The Frequency of the Optimal Hamiltonian Cycle Computed with Frequency Quadrilaterals for Traveling Salesman Problem

2020 ◽  
pp. 513-524
Author(s):  
Yong Wang ◽  
Zunpu Han
Keyword(s):  
Traveling Salesman Problem ◽  
Hamiltonian Cycle ◽  
Traveling Salesman

scholarly journals Solution of Cluster Traveling Salesman Problem using Heuristic Based Genetic Algorithm with Risk Constraint

2019 ◽  
Vol 9 (2) ◽  
pp. 2523-2526
Keyword(s):  
Genetic Algorithm ◽  
Traveling Salesman Problem ◽  
Hamiltonian Cycle ◽  
Hamiltonian Path ◽  
Traveling Salesman ◽  
Computational Results ◽  
Number Of Clusters ◽  
Risk Constraint ◽  
The Traveling Salesman Problem

This is a heuristic investigation with risk constraint for solving the traveling salesman problem (TSP) dividing given vertices (nodes) between a prespecified number of clusters. A Heuristic based Genetic Algorithm (HbGA) is applied on each cluster to produce a Hamiltonian path based on prespecified nodes of a cluster. Each cluster must have a unique set of nodes. Finally, all Hamiltonian path of each cluster together prepare a possible Hamiltonian cycle. The efficiency of our proposed algorithm has been tested for a number of symmetric TSPLIB instances of various sizes. The computational results show the proposed algorithm works well in realistic manner.

EVERY LONGEST HAMILTONIAN PATH IN EVEN n-GONS

2012 ◽  
Vol 04 (04) ◽  
pp. 1250057 ◽  
Author(s):  
BLANCA I. NIEL
Keyword(s):  
Traveling Salesman Problem ◽  
Hamiltonian Cycle ◽  
Hamiltonian Path ◽  
Traveling Salesman ◽  
Maximum Traveling Salesman Problem ◽  
Longest Path ◽  
Hamiltonian Path Problems ◽  
Planar Rotations

We single out every longest path of n-1 order that solves each of the [Formula: see text] Longest Euclidean Hamiltonian Path Problems on the even nth root of the unity, by means of a geometric and arithmetic procedure. This identification is done regardless of planar rotations and orientation. In addition, the uniqueness of the Euclidean Hamiltonian cycle that resolves the Maximum Traveling Salesman Problem is shown.

scholarly journals Approximation Algorithms for the Bottleneck Asymmetric Traveling Salesman Problem

2021 ◽  
Vol 17 (4) ◽  
pp. 1-12
Author(s):  
Hyung-Chan An ◽  
Robert Kleinberg ◽  
David B. Shmoys
Keyword(s):  
Approximation Algorithms ◽  
Approximation Algorithm ◽  
Traveling Salesman Problem ◽  
Hamiltonian Cycle ◽  
Related Result ◽  
Traveling Salesman ◽  
Performance Guarantee ◽  
Asymmetric Traveling Salesman Problem ◽  
Algorithmic Technique ◽  
Edge Cost

We present the first nontrivial approximation algorithm for the bottleneck asymmetric traveling salesman problem . Given an asymmetric metric cost between n vertices, the problem is to find a Hamiltonian cycle that minimizes its bottleneck (or maximum-length edge) cost. We achieve an O (log n / log log n ) approximation performance guarantee by giving a novel algorithmic technique to shortcut Eulerian circuits while bounding the lengths of the shortcuts needed. This allows us to build on a related result of Asadpour, Goemans, Mądry, Oveis Gharan, and Saberi to obtain this guarantee. Furthermore, we show how our technique yields stronger approximation bounds in some cases, such as the bounded orientable genus case studied by Oveis Gharan and Saberi. We also explore the possibility of further improvement upon our main result through a comparison to the symmetric counterpart of the problem.

scholarly journals A quick method to compute sparse graphs for traveling salesman problem using random frequency quadrilaterals

Filomat ◽  
2018 ◽  
Vol 32 (5) ◽  
pp. 1697-1702
Author(s):  
Yong Wang
Keyword(s):  
Combinatorial Optimization ◽  
Traveling Salesman Problem ◽  
Complete Graph ◽  
Hamiltonian Cycle ◽  
Computation Time ◽  
Traveling Salesman ◽  
The Other ◽  
Quick Method ◽  
Sparse Graphs ◽  
Random Frequency

Traveling salesman problem (TSP) is extensively studied in combinatorial optimization and computer science. This paper gives a quick method to compute the sparse graphs for TSP based on the random frequency quadrilaterals so as to reduce the TSP on the complete graph to the TSP on the sparse graphs. When we choose N frequency quadrilaterals containing an edge e to compute its total frequency, the frequency of e in the optimal Hamiltonian cycle will be bigger than that of most of the other edges. We fix N to compute the frequency of each edge and the computation time of the quick method is O(n2). We suggest two frequency thresholds to trim the edges with the frequency below the two frequency thresholds and generate the sparse graphs for TSP. The experimental results show we compute the sparse graphs for these TSP instances in the TSPLIB.

Grafos hamiltonianos aplicado al turismo de Panamá

2019 ◽  
Vol 7 (1) ◽  
pp. 109-113
Author(s):  
Julio Trujillo
Keyword(s):  
Traveling Salesman Problem ◽  
Traveling Salesman

Un problema clásico de Teoría de Grafos es encontrar un camino que pase por varios puntos, sólo una vez, empezando y terminando en un lugar (camino hamiltoniano). Al agregar la condición de que sea la ruta más corta, el problema se convierte uno de tipo TSP (Traveling Salesman Problem). En este trabajo nos centraremos en un problema de tour turístico por la ciudad de Panamá, transformándolo a un problema de grafo de tal manera que represente la situación planteada.

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