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Characterization of the probabilistic traveling salesman problem

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Bowler, Neill E., Fink, Thomas M. A. and Ball, R. C.. (2003) Characterization of the probabilistic traveling salesman problem. Physical Review E, Vol.68 (No.3). ISSN 1063-651X

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Official URL: http://dx.doi.org/10.1103/PhysRevE.68.036703

Abstract

We show that stochastic annealing can be successfully applied to gain new results on the probabilistic traveling salesman problem. The probabilistic "traveling salesman" must decide on an a priori order in which to visit n cities (randomly distributed over a unit square) before learning that some cities can be omitted. We find the optimized average length of the pruned tour follows E((L) over bar (pruned))=rootnp(0.872-0.105p)f(np), where p is the probability of a city needing to be visited, and f(np)-->1 as np-->infinity. The average length of the a priori tour (before omitting any cities) is found to follow E(L-a priori)=rootn/pbeta(p), where beta(p)=1/[1.25-0.82 ln(p)] is measured for 0.05less than or equal topless than or equal to0.6. Scaling arguments and indirect measurements suggest that beta(p) tends towards a constant for p<0.03. Our stochastic annealing algorithm is based on limited sampling of the pruned tour lengths, exploiting the sampling error to provide the analog of thermal fluctuations in simulated (thermal) annealing. The method has general application to the optimization of functions whose cost to evaluate rises with the precision required.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Physics
Library of Congress Subject Headings (LCSH):	Simulated annealing (Mathematics), Traveling-salesman problem
Journal or Publication Title:	Physical Review E
Publisher:	American Physical Society
ISSN:	1063-651X
Date:	9 September 2003
Volume:	Vol.68
Number:	No.3
Number of Pages:	7
Identification Number:	10.1103/PhysRevE.68.036703
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access
Funder:	BP Amoco, Engineering and Physical Sciences Research Council (EPSRC)
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URI:	http://wrap.warwick.ac.uk/id/eprint/9242