Optimal searching for a Helix target motion

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• 作者：Abd Allah El-Hadidy Mohamed (1)
  
  1. Department of Mathematics ; Faculty of Science ; Tanta University ; Tanta ; 31527 ; Egypt
  
• 关键词：Helix motion ; optimal search plan ; first meeting time ; probability measure ; multiobjective nonlinear programming problem ; 90B40 ; 60K30 ; 60D05
• 刊名：SCIENCE CHINA Mathematics
• 出版年：2015
• 出版时间：April 2015
• 年：2015
• 卷：58
• 期：4
• 页码：749-762
• 全文大小：564 KB
• 参考文献：1. Balkhi, Z (1987) Generalized optimal search paths for continuous univariate random variable. Oper Res 23: pp. 67-96
  2. Balkhi, Z (1987) The generalized linear search problem, existence of optimal search paths. J Oper Res Soc Japan 30: pp. 399-420
  3. Beck, A, Beck, M (1992) The Revenge of the linear search problem. SIAM J Control Optim 30: pp. 112-122 CrossRef
  4. Beltagy, M, El-Hadidy, M (2013) Parabolic spiral search plan for a randomly located target in the plane. ISRN Math Anal 2013: pp. 151598
  5. Benkoski, S, Monticino, M, Weisinger, J (1991) A survey of the search theory literature. Naval Res Logist 38: pp. 469-494 2/1520-6750(199108)38:4<469::AID-NAV3220380404>3.0.CO;2-E" target="_blank" title="It opens in new window">CrossRef
  6. Bourgault, F, Furukawa, T, Durrant-Whyte, H (2003) Coordinated decentralized search for a lost target in a bayesian world. Proc IEEE/RSJ Int Conf Intel Robot Sys 1: pp. 48-53
  7. Bourgault, F, Furukawa, T, Durrant-Whyte, H (2006) Optimal search for a lost target in a Bayesian world. Field Serv Robot 24: pp. 209-222 21" target="_blank" title="It opens in new window">CrossRef
  8. El-Hadidy, M (2013) Optimal spiral search plan for a randomly located target in the plane. Int J Oper Res.
  9. El-Hadidy, M, Abou-Gabal, H (2014) Optimal searching for a randomly located target in a bounded known region. Int J Comput Sci Math.
  10. El-Rayes, A, Mohamed, A, Abou-Gabal, H (2003) Linear search for a brownian target motion. Acta Math Sci J Ser B 23: pp. 321-327
  11. Franck, W (1965) An optimal search problem. SIAM Rev 7: pp. 503-512 CrossRef
  12. Gan, S, Sukkarieh, S (2011) Multi-uav target search using explicit decentralized gradient-based negotiation. Proceeding IEEE International Conference on Robotics and Automation. IEEE, New York, pp. 751-756
  13. Hong, S, Cho, S, Park, M (2009) Optimal search-relocation trade-off in markovian-target searching. Comp Oper Res 36: pp. 2097-2104 2008.07.007" target="_blank" title="It opens in new window">CrossRef
  14. Iida, K (1992) Studies on the Optimal Search Plan. Springer-Verlag, New York 2-2876-9" target="_blank" title="It opens in new window">CrossRef
  Annual Report. La Jolla, California
  15. Koopman, B S (1946) earch and screening. OEG Report 56. US Government Printing Office, Washington, DC
  16. Lanillos, P, Besada-Portas, E, Pajares, G (2012) Minimum time search for lost targets using cross entropy optimization. IEEE/RSJ International Conference on Intelligent Robots and Systems. IEEE, New York, pp. 602-609
  17. Lukka, M (1974) On the Optimal Searching Tracks for A Stationary Target. University of Turku, Turku
  18. Miller, A, Moskowitz, I (1996) Generalizations of the carlton-kimball distribution for a target鈥檚 future location. Comput Math Appl 31: pp. 61-68 221(96)00031-4" target="_blank" title="It opens in new window">CrossRef
  19. Mohamed, A (2005) The generalized search for one dimensional random walker. Int J Pure Appl Math 19: pp. 375-387
  20. Mohamed, A, Abou-Gabal, H, El-Hadidy, M (2009) Coordinated search for a randomly located target on the plane. Eur J Pure Appl Math 2: pp. 97-111
  21. Mohamed, A, El-Hadidy, M (2013) Coordinated search for a conditionally deterministic target motion in the plane. Eur J Math Sci 2: pp. 272-295
  22. Mohamed, A, El-Hadidy, M (2013) Existence of a periodic search strategy for a parabolic spiral target motion in the plane. Afrika Matematika J 24: pp. 145-160 CrossRef
  23. Mohamed, A, El-Hadidy, M (2013) Optimal multiplicative generalized linear search plan for a discrete random walker. J Optim 2013: pp. 706176
  24. Mohamed, A, Fergany, H, El-Hadidy, M (2012) On the coordinated search problem on the plane. Istan Univ J Sch Busin Admin 41: pp. 80-102
  25. Mohamed, A, Kassem, M, El-Hadidy, M (2011) Multiplicative linear search for a brownian target motion. Appl Math Model 35: pp. 4127-4139 2011.03.024" target="_blank" title="It opens in new window">CrossRef
  26. Reyniers, D (1995) Coordinated two searchers for an object hidden on an interval. J Operational Res Soc 46: pp. 1386-1392 CrossRef
  27. Reyniers, D (1996) Coordinated search for an object on the line. Eur J Oper Res 95: pp. 663-670 2217(96)00314-1" target="_blank" title="It opens in new window">CrossRef
  28. Sarmiento, A, Murrieta-Cid, R, Hutchinson, S (2009) An efficient motion strategy to compute expected-time locally optimal continuous search paths in known environments. Adv Robot 23: pp. 1533-1560 2496339799170" target="_blank" title="It opens in new window">CrossRef
  29. Song, N, Teneketizs, D (2004) Discrete search with multiple sensors. Math Meth Oper Res 60: pp. 1-13 CrossRef
  30. Stone, L (1975) Theory of Optimal Search. Academic Press, New York
  31. Stone, L (1989) What is happened in search theory since the 1975 Lanchester prize?. Oper Res 37: pp. 501-506 287/opre.37.3.501" target="_blank" title="It opens in new window">CrossRef
  32. Stone, L, Keller, C, Kratzke, T (2011) Search Analysis for the Location of the AF447 Underwater Wreckage. Report to BEA, Metron
  33. Zhu, Q, Oommen, B (2009) Estimation of distributions involving unobservable events: The case of optimal search with unknown target distributions. Pat Anal Appl 12: pp. 37-53 CrossRef
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Chinese Library of Science
  Applications of Mathematics
  
• 出版者：Science China Press, co-published with Springer
• ISSN：1869-1862

文摘

This paper discusses a search problem for a Helix target motion in which any information of the target position is not available to the searchers. There exist three searchers start searching for the target from the origin. The purpose of this paper is to formulate a search model and finds the conditions under which the expected value of the first meeting time between one of the searchers and the target is finite. Also, the existence of the optimal search plan that minimizes the expected value of the first meeting time is shown. Furthermore, this optimal search plan is found. The effectiveness of this method is illustrated by using an example with numerical results.