Metaheuristics Approaches for the Travelling Salesman Problem on a Spherical Surface

2021 ◽  
pp. 94-113
Author(s):  
Yusuf Sahin ◽  
Erdal Aydemir ◽  
Kenan Karagul ◽  
Sezai Tokat ◽  
Burhan Oran
Keyword(s):  
Genetic Algorithms ◽  
Traveling Salesman Problem ◽  
Spherical Surface ◽  
Travelling Salesman Problem ◽  
Traveling Salesman ◽  
Heuristic Methods ◽  
Approximate Algorithms ◽  
Travelling Salesman ◽  
The Traveling Salesman Problem ◽  
Special Case

Traveling salesman problem in which all the vertices are assumed to be on a spherical surface is a special case of the conventional travelling salesman problem. There are exact and approximate algorithms for the travelling salesman problem. As the solution time is a performance parameter in most real-time applications, approximate algorithms always have an important area of research for both researchers and engineers. In this chapter, approximate algorithms based on heuristic methods are considered for the travelling salesman problem on the sphere. Firstly, 28 test instances were newly generated on the unit sphere. Then, using various heuristic methods such as genetic algorithms, ant colony optimization, and fluid genetic algorithms, the initial solutions for solving test instances of the traveling salesman problem are obtained in Matlab®. Then, the initial heuristic solutions are used as input for the 2-opt algorithm. The performances and time complexities of the applied methods are analyzed as a conclusion.

The Algorithm Animation of Genetic Algorithm of Travelling Salesman Problem

2013 ◽  
Vol 411-414 ◽  
pp. 2013-2016 ◽  
Author(s):  
Guo Zhi Wen
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Traveling Salesman Problem ◽  
Travelling Salesman Problem ◽  
Traveling Salesman ◽  
Travelling Salesman ◽  
Algorithm Animation ◽  
The Traveling Salesman Problem

The traveling salesman problem is analyzed with genetic algorithms. The best route map and tendency of optimal grade of 500 cities before the first mutation, best route map after 15 times of mutation and tendency of optimal grade of the final mutation are displayed with algorithm animation. The optimal grade is about 0.0455266 for the best route map before the first mutation, but is raised to about 0.058241 for the 15 times of mutation. It shows that through the improvements of algorithms and coding methods, the efficiency to solve the traveling problem can be raised with genetic algorithms.

scholarly journals Travelling Salesman Problem Analysis with Complete Enumeration Method, Branch & Bound and Greedy Heuristic

2021 ◽  
Vol 1 (8) ◽  
pp. 752-756
Author(s):  
Ifham Azizi Surya Syafiin ◽  
Sarah Nur Fatimah ◽  
Muchammad Fauzi
Keyword(s):  
Traveling Salesman Problem ◽  
Travelling Salesman Problem ◽  
Traveling Salesman ◽  
Greedy Heuristic ◽  
Problem Analysis ◽  
Heuristic Methods ◽  
Travelling Salesman ◽  
Complete Enumeration ◽  
The Traveling Salesman Problem ◽  
The City

PT XYZ as the best and largest Bed Sheet Set company in Indonesia with products such as Bed Covers, Bed Sheets, Pillowcases, Bolsters and Blankets. The Traveling Salesman Problem (TSP) is a problem faced in finding the best route to visit shops that sell products from PT BIG. A visit to the shop is carried out on the condition that each city can only be visited once except the city of origin. The algorithms applied in this TSP problem include the Complete Enumeration, Branch & Bound and Greedy Heuristic methods.

scholarly journals Multi Integer Linear Programming and the Traveling Salesman Problem

2021 ◽  
Vol 9 (VI) ◽  
pp. 2417-2421
Author(s):  
S. Sathyapriya
Keyword(s):  
Linear Programming ◽  
Traveling Salesman Problem ◽  
Integer Linear Programming ◽  
Travelling Salesman Problem ◽  
Initial Problem ◽  
Traveling Salesman ◽  
Travelling Salesman ◽  
Integer Problem ◽  
The Traveling Salesman Problem

The Travelling Salesman problem is considered as a binary integer problem. For this problem, several stop variables and subtours are discussed. The stops are generated and the distance between those stops are found, consequently the graphs are drawn. Further the variables are declared and the constraints are framed. Then the initial problem is visualised along with the subtour constraints in order to achieve the required output.

scholarly journals Some Analytical Considerations Regarding the Traveling Salesman Problem Solved with Wolfram Mathematica Applications

2020 ◽  
pp. 68-77
Author(s):  
Bogdan-Vasile Cioruța ◽  
Alexandru Lauran ◽  
Mirela Coman
Keyword(s):  
Traveling Salesman Problem ◽  
Execution Time ◽  
Travelling Salesman Problem ◽  
Emergent Behavior ◽  
Traveling Salesman ◽  
Ant Colony Optimisation ◽  
Travelling Salesman ◽  
Wolfram Mathematica ◽  
Computational Program ◽  
The Traveling Salesman Problem

The paper presents an introduction to the Ant Colony Optimisation (ACO) algorithm and methods for solving the Travelling Salesman Problem (TSP). Documenting, understanding and knowledge of concepts regarding the emergent behavior and intelligence swarms optimization, easily led on solving the Travelling Salesman Problem using a computational program, such as Mathematics Wolfram via Creative Demostration Projects (*.cdf) module. The proposed application runs for a different number of ants, a different number of ants, a different number of leaders (elite ants), and a different pheromone evaporation index. As a result it can be stated that the execution time of the algorithm to solve the TSP is direct and strictly proportional to the number of ants, cities and elite ants considered, the increase of the execution time increasing significantly with the increase of the variables.

scholarly journals A COMPARATIVE STUDY OF CROSSOVER OPERATORS FOR GENETIC ALGORITHMS TO SOLVE TRAVELLING SALESMAN PROBLEM

2017 ◽  
Vol 5 (2) ◽  
pp. 284-291
Author(s):  
Wafaa Mustafa Hameed ◽  
Asan Baker Kanbar
Keyword(s):  
Genetic Algorithms ◽  
Comparative Study ◽  
Traveling Salesman Problem ◽  
Travelling Salesman Problem ◽  
Traveling Salesman ◽  
Crossover Operator ◽  
Natural Evolution ◽  
Different Types ◽  
The Traveling Salesman Problem

Genetic algorithms (GAs) represent a method that mimics the process of natural evolution in effort to find good solutions. In that process, crossover operator plays an important role. To comprehend the genetic algorithms as a whole, it is necessary to understand the role of a crossover operator. Today, there are a number of different crossover operators that can be used , one of the problems in using genetic algorithms is the choice of crossover operator Many crossover operators have been proposed in literature on evolutionary algorithms, however, it is still unclear which crossover operator works best for a given optimization problem. This paper aims at studying the behavior of different types of crossover operators in the performance of genetic algorithm. These types of crossover are implemented on Traveling Salesman Problem (TSP); Whitley used the order crossover (OX) depending on specific parameters to solve the traveling salesman problem, the aim of this paper is to make a comparative study between order crossover (OX) and other types of crossover using the same parameters which was Whitley used.

GENERALISATIONS OF THE GILMORE-GOMORY TRAVELING SALESMAN PROBLEM AND THE GILMORE-GOMORY SCHEME: A SURVEY

2001 ◽  
Vol 03 (02n03) ◽  
pp. 213-235 ◽  
Author(s):  
SANTOSH N. KABADI
Keyword(s):  
Traveling Salesman Problem ◽  
Traveling Salesman ◽  
Major Portion ◽  
Polynomially Solvable ◽  
The Traveling Salesman Problem ◽  
Special Case

One of the first and perhaps the most well-known polynomially solvable special case of the traveling salesman problem (TSP) is the Gilmore-Gomory case (G-G TSP). Gilmore and Gomory presented an interesting patching algorithm for this case with a fairly non-trivial proof of its validity. Their work has motivated a great deal of research in the area leading to various generalisations of their results and thereby identification of fairly large polynomially solvable subclasses of the TSP. These results form a major portion of the literature on solvable cases of the TSP. In this paper, we survey the main results on solvable cases of the TSP which are direct generalisations of the G-G TSP and/or the Gilmore-Gomory patching scheme.

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