Computational aspects of the optimal transit path problem

Louis Caccetta; Ian Loosen; Volker Rehbock

doi:10.3934/jimo.2008.4.95

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2008, Volume 4, Issue 1: 95-105. Doi: 10.3934/jimo.2008.4.95

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Computational aspects of the optimal transit path problem

1.
Western Australian Centre of Excellence in Industrial Optimisation, Department of Mathematics and Statistics, Curtin University of Technology, Bentley, WA, 6102

Received: August 31, 2006

Revised: December 31, 2006

Published: December 2007

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Abstract

We consider a class of path design problems which arise when an object needs to traverse between two points through a specified region. The path must optimise a prescribed criterion such as risk, reliability or cost and satisfy a number of constraints such as total travel time. Problems of this type readily arise in the defence, transport and communication industries. We specifically look at the problem of determining an optimal (in terms of minimizing the overall probability of detection) transit path for a submarine moving through a field of sonar sensors, subject to a total time constraint. A computational strategy along with results are presented.

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Mathematics Subject Classification: Primary: 49J15, 49N90; Secondary: 90B10.

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