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Searching for a Target Traveling between a Hiding Area and an Operating Area over Multiple Routes

DOI: 10.4236/ajor.2015.54020, PP. 258-273

Keywords: Optimal Search Design, Moving Target with Constrained Pathways, Single or Multiple Searchers, Escape Probability, Mean Time to Detection

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Abstract:

We consider the problem of searching for a target that moves between a hiding area and an operating area over multiple fixed routes. The search is carried out with one or more cookie-cutter sensors, which can detect the target instantly once the target comes within the detection radius of the sensor. In the hiding area, the target is shielded from being detected. The residence times of the target, respectively, in the hiding area and in the operating area, are exponentially distributed. These dwell times are mathematically described by Markov transition rates. The decision of which route the target will take on each travel to and back from the operating area is governed by a probability distribution. We study the mathematical formulation of this search problem and analytically solve for the mean time to detection. Based on the mean time to capture, we evaluate the performance of placing the searcher(s) to monitor various travel route(s) or to scan the operating area. The optimal search design is the one that minimizes the mean time to detection. We find that in many situations the optimal search design is not the one suggested by the straightforward intuition. Our analytical results can provide operational guidances to homeland security, military, and law enforcement applications.

References

[1]  Koopman, B.O. (1999) Search and Screening: General Principles with Historical Applications. The Military Operations Research Society, Inc., Alexandria.
[2]  Stone, L.D. (1989) Theory of Optimal Search. 2nd Edition, Operations Research Society of America, Arlington.
[3]  Wagner, D.H., Mylander, W.C. and Sanders, T.J. (1999) Naval Operations Analysis. 3rd Edition, Naval Institute Press, Annapolis.
[4]  Washburn, A. (2014) Search and Detection. 5th Edition, Create Space Independent Publishing Platforms.
[5]  Chung, H., Polak, E., Royset, J.O. and Sastry, S. (2011) On the Optimal Detection of an Underwater Intruder in a Channel Using Unmanned Underwater Vehicles. Naval Research Logistics, 58, 804-820.
http://dx.doi.org/10.1002/nav.20487
[6]  Chung, T.H., Hollinger, G.A. and Isler, V. (2011) Search and Pursuit-Evasion in Mobile Robotics. Autonomous Robots, 31, 299-316.
http://dx.doi.org/10.1007/s10514-011-9241-4
[7]  Chung, T.H. and Silvestrini, R.T. (2014) Modeling and Analysis of Exhaustive Probabilistic Search. Naval Research Logistics, 61, 164-178.
http://dx.doi.org/10.1002/nav.21574
[8]  Kress, M. and Royset, J.O. (2008) Aerial Search Optimization Model (ASOM) for UAVs in Special Operations. Military Operations Research, 13, 23-33.
http://dx.doi.org/10.5711/morj.13.1.23
[9]  Wang, H. and Zhou, H. (2015) Computational Studies on Detecting a Diffusing Target in a Square Region by a Stationary or Moving Searcher. American Journal of Operations Research, 5, 47-68.
http://dx.doi.org/10.4236/ajor.2015.52005
[10]  Wilson, K.E., Szechtman, R. and Atkinson, M.P. (2011) A Sequential Perspective on Searching for Static Targets. European Journal of Operational Research, 215, 218-226.
http://dx.doi.org/10.1016/j.ejor.2011.05.045

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