An Approximation Algorithm for the Traveling Salesman Problem and Its Probabilistic Analysis

1996 ◽  
pp. 35-43
Author(s):  
È. Kh. Gimadi ◽  
N. I. Glebov ◽  
A. I. Serdyukov
Keyword(s):  
Approximation Algorithm ◽  
Traveling Salesman Problem ◽  
Probabilistic Analysis ◽  
Traveling Salesman ◽  
The Traveling Salesman Problem

scholarly journals An Approximation Algorithm for the Traveling Salesman Problem with Backhauls

1997 ◽  
Vol 45 (4) ◽  
pp. 639-641 ◽  
Author(s):  
Michel Gendreau ◽  
Gilbert Laporte ◽  
Alain Hertz
Keyword(s):  
Approximation Algorithm ◽  
Traveling Salesman Problem ◽  
Traveling Salesman ◽  
The Traveling Salesman Problem

scholarly journals An Improved Approximation Algorithm for the Subpath Planning Problem and Its Generalization

2017 ◽  
Author(s):  
Hanna Sumita ◽  
Yuma Yonebayashi ◽  
Naonori Kakimura ◽  
Ken-ichi Kawarabayashi
Keyword(s):  
Artificial Intelligence ◽  
Approximation Algorithm ◽  
Traveling Salesman Problem ◽  
Numerical Experiments ◽  
Traveling Salesman ◽  
Planning Problem ◽  
Solution Quality ◽  
The Traveling Salesman Problem ◽  
Direct Use ◽  
And Robotics

This paper focuses on a generalization of the traveling salesman problem (TSP), called the subpath planning problem (SPP). Given 2n vertices and n independent edges on a metric space, we aim to find a shortest tour that contains all the edges. SPP is one of the fundamental problems in both artificial intelligence and robotics. Our main result is to design a 1.5-approximation algorithm that runs in polynomial time, improving the currently best approximation algorithm. The idea is direct use of techniques developed for TSP. In addition, we propose a generalization of SPP called the subgroup planning problem (SGPP). In this problem, we are given a set of disjoint groups of vertices, and we aim to find a shortest tour such that all the vertices in each group are traversed sequentially. We propose a 3-approximation algorithm for SGPP. We also conduct numerical experiments. Compared with previous algorithms, our algorithms improve the solution quality by more than 10% for large instances with more than 10,000 vertices.

A New Heuristic Procedure To Solve The Traveling Salesman Problem

2007 ◽  
Vol 5 (1) ◽  
pp. 1-9
Author(s):  
Paulo Henrique Siqueira ◽  
Sérgio Scheer ◽  
Maria Teresinha Arns Steiner
Keyword(s):  
Traveling Salesman Problem ◽  
Traveling Salesman ◽  
Heuristic Procedure ◽  
The Traveling Salesman Problem

scholarly journals An Improved Whale Optimization Algorithm for the Traveling Salesman Problem

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 48
Author(s):  
Jin Zhang ◽  
Li Hong ◽  
Qing Liu
Keyword(s):  
Traveling Salesman Problem ◽  
Optimization Algorithm ◽  
Optimization Problems ◽  
Relevant Literature ◽  
Population Diversity ◽  
Traveling Salesman ◽  
Whale Optimization Algorithm ◽  
Neighborhood Search ◽  
Whale Optimization ◽  
The Traveling Salesman Problem

The whale optimization algorithm is a new type of swarm intelligence bionic optimization algorithm, which has achieved good optimization results in solving continuous optimization problems. However, it has less application in discrete optimization problems. A variable neighborhood discrete whale optimization algorithm for the traveling salesman problem (TSP) is studied in this paper. The discrete code is designed first, and then the adaptive weight, Gaussian disturbance, and variable neighborhood search strategy are introduced, so that the population diversity and the global search ability of the algorithm are improved. The proposed algorithm is tested by 12 classic problems of the Traveling Salesman Problem Library (TSPLIB). Experiment results show that the proposed algorithm has better optimization performance and higher efficiency compared with other popular algorithms and relevant literature.

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