Travelling Salesman Problem Using Branch And Bound Technique

P.Rajarajeswari; D.Maheswari

doi:https://doi.org/10.14445/22315373/IJMTT-V66I5P528

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 66 | Issue 5 | Year 2020 | Article Id. IJMTT-V66I5P528 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I5P528

Travelling Salesman Problem Using Branch And Bound Technique

P.Rajarajeswari, D.Maheswari

Citation :

P.Rajarajeswari, D.Maheswari, "Travelling Salesman Problem Using Branch And Bound Technique," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 5, pp. 202-206, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I5P528

Abstract

In this paper Branch and bound technique is applied to solve the Travelling Salesman Problem (TSP) whose objective is to minimize the cost. Given a set of cities and the distance between every pair of cities, the problem of finding the shortest route between a set of points and locations that must be visited. Here fuzzy cost is considered as an interval number and further they are transformed into a crisp problem that is solved by branch and bound technique. This is illustrated by means of a numerical example.

Keywords

Interval numbers, Hexagonal numbers, Branch and Bound technique, ranking function

References

[1] Balas.B, Branch and Bound methods for the Travelling Salesman Problem, Management Science Research Report no. MSRR 488, March 1983.
[2] Chandrasekaran.S, Kokila.G, Saju.J, A New Approach to solve Fuzzy Travelling salesman Problems by using Ranking Functions, International Journal of Science and Research, Vol.4, 5 May 2015.
[3] Dhanasekar.S, Hariharan.S, Sekar.P, “Classical Travelling Salesman Problem based approach to solving Fuzzy TSP using Yagers Ranking, International Journal of Computer Applications, Vol.74, 2013, no.13, (0975-8887).
[4] Ding, Cheng, Y, He, M.: Two-Level Genetic algorithm for Clustered Traveling Salesman Problem with Application in Large Scale TSPs, Tsinghua Science and Technology, Vol.12.No.4 (2007) pp. 459-465.
[5] Nilofer et al,” The New Approach to Traveling Salesman Problem using Branch and Bound Method with case study of Domino‟s Pizza Centers”, Advances in Fuzzy Mathematics. ISSN 0973-533X Volume 12, Number 4 (2017), pp. 1017-1033.
[6] Rajarajeswari.P, Maheswari.D, “A New Approach For Solving Travelling Salesman Problem”, Journal of Applied Science and Computations, ISSN NO: 1076-5131, Volume VII, Issue IV, April/2020.
[7] Rastogi. A.K, Shrivastava. A. K, Payal. N, Singh. R, A Proposed solution to Travelling Salesman Problem using Branch and Bound, International Journal of Computer Applications, Vol.65, 2013, No.5, (0975-8887).
[8] Weiner.R, Branch and Bound Implementation for the Traveling salesperson Problem, Journal of Object Technology, Vol.2, 2003, no.2.