Theoretical and Natural Science
- The Open Access Proceedings Series for Conferences
Theoretical and Natural Science
Vol. 28, 26 December 2023
Open
Access | Article
Analysis of various methodologies for the TSP problem
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Abstract
Linear algebra is an important mathematical method used to solve real-life problems such as optimization. This paper chose the Travelling Salesman Problem as the topic. TSP Problem had a lot of different methods and algorithms. In this paper, the principle of each method is explained, and the comparison with the test data is shown at the end of the paper. Matlab was used to support the research. The source codes of each method were uploaded to Github. According to the test data, the branch-and-bound method performed the best because it takes the least time to run and can handle the most data. TSP Problem is widely used in real life, such as transportation. The faster the code, the better the performance of the program.
Keywords
Travelling Salesman Problem, comparison, source code
References
1. Nigel Cummings (2000) The OR Society, “A Brief History of the Travelling Salesman Problem”, https://www.theorsociety.com/about-or/or-methods/heuristics/a-brief-history-of-the-travelling-salesman-problem/
2. Damon Cook, “Evolved and Timed Ants: Optimizing the Parameters of a Time-Based Ant System Approach to the Traveling Salesman Problem Using a Genetic,” accessed March 2, 2023, https://www.cs.nmsu.edu/ dcook/thesis/paper2.html.
3. Florian Arnold, Michel Gendreau, Kenneth S¨orensen,”Efficiently solving very large-scale routing problems,” Computers & Operations Research, Volume 107, 2019, Pages 32-42, ISSN 0305-0548, https://doi.org/10.1016/j.cor.2019.03.006.
4. D. S. Johnson, L. A. McGeoch, E. E. Rothberg, “Asymptotic Experimental Analysis for the Held-Karp Traveling Salesman Bound,” Proceedings of the 7th Annual ACMSIAM Symposium on Discrete Algorithms (1996), 341-350, http://dimacs.rutgers.edu/ archive/Challenges/TSP/papers/HKsoda.pdf
5. Pascal Benchimol, Jean-Charles R´egin, Louis-Martin Rousseau, Michel Rueher, Willem-Jan Hoeve, integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, 2010, Volume 6140 ISBN: 978-3-642-13519- 4, https://citations.springernature.com/item?doi=10.1007/978-3-642- 13520-0 6
6. Luís Machado, Simes M D G , Souza R R ,et al.cincia da informao e web semntica: uma relao efetiva ou apcrifa? information science and semantic web: an effective or apocryphal relationship?[J]. 2019.DOI:10.1007/978-3-642-28977-4_12.
Data Availability
The datasets used and/or analyzed during the current study will be available from the authors upon reasonable request.
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- Volume Title
- Proceedings of the 2023 International Conference on Mathematical Physics and Computational Simulation
- ISBN (Print)
- 978-1-83558-261-9
- ISBN (Online)
- 978-1-83558-262-6
- Published Date
- 26 December 2023
- Series
- Theoretical and Natural Science
- ISSN (Print)
- 2753-8818
- ISSN (Online)
- 2753-8826
- DOI
- 10.54254/2753-8818/28/20230393
- Copyright
- 26 December 2023
- Open Access
- This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited