scholarly journals Dhouib-Matrix-TSP1 Method to Optimize Octagonal Fuzzy Travelling Salesman Problem Using α-Cut Technique

2021 ◽  
Vol 10 (3) ◽  
Author(s):  
Mariem Miledi ◽  
Souhail Dhouib ◽  
Taicir Loukil
Keyword(s):  
Standard Deviation ◽  
Approximation Method ◽  
Travel Salesman Problem ◽  
Fuzzy Numbers ◽  
Travelling Salesman Problem ◽  
Distance Matrix ◽  
Ranking Function ◽  
Travelling Salesman ◽  
Fuzzy Distance ◽  
Fuzzy Environment

This paper proposes the optimization of the fuzzy travel salesman problem by using the α-Cut technique as a ranking function and the Dhouib-Matrix-TSP1 as an approximation method. This method is enhanced by the standard deviation metric and obtains a minimal tour in fuzzy environment where all parameters are octagonal fuzzy numbers. Fuzzy numbers are converted into a crisp number thanks to the ranking function α-Cut. The proposed approach in details is discussed and illustrated by a numerical example. This method helps in designing successfully the tour to a salesman on navigation through the distance matrix so that it minimizes the total fuzzy distance.

scholarly journals Intuitionistic Fuzzy Modeling to Travelling Salesman Problem

2013 ◽  
Vol 11 (9) ◽  
pp. 3015-3024
Author(s):  
Arindam Garai ◽  
Tapan Kumar Roy
Keyword(s):  
Travelling Salesman Problem ◽  
Optimization Technique ◽  
Theoretical Computer Science ◽  
Solution Technique ◽  
Travelling Salesman ◽  
Programming Technique ◽  
Theoretical Computer ◽  
Multi Objective ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment

This paper presents solution technique for travelling salesman problem (TSP) under intuitionistic fuzzy environment. Travelling salesman problem is a non-deterministic polynomial-time (NP) hard problem in combinatorial optimization, studied in graph theory, operations research and theoretical computer science. It must be noted that a traveling sales man even face a situation in which he is not able to achieve his objectives completely. There must be a set of alternatives from which he can select one that best meets his aspiration level. For Multi-Objective Symmetric TSP, in fuzzy environment, it is converted into a Linear Program using Fuzzy Multi-Objective Linear Programming technique. A route cannot be simply chosen just as it will most minimize time or it will cover the least possible distance. Examples with requirements to consider the degree of rejection or hesitation (or both) are overflowing in our materialistic world. Here comes the need to consider TSP under intuitionistic fuzzy environment. The degree of rejection as well as the degree of hesitancy must be studied to find the solution in a truly optimum sense! Proposed technique is an extension as well as collaboration of ideas of fuzzy traveling salesperson problem and intuitionistic fuzzy (IF) optimization technique.

scholarly journals Neutrosophic Triangular Fuzzy Travelling Salesman Problem Based on Dhouib-Matrix-TSP1 Heuristic

2021 ◽  
Vol 10 (5) ◽  
Author(s):  
Souhail Dhouib
Keyword(s):  
Real World ◽  
Fuzzy Number ◽  
Travelling Salesman Problem ◽  
Numerical Test ◽  
Optimal Solution ◽  
Triangular Fuzzy Number ◽  
Travelling Salesman ◽  
Total Cost ◽  
Fuzzy Environment ◽  
Neutrosophic Number

In this paper, the Travelling Salesman Problem is considered in neutrosophic environment which is more realistic in real-world industries. In fact, the distances between cities in the Travelling Salesman Problem are presented as neutrosophic triangular fuzzy number. This problem is solved in two steps: At first, the Yager’s ranking function is applied to convert the neutrosophic triangular fuzzy number to neutrosophic number then to generate the crisp number. At second, the heuristic Dhouib-Matrix-TSP1 is used to solve this problem. A numerical test example on neutrosophic triangular fuzzy environment shows that, by the use of Dhouib-Matrix-TSP1 heuristic, the optimal or a near optimal solution as well as the crisp and fuzzy total cost can be reached.

scholarly journals Sorting Out Fuzzy Transportation Problems via ECCT and Standard Deviation

2021 ◽  
Vol 12 (2) ◽  
pp. 1-14
Author(s):  
Krishna Prabha Sikkannan ◽  
Vimala Shanmugavel
Keyword(s):  
Standard Deviation ◽  
Approximation Method ◽  
Fuzzy Numbers ◽  
Optimal Solution ◽  
New Method ◽  
Transportation Problems ◽  
North West ◽  
Numerical Example ◽  
Optimum Solution ◽  
Better Than

A well-organized arithmetical procedure entitled standard deviation is employed to find the optimum solution in this paper. This technique has been divided into two parts. The first methodology deals with constructing the entire contingency cost table, and the second deals with optimum allocation. In this work, the method of magnitude is used for converting fuzzy numbers into crisp numbers as this method is better than the existing methods. This technique gives a better optimal solution than other methods. A numerical example for the new method is explained, and the authors compared their method with existing methods such as north west corner method, least cost method, and Vogel's approximation method.

scholarly journals Tourist Route Optimization in the Context of Covid-19 Pandemic

2021 ◽  
Vol 13 (10) ◽  
pp. 5492
Author(s):  
Cristina Maria Păcurar ◽  
Ruxandra-Gabriela Albu ◽  
Victor Dan Păcurar
Keyword(s):  
Travelling Salesman Problem ◽  
Route Planning ◽  
Route Optimization ◽  
Travelling Salesman ◽  
Social Distancing ◽  
Tourist Destinations ◽  
Innovative Method ◽  
The Social ◽  
Immediate Response

The paper presents an innovative method for tourist route planning inside a destination. The necessity of reorganizing the tourist routes within a destination comes as an immediate response to the Covid-19 crisis. The implementation of the method inside tourist destinations can bring an important advantage in transforming a destination into a safer one in times of Covid-19 and post-Covid-19. The existing trend of shortening the tourist stay length has been accelerated while the epidemic became a pandemic. Moreover, the wariness for future pandemics has brought into spotlight the issue of overcrowded attractions inside a destination at certain moments. The method presented in this paper proposes a backtracking algorithm, more precisely an adaptation of the travelling salesman problem. The method presented is aimed to facilitate the navigation inside a destination and to revive certain less-visited sightseeing spots inside a destination while facilitating conformation with the social distancing measures imposed for Covid-19 control.

A column-and-row generation approach for the flying sidekick travelling salesman problem

2021 ◽  
Vol 124 ◽  
pp. 102913
Author(s):  
Maurizio Boccia ◽  
Adriano Masone ◽  
Antonio Sforza ◽  
Claudio Sterle
Keyword(s):  
Travelling Salesman Problem ◽  
Travelling Salesman
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