Authors :
Kalyan Kumar Mallick; Tapan Kumar Biswas; Md. Mostafa Kamal; Foyjun Nahar; Ramani Ranjan Sikder; Most. Arzu Banu; Md. Tareq Hasan
Volume/Issue :
Volume 9 - 2024, Issue 9 - September
Google Scholar :
https://tinyurl.com/3nhpt8n7
Scribd :
https://tinyurl.com/5n8t54v5
DOI :
https://doi.org/10.38124/ijisrt/IJISRT24SEP527
Note : A published paper may take 4-5 working days from the publication date to appear in PlumX Metrics, Semantic Scholar, and ResearchGate.
Abstract :
The Traveling Salesman Problem (TSP) is a
combinatorial problem related to computer science and
operations research. There are many methods proposed
in the literature to solve TSP with profit and losses. In this
classical problem, the objective is to visit a finite number
of locations exactly once, one by one, while minimizing the
total distance traveled by the connecting links (arcs)
needed to reach these sites (nodes). This study presents a
new procedure that applies TSP and makes use of the
decision tree notion. Anywhere in the TSP network,
where n is the total number of places (nodes) in the
network, this system ends after n-1 iterations. The
method's step-by-step computational criteria make it
efficient and readily applicable. To demonstrate the
process's validity and efficiency, numerical examples are
provided.
Keywords :
Traveling Salesman Problem (TSP), Minimum Distance Tour, Symmetric TSP, Optimization.
References :
- Mallick, K.K., Khan, A.R., Ahmed, M.M., Arefin, Md.S. and Uddin, Md.S. (2016) Modified EDMONDSKARP Algorithm to Solve Maximum Flow Problems. Open Journal of Applied Sciences, Vol. 6, pp.131-140
- Khan, Md.A., Rashid, A., Khan, A.R. and Uddin, Md.S. (2013) An Innovative Approach for Solving Maximal-Flow Problems, Journal of Physical Sciences, Vol. 17, pp. 143-154.
- Ahmed, F., Khan, Md.A., Khan, A.R., Ahmed, S.S. and Uddin, Md.S. (2014) An Efficient Algorithm for Finding Maximum Flow in a Network-Flow. Journal of Physical Sciences, Vol. 19, pp. 41-50.
- Akter, D., Uddin, M. S. and Shami F. A. 2021. Modification of EDMONDS –KARP algorithm for solving maximum flow problem, international journal of innovation and applied studies, Vol. 31, No. 4, pp. 703 -711.
- S.Mandal and M.Pal, A sequential algorithm to solve next-to-shortest path problem on circular-arc graphs, Journal of Physical Sciences, 10 (2006) 201- 217.
- M.Bazarra and J.Jarvis, Linear Programming and Network Flows, John Wiley & Sons, 1977.
- J.Edmonds and R.M.Karp, Theoretical improvements in algorithmic efficiency for network flow problems, Journal of the ACM, 19(2) (1972) 248-264.
- L.R.Ford and D.R.Fulkerson, Maximal flow through a network, Canadian Journal of Mathematics, 8 (1956) 399-404.
- D.R.Fulkerson and G.B.Dantzig, Computation of maximum flow in network, Naval Research Logistics Quarterly, 2 (1955) 277-283.
- V.A.Goldberg and R.E.Tarjan, A new approach to the maximum-flow problem, Journal of the ACM, 35(4) (1988) 921-940.
- 11.Jayanth Kumar, T. and Purusotham, S., 2018. The degree constrained kcardinality minimum spanning tree problem: a Lexi-search algorithm. Decision Science Letters, 7(3), pp.301–310.
- Kumar Amit, Gupta Anil “Assignment And Travelling Salesman Problems With Coefficient As LR Parameters,” Int.Journal Of Applied Science And Engineering, Vol.10, No.3, Pp155-170. 2012.
- Z. H. Ahmed, A Sequential Constructive Sampling and Related Approaches to Combinatorial Optimization, Ph.D. thesis, Tezpur University, Assam, India, 2000. 18 Mathematical Problems in Engineering.
- C. P. Ravikumar, “Solving larege-scale travelling salesperson problems on parallel machines,”Microprocessors and Microsystems, vol. 16, no. 3, pp. 149–158, 1992.
The Traveling Salesman Problem (TSP) is a
combinatorial problem related to computer science and
operations research. There are many methods proposed
in the literature to solve TSP with profit and losses. In this
classical problem, the objective is to visit a finite number
of locations exactly once, one by one, while minimizing the
total distance traveled by the connecting links (arcs)
needed to reach these sites (nodes). This study presents a
new procedure that applies TSP and makes use of the
decision tree notion. Anywhere in the TSP network,
where n is the total number of places (nodes) in the
network, this system ends after n-1 iterations. The
method's step-by-step computational criteria make it
efficient and readily applicable. To demonstrate the
process's validity and efficiency, numerical examples are
provided.
Keywords :
Traveling Salesman Problem (TSP), Minimum Distance Tour, Symmetric TSP, Optimization.