A New Column-Row Method for Traveling Salesman Problem: The Dhouib-Matrix-TSP1

  IJETT-book-cover  International Journal of Recent Engineering Science (IJRES)          
  
© 2021 by IJRES Journal
Volume-8 Issue-1
Year of Publication : 2021
Authors : Souhail Dhouib
  10.14445/23497157/IJRES-V8I1P102

MLA 

MLA Style: Souhail Dhouib "A New Column-Row Method for Traveling Salesman Problem: The Dhouib-Matrix-TSP1" International Journal of Recent Engineering Science 8.1(2021):6-10. 

APA Style: Souhail Dhouib. A New Column-Row Method for Traveling Salesman Problem: The Dhouib-Matrix-TSP1  International Journal of Recent Engineering Science, 8(1), 6-10.

Abstract
In this paper, a new column-row method named Dhouib-Matrix-TSP1 is designed to solve in polynomial time the Traveling Salesman Problem (TSP). At first, the distance matrix is defined, and then four steps are launched: 1) Selecting the starting position 2) Choosing Rows 3) Discarding by column 3) Transforming route to a tour. Some numerical examples are presented to illustrate the effectiveness of the proposed method. It can be concluded that the Dhouib-Matrix-TSP1 method consumes a small number of iterations (just n iterations, where n represents the number of cities) to solve the TSP, and its result is the closest to the optimum solution.

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Keywords
Traveling Salesman Problem, Combinatorial Optimization, Polynomial Time