The approximation ratio of the greedy algorithm for the metric traveling salesman problem

Brecklinghaus, Judith; Hougardy, Stefan

doi:10.1016/j.orl.2015.02.009

Cited by 10 publications

(4 citation statements)

References 5 publications

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“…However, as the problem snowballs in scale, these methods fail to work anymore. erefore, in later research, scholars turn to approximate or heuristic algorithms, mainly including Genetic Algorithm [26,27], Simulated Annealing [28,29], Ant Colony Algorithm [30,31], Tabu Search Algorithm [29,32], Greedy Algorithms [33,34], and neural networks [35].…”

Section: Cnn-based Optimization Calculation Of Tsp Problemmentioning

confidence: 99%

Dynamic Analysis and FPGA Implementation of New Chaotic Neural Network and Optimization of Traveling Salesman Problem

Cui

Chen

2021

Complexity

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A neural network is a model of the brain’s cognitive process, with a highly interconnected multiprocessor architecture. The neural network has incredible potential, in the view of these artificial neural networks inherently having good learning capabilities and the ability to learn different input features. Based on this, this paper proposes a new chaotic neuron model and a new chaotic neural network (CNN) model. It includes a linear matrix, a sine function, and a chaotic neural network composed of three chaotic neurons. One of the chaotic neurons is affected by the sine function. The network has rich chaotic dynamics and can produce multiscroll hidden chaotic attractors. This paper studied its dynamic behaviors, including bifurcation behavior, Lyapunov exponent, Poincaré surface of section, and basins of attraction. In the process of analyzing the bifurcation and the basins of attraction, it was found that the network demonstrated hidden bifurcation phenomena, and the relevant properties of the basins of attraction were obtained. Thereafter, a chaotic neural network was implemented by using FPGA, and the experiment proved that the theoretical analysis results and FPGA implementation were consistent with each other. Finally, an energy function was constructed to optimize the calculation based on the CNN in order to provide a new approach to solve the TSP problem.

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Section: Cnn-based Optimization Calculation Of Tsp Problemmentioning

confidence: 99%

Dynamic Analysis and FPGA Implementation of New Chaotic Neural Network and Optimization of Traveling Salesman Problem

Cui

Chen

2021

Complexity

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“…The multi-fragment algorithm was proposed by Bentley [12] specifically in the geometric setting. Its approximation ratio is O(log n) [64,19]. Nonetheless, it is used in practice due to its simplicity and empirical support that it generally performs better than other heuristics [34,51,57,59,13].…”

Section: Multi-fragment Euclidean Tspmentioning

confidence: 99%

Euclidean TSP, Motorcycle Graphs, and Other New Applications of Nearest-Neighbor Chains

Mamano,

Efrat,

Eppstein

et al. 2019

Preprint

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We show new applications of the nearest-neighbor chain algorithm, a technique that originated in agglomerative hierarchical clustering. We apply it to a diverse class of geometric problems: we construct the greedy multi-fragment tour for Euclidean TSP in O(n log n) time in any fixed dimension and for Steiner TSP in planar graphs in O(n √ n log n) time; we compute motorcycle graphs (which are a central part in straight skeleton algorithms) in O(n 4/3+ε ) time for any ε > 0; we introduce a narcissistic variant of the k-attribute stable matching model, and solve it in O(n 2−4/(k(1+ε)+2) ) time; we give a linear-time 2-approximation for a 1D geometric set cover problem with applications to radio station placement.

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“…Starting from defining the initial group, deciding the better search area up to iterating from level to level, the results of each level is taken from best and then compared, so they can get more optimal [7]. This TSP method is used to determine the nodes that has been given the distance among other nodes by comparing the existing node based on selection of the shortest distance from the initial position [8].…”

Section: Introductionmentioning

confidence: 99%

Comparison of Genetic Algorithm and Hill Climbing for Shortest Path Optimization Mapping

2018

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Abstract. Traveling Salesman Problem (TSP) is an optimization to find the shortest path to reach several destinations in one trip without passing through the same city and back again to the early departure city, the process is applied to the delivery systems. This comparison is done using two methods, namely optimization genetic algorithm and hill climbing. Hill Climbing works by directly selecting a new path that is exchanged with the neighbour's to get the track distance smaller than the previous track, without testing. Genetic algorithms depend on the input parameters, they are the number of population, the probability of crossover, mutation probability and the number of generations. To simplify the process of determining the shortest path supported by the development of software that uses the google map API. Tests carried out as much as 20 times with the number of city 8, 16, 24 and 32 to see which method is optimal in terms of distance and time computation. Based on experiments conducted with a number of cities 3, 4, 5 and 6 producing the same value and optimal distance for the genetic algorithm and hill climbing, the value of this distance begins to differ with the number of city 7. The overall results shows that these tests, hill climbing are more optimal to number of small cities and the number of cities over 30 optimized using genetic algorithms.

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The approximation ratio of the greedy algorithm for the metric traveling salesman problem

Cited by 10 publications

References 5 publications

Dynamic Analysis and FPGA Implementation of New Chaotic Neural Network and Optimization of Traveling Salesman Problem

Dynamic Analysis and FPGA Implementation of New Chaotic Neural Network and Optimization of Traveling Salesman Problem

Euclidean TSP, Motorcycle Graphs, and Other New Applications of Nearest-Neighbor Chains

Comparison of Genetic Algorithm and Hill Climbing for Shortest Path Optimization Mapping

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