the orientations of item placement. (<b>a</b>–<b>f</b>) diagrams represent the six orientations of the cargo in three-dimensional space.</p>
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<p>The schematic diagram of the process of crossover.</p>
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<p>The schematic diagram of the process of mutation.</p>
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<p>The schematic diagram of the flowchart of the algorithm.</p>
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<p>The schematic diagram of the depth table.</p>
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<p>The schematic diagram of the process of crossover.</p>
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<p>Explanation diagram of the solution.</p>
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<p>The packing effect diagram for instance BR1.</p>
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<p>The packing effect diagram for instance BR2.</p>
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<p>The packing effect diagram for instance BR3.</p>
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<p>The packing effect diagram for instance BR4.</p>
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<p>The packing effect diagram for instance BR5.</p>
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23 pages, 4680 KiB  
Article
Order Distribution and Routing Optimization for Takeout Delivery under Drone–Rider Joint Delivery Mode
by Fuqiang Lu, Runxue Jiang, Hualing Bi and Zhiyuan Gao
J. Theor. Appl. Electron. Commer. Res. 2024, 19(2), 774-796; https://doi.org/10.3390/jtaer19020041 - 3 Apr 2024
Cited by 7 | Viewed by 1218
Abstract
Order distribution and routing optimization of takeout delivery is a challenging research topic in the field of e-commerce. In this paper, we propose a drone–rider joint delivery mode with multi-distribution center collaboration for the problems of limited-service range, unreasonable distribution, high delivery cost, [...] Read more.
Order distribution and routing optimization of takeout delivery is a challenging research topic in the field of e-commerce. In this paper, we propose a drone–rider joint delivery mode with multi-distribution center collaboration for the problems of limited-service range, unreasonable distribution, high delivery cost, and tight time windows in the takeout delivery process. The model is constructed with the minimum delivery cost and the overall maximum customer satisfaction as the objective function, and a two-stage heuristic algorithm is designed to solve the model. In the first stage, Euclidean distance is used to classify customers into the regions belonging to different distribution centers, and the affinity propagation (AP) clustering algorithm is applied to allocate orders from different distribution centers. The second stage uses an improved tabu search algorithm for route optimization based on specifying the number of rider and drone calls. This paper takes China’s Ele.me and Meituan takeout as the reference object and uses the Solomon data set for research. The experimental results show that compared with the traditional rider delivery mode, the drone–rider joint delivery mode with multiple distribution center collaboration can effectively reduce the number of riders used, lower the delivery cost, and improve the overall customer satisfaction. Full article
(This article belongs to the Section e-Commerce Analytics)
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<p>Drone–rider joint delivery mode.</p>
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<p>Traditional rider delivery mode and drone–rider joint delivery mode.</p>
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<p>Customer satisfaction function.</p>
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<p>Improved tabu search algorithm flowchart.</p>
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<p>2-opt operators.</p>
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<p>Insert operators.</p>
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<p>Reverse operators.</p>
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<p>Two-stage heuristic algorithm flowchart.</p>
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<p>Required delivery order locations in both modes: (<b>a</b>) rider delivery mode and (<b>b</b>) drone–rider joint delivery mode.</p>
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<p>Results of order distribution under traditional rider delivery mode and joint drone–rider delivery mode.</p>
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<p>Traditional rider delivery route diagram.</p>
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<p>Drone–rider joint delivery route diagram.</p>
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<p>Comparison of running time of different algorithms under different instances (<b>left</b>) and comparison of customer satisfaction of different algorithms under different instances (<b>right</b>).</p>
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<p>Comparison of fitness of different algorithms under three different instances.</p>
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<p>Comparison of fitness of different algorithms under three different instances.</p>
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<p>Comparison of standard deviations of different algorithms under three different instances.</p>
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14 pages, 927 KiB  
Article
Enhancing Security in Visible Light Communication: A Tabu-Search-Based Method for Transmitter Selection
by Ge Shi, Wei Cheng, Xiang Gao, Fupeng Wei, Heng Zhang and Qingzheng Wang
Sensors 2024, 24(6), 1906; https://doi.org/10.3390/s24061906 - 16 Mar 2024
Viewed by 663
Abstract
In this paper, we explore the secrecy performance of a visible light communication (VLC) system consisting of distributed light-emitting diodes (LEDs) and multiple users (UEs) randomly positioned within an indoor environment while considering the presence of an eavesdropper. To enhance the confidentiality of [...] Read more.
In this paper, we explore the secrecy performance of a visible light communication (VLC) system consisting of distributed light-emitting diodes (LEDs) and multiple users (UEs) randomly positioned within an indoor environment while considering the presence of an eavesdropper. To enhance the confidentiality of the system, we formulate a problem of maximizing the sum secrecy rate for UEs by searching for an optimal LED for each UE. Due to the non-convex and non-continuous nature of this security maximization problem, we propose an LED selection algorithm based on tabu search to avoid getting trapped in local optima and expedite the search process by managing trial vectors from previous iterations. Moreover, we introduce three LED selection strategies with a low computational complexity. The simulation results demonstrate that the proposed algorithm achieves a secrecy performance very close to the global optimal value, with a gap of less than 1%. Additionally, the proposed strategies exhibit a performance gap of 28% compared to the global optimal. Full article
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<p>System model.</p>
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<p>The procedure of the proposed algorithm (Orange diamond and blue rectangle are depicted for the decision and process in the algorithm, respectively).</p>
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<p>Comparison of the proposed algorithm and global search regarding convergence performance.</p>
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<p>Placement of LEDs (blue) and example of a layout for UEs (magenta) and an Eve (green).</p>
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<p>Average sum secrecy rate with respect to the maximum power of each LED (randomly generated positions of UEs and Eves for each instance).</p>
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<p>Average sum secrecy rate with respect to the total number of randomly placed UEs.</p>
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<p>Average sum secrecy rate with respect to the Eve’s FoV (randomly generated positions of UEs and Eves for each instance).</p>
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<p>Average sum secrecy rate with respect to the UEs’ FoVs (randomly generated positions of UEs and Eves for each instance).</p>
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<p>Average sum secrecy rate with respect to the localization error of the Eve (randomly generated positions of UEs and Eves for each instance).</p>
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40 pages, 23417 KiB  
Article
MTS-PRO2SAT: Hybrid Mutation Tabu Search Algorithm in Optimizing Probabilistic 2 Satisfiability in Discrete Hopfield Neural Network
by Ju Chen, Yuan Gao, Mohd Shareduwan Mohd Kasihmuddin, Chengfeng Zheng, Nurul Atiqah Romli, Mohd. Asyraf Mansor, Nur Ezlin Zamri and Chuanbiao When
Mathematics 2024, 12(5), 721; https://doi.org/10.3390/math12050721 - 29 Feb 2024
Cited by 1 | Viewed by 865
Abstract
The primary objective of introducing metaheuristic algorithms into traditional systematic logic is to minimize the cost function. However, there is a lack of research on the impact of introducing metaheuristic algorithms on the cost function under different proportions of positive literals. In order [...] Read more.
The primary objective of introducing metaheuristic algorithms into traditional systematic logic is to minimize the cost function. However, there is a lack of research on the impact of introducing metaheuristic algorithms on the cost function under different proportions of positive literals. In order to fill in this gap and improve the efficiency of the metaheuristic algorithm in systematic logic, we proposed a metaheuristic algorithm based on mutation tabu search and embedded it in probabilistic satisfiability logic in discrete Hopfield neural networks. Based on the traditional tabu search algorithm, the mutation operators of the genetic algorithm were combined to improve its global search ability during the learning phase and ensure that the cost function of the systematic logic converged to zero at different proportions of positive literals. Additionally, further optimization was carried out in the retrieval phase to enhance the diversity of solutions. Compared with nine other metaheuristic algorithms and exhaustive search algorithms, the proposed algorithm was superior to other algorithms in terms of time complexity and global convergence, and showed higher efficiency in the search solutions at the binary search space, consolidated the efficiency of systematic logic in the learning phase, and significantly improved the diversity of the global solution in the retrieval phase of systematic logic. Full article
(This article belongs to the Section Fuzzy Sets, Systems and Decision Making)
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<p>Generation process of neighborhood solution.</p>
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<p>Generation strategy to candidate solution.</p>
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<p>Flowchart of MTS.</p>
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<p><math display="inline"><semantics> <mrow> <mi>M</mi> <mi>A</mi> <msub> <mi>E</mi> <mrow> <mi>l</mi> <mi>e</mi> <mi>a</mi> <mi>r</mi> <mi>n</mi> </mrow> </msub> </mrow> </semantics></math> evaluation for all experimental models.</p>
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<p><math display="inline"><semantics> <mrow> <mi>M</mi> <mi>A</mi> <msub> <mi>E</mi> <mrow> <mi>l</mi> <mi>e</mi> <mi>a</mi> <mi>r</mi> <mi>n</mi> </mrow> </msub> </mrow> </semantics></math> evaluation for all experimental models.</p>
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<p><math display="inline"><semantics> <mrow> <mi>G</mi> <mi>L</mi> <msub> <mi>I</mi> <mrow> <mi>a</mi> <mi>v</mi> <mi>g</mi> </mrow> </msub> </mrow> </semantics></math> evaluation for all experimental models.</p>
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<p><math display="inline"><semantics> <mrow> <mi>G</mi> <mi>L</mi> <msub> <mi>I</mi> <mrow> <mi>a</mi> <mi>v</mi> <mi>g</mi> </mrow> </msub> </mrow> </semantics></math> evaluation for all experimental models.</p>
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<p><math display="inline"><semantics> <mrow> <mi>C</mi> <mi>T</mi> </mrow> </semantics></math> evaluation for all PRO2SAT embedded in metaheuristic algorithms.</p>
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<p><math display="inline"><semantics> <mrow> <mi>C</mi> <mi>T</mi> </mrow> </semantics></math> evaluation for all PRO2SAT embedded in metaheuristic algorithms.</p>
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<p><math display="inline"><semantics> <mrow> <mi>A</mi> <mi>I</mi> </mrow> </semantics></math> evaluation for all PRO2SAT embedded in metaheuristic algorithms.</p>
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<p><math display="inline"><semantics> <mrow> <mi>A</mi> <mi>I</mi> </mrow> </semantics></math> evaluation for all PRO2SAT embedded in metaheuristic algorithms.</p>
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<p><math display="inline"><semantics> <mrow> <mi>T</mi> <msub> <mi>V</mi> <mrow> <mi>s</mi> <mi>i</mi> <mi>m</mi> <mi>i</mi> <mi>l</mi> <mi>a</mi> <mi>r</mi> </mrow> </msub> </mrow> </semantics></math> evaluation for all experimental models.</p>
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<p><math display="inline"><semantics> <mrow> <mi>T</mi> <msub> <mi>V</mi> <mrow> <mi>s</mi> <mi>i</mi> <mi>m</mi> <mi>i</mi> <mi>l</mi> <mi>a</mi> <mi>r</mi> </mrow> </msub> </mrow> </semantics></math> evaluation for all experimental models.</p>
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