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Keywords = generalized travelling salesman problem

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21 pages, 7362 KiB  
Article
Multi-Layer Path Planning for Complete Structural Inspection Using UAV
by Ho Wang Tong, Boyang Li, Hailong Huang and Chih-Yung Wen
Drones 2025, 9(8), 541; https://doi.org/10.3390/drones9080541 (registering DOI) - 31 Jul 2025
Viewed by 129
Abstract
This article addresses the path planning problem for complete structural inspection using an unmanned aerial vehicle (UAV). The proposed method emphasizes the scalability of the viewpoints and aims to provide practical solutions to different inspection distance requirements, eliminating the need for extra view-planning [...] Read more.
This article addresses the path planning problem for complete structural inspection using an unmanned aerial vehicle (UAV). The proposed method emphasizes the scalability of the viewpoints and aims to provide practical solutions to different inspection distance requirements, eliminating the need for extra view-planning procedures. First, the mixed-viewpoint generation is proposed. Then, the Multi-Layered Angle-Distance Traveling Salesman Problem (ML-ADTSP) is solved, which aims to reduce overall energy consumption and inspection path complexity. A two-step Genetic Algorithm (GA) is used to solve the combinatorial optimization problem. The performance of different crossover functions is also discussed. By solving the ML-ADTSP, the simulation results demonstrate that the mean accelerations of the UAV throughout the inspection path are flattened significantly, improving the overall path smoothness and reducing traversal difficulty. With minor low-level optimization, the proposed framework can be applied to inspect different structures. Full article
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26 pages, 6624 KiB  
Article
Data-Efficient Sowing Position Estimation for Agricultural Robots Combining Image Analysis and Expert Knowledge
by Shuntaro Aotake, Takuya Otani, Masatoshi Funabashi and Atsuo Takanishi
Agriculture 2025, 15(14), 1536; https://doi.org/10.3390/agriculture15141536 - 16 Jul 2025
Viewed by 478
Abstract
We propose a data-efficient framework for automating sowing operations by agricultural robots in densely mixed polyculture environments. This study addresses the challenge of enabling robots to identify suitable sowing positions with minimal labeled data by integrating image-based field sensing with expert agricultural knowledge. [...] Read more.
We propose a data-efficient framework for automating sowing operations by agricultural robots in densely mixed polyculture environments. This study addresses the challenge of enabling robots to identify suitable sowing positions with minimal labeled data by integrating image-based field sensing with expert agricultural knowledge. We collected 84 RGB-depth images from seven field sites, labeled by synecological farming practitioners of varying proficiency levels, and trained a regression model to estimate optimal sowing positions and seeding quantities. The model’s predictions were comparable to those of intermediate-to-advanced practitioners across diverse field conditions. To implement this estimation in practice, we mounted a Kinect v2 sensor on a robot arm and integrated its 3D spatial data with axis-specific movement control. We then applied a trajectory optimization algorithm based on the traveling salesman problem to generate efficient sowing paths. Simulated trials incorporating both computation and robotic control times showed that our method reduced sowing operation time by 51% compared to random planning. These findings highlight the potential of interpretable, low-data machine learning models for rapid adaptation to complex agroecological systems and demonstrate a practical approach to combining structured human expertise with sensor-based automation in biodiverse farming environments. Full article
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24 pages, 6297 KiB  
Article
Optimization of Coverage Path Planning for Agricultural Drones in Weed-Infested Fields Using Semantic Segmentation
by Fabian Andres Lara-Molina
Agriculture 2025, 15(12), 1262; https://doi.org/10.3390/agriculture15121262 - 11 Jun 2025
Viewed by 1378
Abstract
The application of drones has contributed to automated herbicide spraying in the context of precision agriculture. Although drone technology is mature, the widespread application of agricultural drones and their numerous advantages still demand improvements in battery endurance during flight missions in agricultural operations. [...] Read more.
The application of drones has contributed to automated herbicide spraying in the context of precision agriculture. Although drone technology is mature, the widespread application of agricultural drones and their numerous advantages still demand improvements in battery endurance during flight missions in agricultural operations. This issue has been addressed by optimizing the path planning to minimize the time of the route and, therefore, the energy consumption. In this direction, a novel framework for autonomous drone-based herbicide applications that integrates deep learning-based semantic segmentation and coverage path optimization is proposed. The methodology involves computer vision for path planning optimization. First, semantic segmentation is performed using a DeepLab v3+ convolutional neural network to identify and classify regions containing weeds based on aerial imagery. Then, a coverage path planning strategy is applied to generate efficient spray routes over each weed-infested area, represented as convex polygons, while accounting for the drone’s refueling constraints. The results demonstrate the effectiveness of the proposed approach for optimizing coverage paths in weed-infested sugarcane fields. By integrating semantic segmentation with clustering and path optimization techniques, it was possible to accurately localize weed patches and compute an efficient trajectory for UAV navigation. The GA-based solution to the Traveling Salesman Problem With Refueling (TSPWR) yielded a near-optimal visitation sequence that minimizes the energy demand. The total coverage path ensured complete inspection of the weed-infected areas, thereby enhancing operational efficiency. For the sugar crop considered in this contribution, the time to cover the area was reduced by 66.3% using the proposed approach because only the weed-infested area was considered for herbicide spraying. Validation of the proposed methodology using real-world agricultural datasets shows promising results in the context of precision agriculture to improve the efficiency of herbicide or fertilizer application in terms of herbicide waste reduction, lower operational costs, better crop health, and sustainability. Full article
(This article belongs to the Section Artificial Intelligence and Digital Agriculture)
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25 pages, 953 KiB  
Article
Energy-Efficient UAV Trajectory Design and Velocity Control for Visual Coverage of Terrestrial Regions
by Hengchao Li, Riheng Jia, Zhonglong Zheng and Minglu Li
Drones 2025, 9(5), 339; https://doi.org/10.3390/drones9050339 - 30 Apr 2025
Viewed by 567
Abstract
In this work, we develop a novel approach for designing the trajectory and controlling the velocity for an unmanned aerial vehicle (UAV) to achieve energy-efficient visual coverage of multiple terrestrial regions. Unlike previous works, our proposed approach allows the UAV to flexibly change [...] Read more.
In this work, we develop a novel approach for designing the trajectory and controlling the velocity for an unmanned aerial vehicle (UAV) to achieve energy-efficient visual coverage of multiple terrestrial regions. Unlike previous works, our proposed approach allows the UAV to flexibly change both its velocity and its flight altitude during its task tour. To minimize the UAV’s total flight energy consumption during its task tour, we propose a novel four-step approach. The first step devises a simulated annealing (SA)-based searching algorithm to optimize the UAV’s photographing altitude for each region, considering various image resolution requirements and safety requirements across regions. Based on the identified photographing altitudes of all regions, the second step formulates a traveling salesman problem (TSP) and uses an efficient approximate method to determine the visiting order of each region. The third step generates all candidate intra-region trajectories used for visual coverage of each region, of which the optimal one will be decided together with the inter-region trajectory used for transitioning between neighboring regions during the fourth step. Finally, the fourth step employs dynamic programming (DP) and geometry to jointly determine the UAV’s velocity control and complete trajectory during its task tour. Extensive experiments validate the effectiveness and superiority of the proposed approach, compared with several existing methods. Full article
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26 pages, 9892 KiB  
Article
Research on 3D Path Optimization for an Inspection Micro-Robot in Oil-Immersed Transformers Based on a Hybrid Algorithm
by Junji Feng, Xinghua Liu, Hongxin Ji, Chun He and Liqing Liu
Sensors 2025, 25(9), 2666; https://doi.org/10.3390/s25092666 - 23 Apr 2025
Viewed by 523
Abstract
To enhance the efficiency and accuracy of detecting insulation faults such as discharge carbon traces in large oil-immersed transformers, this study employs an inspection micro-robot to replace manual inspection for image acquisition and fault identification. While the micro-robot exhibits compactness and agility, its [...] Read more.
To enhance the efficiency and accuracy of detecting insulation faults such as discharge carbon traces in large oil-immersed transformers, this study employs an inspection micro-robot to replace manual inspection for image acquisition and fault identification. While the micro-robot exhibits compactness and agility, its limited battery capacity necessitates the critical optimization of its 3D inspection path within the transformer. To address this challenge, we propose a hybrid algorithmic framework. First, the task of visiting inspection points is formulated as a Constrained Traveling Salesman Problem (CTSP) and solved using the Ant Colony Optimization (ACO) algorithm to generate an initial sequence of inspection nodes. Once the optimal node sequence is determined, detailed path planning between adjacent points is executed through a synergistic combination of the A algorithm*, Rapidly exploring Random Tree (RRT), and Particle Swarm Optimization (PSO). This integrated strategy ensures robust circumvention of complex 3D obstacles while maintaining path efficiency. Simulation results demonstrate that the hybrid algorithm achieves a 52.6% reduction in path length compared to the unoptimized A* algorithm, with the A*-ACO combination exhibiting exceptional stability. Additionally, post-processing via B-spline interpolation yields smooth trajectories, limiting path curvature and torsion to <0.033 and <0.026, respectively. These advancements not only enhance planning efficiency but also provide substantial practical value and robust theoretical support for advancing key technologies in micro-robot inspection systems for oil-immersed transformer maintenance. Full article
(This article belongs to the Section Sensors and Robotics)
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14 pages, 5649 KiB  
Article
One-Shot Autoregressive Generation of Combinatorial Optimization Solutions Based on the Large Language Model Architecture and Learning Algorithms
by Bishad Ghimire, Ausif Mahmood and Khaled Elleithy
AI 2025, 6(4), 66; https://doi.org/10.3390/ai6040066 - 26 Mar 2025
Viewed by 1384
Abstract
Large Language Models (LLMs) have immensely advanced the field of Artificial Intelligence (AI), with recent models being able to perform chain-of-thought reasoning and solve complex mathematical problems, ranging from theorem proving to ones involving advanced calculus. The success of LLMs derives from a [...] Read more.
Large Language Models (LLMs) have immensely advanced the field of Artificial Intelligence (AI), with recent models being able to perform chain-of-thought reasoning and solve complex mathematical problems, ranging from theorem proving to ones involving advanced calculus. The success of LLMs derives from a combination of the Transformer architecture with its attention mechanism, the autoregressive training methodology with masked attention, and the alignment fine-tuning via reinforcement learning algorithms. In this research, we attempt to explore a possible solution to the fundamental NP-hard problem of combinatorial optimization, in particular, the Traveling Salesman Problem (TSP), by following the LLM approach in terms of the architecture and training algorithms. Similar to the LLM design, which is trained in an autoregressive manner to predict the next token, our model is trained to predict the next node in a TSP graph. After the model is trained on random TSP graphs with known near-optimal solutions, we fine-tune the model using Direct Preference Optimization (DPO). The tour generation in a trained model is autoregressive one-step generation with no need for iterative refinement. Our results are very promising and indicate that, for TSP graphs up to 100 nodes, a relatively small amount of training data yield solutions within a few percent of the optimal. This optimization improves if more data are used to train the model. Full article
(This article belongs to the Section AI Systems: Theory and Applications)
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28 pages, 14926 KiB  
Article
Research on Ship Replenishment Path Planning Based on the Modified Whale Optimization Algorithm
by Qinghua Chen, Gang Yao, Lin Yang, Tangying Liu, Jin Sun and Shuxiang Cai
Biomimetics 2025, 10(3), 179; https://doi.org/10.3390/biomimetics10030179 - 13 Mar 2025
Cited by 3 | Viewed by 686
Abstract
Ship replenishment path planning has always been a critical concern for researchers in the field of security. This study proposes a modified whale optimization algorithm (MWOA) to address single-task ship replenishment path planning problems. To ensure high-quality initial solutions and maintain population diversity, [...] Read more.
Ship replenishment path planning has always been a critical concern for researchers in the field of security. This study proposes a modified whale optimization algorithm (MWOA) to address single-task ship replenishment path planning problems. To ensure high-quality initial solutions and maintain population diversity, a hybrid approach combining the nearest neighbor search with random search is employed for initial population generation. Additionally, crossover operations and destroy and repair operators are integrated to update the whale’s position, significantly enhancing the algorithm’s search efficiency and optimization performance. Furthermore, variable neighborhood search is utilized for local optimization to refine the solutions. The proposed MWOA has been tested against several algorithms, including the original whale optimization algorithm, genetic algorithm, ant colony optimization, hybrid particle swarm optimization, and simulated annealing, using traveling salesman problems as benchmarks. Results demonstrate that MWOA outperforms these algorithms in both solution quality and stability. Moreover, when applied to ship replenishment path planning problems of varying scales, MWOA consistently achieves superior performance compared to the other algorithms. The proposed algorithm demonstrates high adaptability in addressing diverse ship replenishment path planning problems, delivering efficient, high-quality, and reliable solutions. Full article
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18 pages, 526 KiB  
Article
Edge-Driven Multiple Trajectory Attention Model for Vehicle Routing Problems
by Dapeng Yan, Bei Ou, Qingshu Guan, Zheng Zhu and Hui Cao
Appl. Sci. 2025, 15(5), 2679; https://doi.org/10.3390/app15052679 - 2 Mar 2025
Cited by 1 | Viewed by 1248
Abstract
The vehicle routing problem (VRP), as one of the classic combinatorial optimization problems, has garnered widespread attention in recent years. Existing deep reinforcement learning (DRL)-based methods predominantly focus on node information, neglecting the edge information inherent in the graph structure. Moreover, the solution [...] Read more.
The vehicle routing problem (VRP), as one of the classic combinatorial optimization problems, has garnered widespread attention in recent years. Existing deep reinforcement learning (DRL)-based methods predominantly focus on node information, neglecting the edge information inherent in the graph structure. Moreover, the solution trajectories produced by these methods tend to exhibit limited diversity, hindering a thorough exploration of the solution space. In this work, we propose a novel Edge-Driven Multiple Trajectory Attention Model (E-MTAM) to solve VRPs with various scales. Our model is built upon the encoder–decoder architecture, incorporating an edge-driven multi-head attention (EDMHA) block within the encoder to better utilize edge information. During the decoding process, we enhance graph embeddings with visitation information, integrating dynamic updates into static graph embeddings. Additionally, we employ a multi-decoder architecture and introduce a regularization term to encourage the generation of diverse trajectories, thus promoting solution diversity. We conduct comprehensive experiments on three types of VRPs: (1) traveling salesman problem (TSP), (2) capacitated vehicle routing problem (CVRP), and (3) orienteering problem (OP). The experimental results demonstrate that our model outperforms existing DRL-based methods and most traditional heuristic approaches, while also exhibiting strong generalization across problems of different scales. Full article
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27 pages, 15528 KiB  
Article
An Improved NSGA-II-Based Method for Cutting Trajectory Planning of Boom-Type Roadheader
by Chao Zhang, Xuhui Zhang, Wenjuan Yang, Jicheng Wan, Guangming Zhang, Yuyang Du, Sihao Tian and Zeyao Wang
Appl. Sci. 2025, 15(4), 2126; https://doi.org/10.3390/app15042126 - 17 Feb 2025
Viewed by 782
Abstract
This paper proposes a cutting trajectory planning method for boom-type roadheaders using an improved Nondominated Sorting Genetic Algorithm II (NSGA-II) with an elitist strategy. Existing methods often overlook constraints related to cutterhead dimensions and target sections, affecting section formation quality. We develop a [...] Read more.
This paper proposes a cutting trajectory planning method for boom-type roadheaders using an improved Nondominated Sorting Genetic Algorithm II (NSGA-II) with an elitist strategy. Existing methods often overlook constraints related to cutterhead dimensions and target sections, affecting section formation quality. We develop a kinematic model for coordinate transformations and design a simplified cutterhead and constraint model to generate feasible cutting points. Bi-objective functions—minimizing cutting trajectory length and turning angle—are formulated as a bi-objective traveling salesman problem (BO-TSP) with adjacency constraints. NSGA-II is adapted with enhancements in adjacency constraint handling, population initialization, and genetic operations. Simulations and experiments demonstrate significant improvements in convergence speed and computation time. Virtual cutting experiments confirm trajectory feasibility under varying postures, achieving high formation quality. A comparison of planned and tracked trajectories shows a maximum deviation of 23.879 mm, supporting autonomous cutting control. This method advances cutting trajectory planning for roadway section formation and autonomous roadheader control. Full article
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16 pages, 4058 KiB  
Article
Autonomous Mission Planning for Fixed-Wing Unmanned Aerial Vehicles in Multiscenario Reconnaissance
by Bei Chen, Jiaxin Yan, Zebo Zhou, Rui Lai and Jiejian Lin
Sensors 2025, 25(4), 1176; https://doi.org/10.3390/s25041176 - 14 Feb 2025
Cited by 1 | Viewed by 1159
Abstract
Before a fixed-wing UAV executes target tracking missions, it is essential to identify targets through reconnaissance mission areas using onboard payloads. This paper presents an autonomous mission planning method designed for such reconnaissance operations, enabling effective target identification prior to tracking. Existing planning [...] Read more.
Before a fixed-wing UAV executes target tracking missions, it is essential to identify targets through reconnaissance mission areas using onboard payloads. This paper presents an autonomous mission planning method designed for such reconnaissance operations, enabling effective target identification prior to tracking. Existing planning methods primarily focus on flight performance, energy consumption, and obstacle avoidance, with less attention to integrating payload. Our proposed method emphasizes the combination of two key functions: flight path planning and payload mission planning. In terms of path planning, we introduce a method based on the Hierarchical Traveling Salesman Problem (HTSP), which utilizes the nearest neighbor algorithm to find the optimal visit sequence and entry points for area targets. When dealing with area targets containing no-fly zones, HTSP quickly calculates a set of waypoints required for coverage path planning (CPP) based on the Generalized Traveling Salesman Problem (GTSP), ensuring thorough and effective reconnaissance coverage. In terms of payload mission planning, our proposed method fully considers payload characteristics such as scan resolution, imaging width, and operating modes to generate predefined mission instruction sets. By meticulously analyzing payload constraints, we further optimized the path planning results, ensuring that each instruction meets the payload performance requirements. Finally, simulations validated the effectiveness and superiority of the proposed autonomous mission planning method in reconnaissance tasks. Full article
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23 pages, 4048 KiB  
Article
Universal and Automated Approaches for Optimising the Processing Order of Geometries in a CAM Tool for Redundant Galvanometer Scanner-Based Systems
by Daniel Kurth, Colin Reiff, Yujiao Jiang and Alexander Verl
Automation 2025, 6(1), 1; https://doi.org/10.3390/automation6010001 - 25 Dec 2024
Viewed by 1171
Abstract
The combination of highly dynamic systems with a limited work envelope with a less dynamic system with a larger working envelope promises to combine the advantages of both systems while eliminating the disadvantages. For these systems, separation algorithms determine the trajectories based on [...] Read more.
The combination of highly dynamic systems with a limited work envelope with a less dynamic system with a larger working envelope promises to combine the advantages of both systems while eliminating the disadvantages. For these systems, separation algorithms determine the trajectories based on the target geometries. However, arbitrary processing orders of these result in inefficient trajectories because successive geometries may be geometrically far apart. This causes the dynamic system to operate below its potential. Current planning tools do not optimise the processing order for such redundant systems. The aim is to design and implement a planning tool for the application of laser marking. The tool considers the processing order of the 2D geometries from a geometric point of view. The resulting sequenced path data can then be used by trajectory generation algorithms to make full use of the potential of redundant systems. The approach analyses literature on Travelling Salesman Problems (TSP), which is then transferred to the given application. A heuristic and a genetic algorithm are developed and integrated into a planning tool. The results show the heuristic algorithm being faster while still producing solutions whose total path length is similar to that of the genetic algorithm. Even though the solutions don’t meet any optimality standards, the presented automated approaches are superior to manual approaches and are to be seen as a starting point for further research. Full article
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24 pages, 27332 KiB  
Article
A Global Coverage Path Planning Method for Multi-UAV Maritime Surveillance in Complex Obstacle Environments
by Yiyuan Li, Weiyi Chen, Bing Fu, Zhonghong Wu and Lingjun Hao
Drones 2024, 8(12), 764; https://doi.org/10.3390/drones8120764 - 17 Dec 2024
Cited by 2 | Viewed by 1404
Abstract
The study of unmanned aerial vehicle (UAV) coverage path planning is of great significance for ensuring maritime situational awareness and monitoring. In response to the problem of maritime multi-region coverage surveillance in complex obstacle environments, this paper proposes a global path planning method [...] Read more.
The study of unmanned aerial vehicle (UAV) coverage path planning is of great significance for ensuring maritime situational awareness and monitoring. In response to the problem of maritime multi-region coverage surveillance in complex obstacle environments, this paper proposes a global path planning method capable of simultaneously addressing the multiple traveling salesman problem, coverage path planning problem, and obstacle avoidance problem. Firstly, a multiple traveling salesmen problem–coverage path planning (MTSP-CPP) model with the objective of minimizing the maximum task completion time is constructed. Secondly, a method for calculating obstacle-avoidance path costs based on the Voronoi diagram is proposed, laying the foundation for obtaining the optimal access order. Thirdly, an improved discrete grey wolf optimizer (IDGWO) algorithm integrated with variable neighborhood search (VNS) operations is proposed to perform task assignment for multiple UAVs and achieve workload balancing. Finally, based on dynamic programming, the coverage path points of the area are solved precisely to generate the globally coverage path. Through simulation experiments with scenarios of varying scales, the effectiveness and superiority of the proposed method are validated. The experimental results demonstrate that this method can effectively solve MTSP-CPP in complex obstacle environments. Full article
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17 pages, 2499 KiB  
Article
Intelligent Path Planning for UAV Patrolling in Dynamic Environments Based on the Transformer Architecture
by Ching-Hao Yu, Jichiang Tsai and Yuan-Tsun Chang
Electronics 2024, 13(23), 4716; https://doi.org/10.3390/electronics13234716 - 28 Nov 2024
Cited by 2 | Viewed by 1396
Abstract
Due to its NP-Hard property, the Travelling Salesman Problem (TSP) has long been a prominent research topic in path planning. The goal is to design the algorithm with the fastest execution speed in order to find the path with the lowest travelling cost. [...] Read more.
Due to its NP-Hard property, the Travelling Salesman Problem (TSP) has long been a prominent research topic in path planning. The goal is to design the algorithm with the fastest execution speed in order to find the path with the lowest travelling cost. In particular, new generative AI technology is continually emerging. The question of how to exploit algorithms from this realm to perform TSP path planning, especially in dynamic environments, is an important and interesting problem. The TSP application scenario investigated by this paper is that of an Unmanned Aerial Vehicle (UAV) that needs to patrol all specific ship-targets on the sea surface before returning to its origin. Hence, during the flight, we must consider real-time changes in wind velocity and direction, as well as the dynamic addition or removal of ship targets due to mission requirements. Specifically, we implement a Deep Reinforcement Learning (DRL) model based on the Transformer architecture, which is widely used in Generative AI, to solve the TSP path-planning problem in dynamic environments. Finally, we conduct numerous simulation experiments to compare the performance of our DRL model and the traditional heuristic algorithm, the Simulated Annealing (SA) method, in terms of operation time and path distance in solving the ordinary TSP, to verify the advantages of our model. Notably, traditional heuristic algorithms cannot be applied to dynamic environments, in which wind velocity and direction can change at any time. Full article
(This article belongs to the Special Issue Parallel, Distributed, Edge Computing in UAV Communication)
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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
Cited by 4 | Viewed by 2168
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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21 pages, 6413 KiB  
Article
An Efficient Tour Construction Heuristic for Generating the Candidate Set of the Traveling Salesman Problem with Large Sizes
by Boldizsár Tüű-Szabó, Péter Földesi and László T. Kóczy
Mathematics 2024, 12(19), 2960; https://doi.org/10.3390/math12192960 - 24 Sep 2024
Viewed by 1452
Abstract
In this paper, we address the challenge of creating candidate sets for large-scale Traveling Salesman Problem (TSP) instances, where choosing a subset of edges is crucial for efficiency. Traditional methods for improving tours, such as local searches and heuristics, depend greatly on the [...] Read more.
In this paper, we address the challenge of creating candidate sets for large-scale Traveling Salesman Problem (TSP) instances, where choosing a subset of edges is crucial for efficiency. Traditional methods for improving tours, such as local searches and heuristics, depend greatly on the quality of these candidate sets but often struggle in large-scale situations due to insufficient edge coverage or high time complexity. We present a new heuristic based on fuzzy clustering, designed to produce high-quality candidate sets with nearly linear time complexity. Thoroughly tested on benchmark instances, including VLSI and Euclidean types with up to 316,000 nodes, our method consistently outperforms traditional and current leading techniques for large TSPs. Our heuristic’s tours encompass nearly all edges of optimal or best-known solutions, and its candidate sets are significantly smaller than those produced with the POPMUSIC heuristic. This results in faster execution of subsequent improvement methods, such as Helsgaun’s Lin–Kernighan heuristic and evolutionary algorithms. This substantial enhancement in computation time and solution quality establishes our method as a promising approach for effectively solving large-scale TSP instances. Full article
(This article belongs to the Special Issue Fuzzy Logic Applications in Traffic and Transportation Engineering)
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