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A lexisearch algorithm for the Bottleneck Traveling Salesman Problem
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International Journal of Computer Science and Security (IJCSS)
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Volume:  3    Issue:  6
Pages:  448-594
Publication Date:   January 2010
ISSN (Online): 1985-1553
Pages 
569 - 577
Author(s)  
Zakir H. Ahmed - Saudi Arabia
 
Published Date   
22-02-2010 
Publisher 
CSC Journals, Kuala Lumpur, Malaysia
ADDITIONAL INFORMATION
Keywords   Abstract   References   Cited by   Related Articles   Collaborative Colleague
 
KEYWORDS:   Bottleneck traveling salesman, Lexisearch, Bound, Alphabet table. 
 
 
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The Bottleneck Traveling Salesman Problem (BTSP) is a variation of the well-known Traveling Salesman Problem in which the objective is to minimize the maximum lap (arc length) in the tour of the salesman. In this paper, a lexisearch algorithm using adjacency representation for a tour has been developed for obtaining exact optimal solution to the problem. Then a comparative study has been carried out to show the efficiency of the algorithm as against existing exact algorithm for some randomly generated and TSPLIB instances of different sizes. 
 
 
 
1 G.L. Vairaktarakis. "On Gilmore-Gomory’s open question for the bottleneck TSP". Operations Research Letters 31, pp. 483–491, 2003.
2 M.-Y. Kao and M. Sanghi. "An approximation algorithm for a bottleneck traveling salesman problem". Journal of Discrete Algorithms, doi: 10.1016/j.jda.2008.11.007 (2009)
3 P.C. Gilmore and R.E. Gomory. "Sequencing a one state-variable machine: a solvable case of the traveling salesman problem". Operations Research 12, pp. 655–679, 1964.
4 R.S. Garfinkel and K.C. Gilbert. "The bottleneck traveling salesman problem: Algorithms and probabilistic analysis". Journal of ACM 25, pp. 435-448, 1978.
5 G. Carpaneto, S. Martello and P. Toth. "An algorithm for the bottleneck traveling salesman problems". Operations Research 2, pp. 380-389, 1984.
6 M. Ramesh. "A lexisearch approach to some combinatorial programming problems”. PhD Thesis, University of Hyderabad, India, 1997.
7 Z.H. Ahmed, S.N.N. Pandit, and M. Borah. "Genetic Algorithms for the Min-Max Travelling Salesman Problem". Proceedings of the Annual Technical Session, Assam Science Society, India, pp. 64-71, 1999.
8 Z.H. Ahmed. "A sequential constructive sampling and related approaches to combinatorial optimization". PhD Thesis, Tezpur University, India, 2000.
9 R. Ramakrishnan, P. Sharma and A.P. Punnen. "An efficient heuristic algorithm for the bottleneck traveling salesman problem". Opsearch 46(3), pp.275-288, 2009.
10 J. Larusic, A.P. Punnen and E. Aubanel. "Experimental analysis of heuristics for the bottleneck traveling salesman problem". Technical report, Simon Fraster University, Canada, 2010.
11 J.M. Phillips, A.P. Punnen and S.N. Kabadi. "A linear time algorithm for the bottleneck traveling salesman problem on a Halin graph". Information Processing Letters 67, pp. 105-110, 1998.
12 S.N.N. Pandit. “Some quantitative combinatorial search problems”. PhD Thesis, Indian Institute of Technology, Kharagpur, India, 1963.
13 TSPLIB, http://www.iwr.uni-heidelberg.de/iwr/comopt/software/TSPLIB95/
 
 
 
1 Z. H. Ahmed, “A Data-Guided Lexisearch Algorithm for the Bottleneck Travelling Salesman Problem”, International Journal of Operational Research, 12(1), pp. 20-33, 2011.
2 Z. H. Ahmed, “Solution Algorithms for A Deterministic Replacement Problem”, International Journal of Engineering (IJE), 4(3), pp. 233 – 242, 2010.
3 Z. H. Ahmed, “A Data-Guided Lexisearch Algorithm for the Asymmetric Traveling Salesman Problem”, Mathematical Problems in Engineering, Vol. 2011, Article ID 750968, 18 pages, 2011.
 
 
 
1 PeekYou
 
2 yasni
 
 
 
Zakir H. Ahmed : Colleagues  
 
 
 
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