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Optimal Search for a Moving Target in Discrete Time and Space

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  • Scott Shorey Brown

    (Daniel H. Wagner, Associates, Paoli, Pennsylvania)

Abstract

We consider optimal search for a moving target in discrete space. A limited amount of search effort is available at each of a fixed number of time intervals and we assume an exponential detection function. We show that a search plan maximizes the overall probability of detection if and only if for each time interval i the search conducted at time i maximizes the probability of detecting a stationary target with the probability that the stationary target occupies cell c equal to the probability that the moving target occupies cell c at time i and is not detected by the search at any time interval other than i . This characterization gives an iterative algorithm to compute optimal search plans. These plans are compared with incrementally optimal plans.

Suggested Citation

  • Scott Shorey Brown, 1980. "Optimal Search for a Moving Target in Discrete Time and Space," Operations Research, INFORMS, vol. 28(6), pages 1275-1289, December.
    • Handle: RePEc:inm:oropre:v:28:y:1980:i:6:p:1275-1289
    DOI: 10.1287/opre.28.6.1275
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    Cited by:

    1. Joseph Kadane, 2015. "Optimal discrete search with technological choice," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 81(3), pages 317-336, June.
    2. Patriksson, Michael, 2008. "A survey on the continuous nonlinear resource allocation problem," European Journal of Operational Research, Elsevier, vol. 185(1), pages 1-46, February.
    3. Robert F. Dell & James N. Eagle & Gustavo Henrique Alves Martins & Almir Garnier Santos, 1996. "Using multiple searchers in constrained‐path, moving‐target search problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(4), pages 463-480, June.
    4. Lau, Haye & Huang, Shoudong & Dissanayake, Gamini, 2008. "Discounted MEAN bound for the optimal searcher path problem with non-uniform travel times," European Journal of Operational Research, Elsevier, vol. 190(2), pages 383-397, October.
    5. Ron Teller & Moshe Zofi & Moshe Kaspi, 2019. "Minimizing the average searching time for an object within a graph," Computational Optimization and Applications, Springer, vol. 74(2), pages 517-545, November.
    6. Lawrence D. Stone & Alan R. Washburn, 1991. "Introduction special issue on search theory," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(4), pages 465-468, August.
    7. Hohzaki, Ryusuke & Iida, Koji, 2001. "Optimal ambushing search for a moving target," European Journal of Operational Research, Elsevier, vol. 133(1), pages 120-129, August.
    8. Hohzaki, Ryusuke & Iida, Koji, 1997. "Optimal strategy of route and look for the path constrained search problem with reward criterion," European Journal of Operational Research, Elsevier, vol. 100(1), pages 236-249, July.
    9. Duvocelle, Benoit & Flesch, János & Staudigl, Mathias & Vermeulen, Dries, 2022. "A competitive search game with a moving target," European Journal of Operational Research, Elsevier, vol. 303(2), pages 945-957.
    10. Joseph B. Kadane, 2015. "Optimal discrete search with technological choice," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 81(3), pages 317-336, June.
    11. Stanley J. Benkoski & Michael G. Monticino & James R. Weisinger, 1991. "A survey of the search theory literature," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(4), pages 469-494, August.
    12. Hong, Sung-Pil & Cho, Sung-Jin & Park, Myoung-Ju, 2009. "A pseudo-polynomial heuristic for path-constrained discrete-time Markovian-target search," European Journal of Operational Research, Elsevier, vol. 193(2), pages 351-364, March.
    13. Brian Lunday & Hanif Sherali, 2012. "Network interdiction to minimize the maximum probability of evasion with synergy between applied resources," Annals of Operations Research, Springer, vol. 196(1), pages 411-442, July.
    14. Delavernhe, Florian & Jaillet, Patrick & Rossi, André & Sevaux, Marc, 2021. "Planning a multi-sensors search for a moving target considering traveling costs," European Journal of Operational Research, Elsevier, vol. 292(2), pages 469-482.
    15. Frédéric Dambreville & Jean‐Pierre Le Cadre, 2002. "Detection of a Markovian target with optimization of the search efforts under generalized linear constraints," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(2), pages 117-142, March.
    16. Lyn C. Thomas & James N. Eagle, 1995. "Criteria and approximate methods for path‐constrained moving‐target search problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(1), pages 27-38, February.
    17. J F J Vermeulen & M van den Brink, 2005. "The search for an alerted moving target," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(5), pages 514-525, May.
    18. Hohzaki, Ryusuke, 2006. "Search allocation game," European Journal of Operational Research, Elsevier, vol. 172(1), pages 101-119, July.
    19. Alan R. Washburn, 1998. "Branch and bound methods for a search problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 45(3), pages 243-257, April.
    20. Calvin Kielas-Jensen & Venanzio Cichella & David Casbeer & Satyanarayana Gupta Manyam & Isaac Weintraub, 2021. "Persistent Monitoring by Multiple Unmanned Aerial Vehicles Using Bernstein Polynomials," Journal of Optimization Theory and Applications, Springer, vol. 191(2), pages 899-916, December.
    21. Johannes O. Royset & Hiroyuki Sato, 2010. "Route optimization for multiple searchers," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(8), pages 701-717, December.
    22. Michael P. Atkinson & Moshe Kress & Roberto Szechtman, 2017. "To catch an intruder: Part A—uncluttered scenario," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(1), pages 29-40, February.
    23. Frédéric Dambreville & Jean‐Pierre Le Cadre, 2007. "Constrained minimax optimization of continuous search efforts for the detection of a stationary target," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(6), pages 589-601, September.

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