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The Optimal Search for a Moving Target When the Search Path Is Constrained

Author

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  • James N. Eagle

    (Naval Postgraduate School, Monterey, California)

Abstract

A search is conducted for a target moving in discrete time among a finite number of cells according to a known Markov process. The searcher must choose one cell in which to search in each time period. The set of cells available for search depends upon the cell chosen in the last time period. The problem is to find a searcher path, i.e., a sequence of search cells, that maximizes the probability of detecting the target in a fixed number of time periods. We formulate the problem as a partially observable Markov decision process and present a finite time horizon POMDP solution technique which is simpler than the standard linear programming methods.

Suggested Citation

  • James N. Eagle, 1984. "The Optimal Search for a Moving Target When the Search Path Is Constrained," Operations Research, INFORMS, vol. 32(5), pages 1107-1115, October.
    • Handle: RePEc:inm:oropre:v:32:y:1984:i:5:p:1107-1115
    DOI: 10.1287/opre.32.5.1107
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    Citations

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    Cited by:

    1. Turgay Ayer & Oguzhan Alagoz & Natasha K. Stout, 2012. "OR Forum---A POMDP Approach to Personalize Mammography Screening Decisions," Operations Research, INFORMS, vol. 60(5), pages 1019-1034, October.
    2. 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.
    3. Jing Li & Ming Dong & Yijiong Ren & Kaiqi Yin, 2015. "How patient compliance impacts the recommendations for colorectal cancer screening," Journal of Combinatorial Optimization, Springer, vol. 30(4), pages 920-937, November.
    4. Givon, Moshe & Grosfeld-Nir, Abraham, 2008. "Using partially observed Markov processes to select optimal termination time of TV shows," Omega, Elsevier, vol. 36(3), pages 477-485, June.
    5. Bourque, François-Alex, 2019. "Solving the moving target search problem using indistinguishable searchers," European Journal of Operational Research, Elsevier, vol. 275(1), pages 45-52.
    6. Malek Ebadi & Raha Akhavan-Tabatabaei, 2021. "Personalized Cotesting Policies for Cervical Cancer Screening: A POMDP Approach," Mathematics, MDPI, vol. 9(6), pages 1-20, March.
    7. Andrej Y U. Garnaev, 1993. "A remark on a helicopter and submarine game," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(5), pages 745-753, August.
    8. 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.
    9. Zong-Zhi Lin & James C. Bean & Chelsea C. White, 2004. "A Hybrid Genetic/Optimization Algorithm for Finite-Horizon, Partially Observed Markov Decision Processes," INFORMS Journal on Computing, INFORMS, vol. 16(1), pages 27-38, February.
    10. James N. Eagle & Alan R. Washburn, 1991. "Cumulative search‐evasion games," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(4), pages 495-510, August.
    11. 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.
    12. Zehra Önen Dumlu & Serpil Sayın & İbrahim Hakan Gürvit, 2023. "Screening for preclinical Alzheimer’s disease: Deriving optimal policies using a partially observable Markov model," Health Care Management Science, Springer, vol. 26(1), pages 1-20, March.
    13. 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.
    14. 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.
    15. V. J. Baston & F. A. Bostock, 1989. "A one‐dimensional helicopter‐submarine game," Naval Research Logistics (NRL), John Wiley & Sons, vol. 36(4), pages 479-490, August.
    16. Corine M. Laan & Ana Isabel Barros & Richard J. Boucherie & Herman Monsuur & Judith Timmer, 2019. "Solving partially observable agent‐intruder games with an application to border security problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(2), pages 174-190, March.
    17. Ali Hajjar & Oguzhan Alagoz, 2023. "Personalized Disease Screening Decisions Considering a Chronic Condition," Management Science, INFORMS, vol. 69(1), pages 260-282, January.
    18. Adel Guitouni & Hatem Masri, 2014. "An orienteering model for the search and rescue problem," Computational Management Science, Springer, vol. 11(4), pages 459-473, October.
    19. 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.
    20. Turgay Ayer & Oguzhan Alagoz & Natasha K. Stout & Elizabeth S. Burnside, 2016. "Heterogeneity in Women’s Adherence and Its Role in Optimal Breast Cancer Screening Policies," Management Science, INFORMS, vol. 62(5), pages 1339-1362, May.
    21. Yanling Chang & Alan Erera & Chelsea White, 2015. "A leader–follower partially observed, multiobjective Markov game," Annals of Operations Research, Springer, vol. 235(1), pages 103-128, December.

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