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An Optimal Branch-and-Bound Procedure for the Constrained Path, Moving Target Search Problem

Author

Listed:
  • James N. Eagle

    (Naval Postgraduate School, Monterey, California)

  • James R. Yee

    (University of Southern California, Los Angeles, California)

Abstract

A searcher and target move among a finite set of cells C = 1, 2, …, N in discrete time. At the beginning of each time period, one cell is searched. If the target is in the selected cell j , it is detected with probability q j . If the target is not in the cell searched, it cannot be detected during the current time period. After each search, a target in cell j moves to cell k with probability p jk . The target transition matrix, P = [ p jk ] is known to the searcher. The searcher's path is constrained in that if the searcher is currently in cell j , the next search cell must be selected from a set of neighboring cells C j . The object of the search is to minimize the probability of not detecting the target in T searches.

Suggested Citation

  • James N. Eagle & James R. Yee, 1990. "An Optimal Branch-and-Bound Procedure for the Constrained Path, Moving Target Search Problem," Operations Research, INFORMS, vol. 38(1), pages 110-114, February.
    • Handle: RePEc:inm:oropre:v:38:y:1990:i:1:p:110-114
    DOI: 10.1287/opre.38.1.110
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Michael Zabarankin & Stan Uryasev & Robert Murphey, 2006. "Aircraft routing under the risk of detection," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(8), pages 728-747, December.
    7. Mohamed Abd Allah El-Hadidy, 2016. "On Maximum Discounted Effort Reward Search Problem," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(03), pages 1-30, June.
    8. 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.
    9. 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.
    10. 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.
    11. Steven M. Shechter & Farhad Ghassemi & Yasin Gocgun & Martin L. Puterman, 2015. "Technical Note—Trading Off Quick versus Slow Actions in Optimal Search," Operations Research, INFORMS, vol. 63(2), pages 353-362, April.
    12. 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.
    13. Jesse Pietz & Johannes O. Royset, 2013. "Generalized orienteering problem with resource dependent rewards," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(4), pages 294-312, June.
    14. Hohzaki, Ryusuke & Iida, Koji, 2000. "A search game when a search path is given," European Journal of Operational Research, Elsevier, vol. 124(1), pages 114-124, July.
    15. 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.
    16. Manon Raap & Silja Meyer-Nieberg & Stefan Pickl & Martin Zsifkovits, 2017. "Aerial Vehicle Search-Path Optimization: A Novel Method for Emergency Operations," Journal of Optimization Theory and Applications, Springer, vol. 172(3), pages 965-983, March.
    17. 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.
    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. Morin, Michael & Abi-Zeid, Irène & Quimper, Claude-Guy, 2023. "Ant colony optimization for path planning in search and rescue operations," European Journal of Operational Research, Elsevier, vol. 305(1), pages 53-63.

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