Title: Optimal 3-dimensional search model to find the underwater randomly hidden target

Authors: Mohamed Abd Allah El-Hadidy; M. Fakharany

Addresses: Mathematics and Statistics Department, Faculty of Science, Taibah University, Yanbu, Saudi Arabia; Mathematics Department, Faculty of Science, Tanta University, Tanta, Egypt ' Mathematics and Statistics Department, Faculty of Science, Taibah University, Yanbu, Saudi Arabia; Mathematics Department, Faculty of Science, Tanta University, Tanta, Egypt

Abstract: The searcher's path for finding a 3-dimensional underwater randomly located target like a black box for the air plan crash is studied. The searcher moves along slinky-turn-spiral curve and starts its motion from a known point (X₀, Y₀, Z₀). We focus on the geometry features such as curvature and torsion of the search path for the target position that has a known distribution. The searcher is desired to search in an optimal manner by obtaining the optimal values of the curvature and the torsion that minimise the expected time for detecting the target. An illustrative example has been given to demonstrate the applicability of this technique.

Keywords: optimal search theory; trivariate normal distribution; slinky-turn-spiral; geometry features.

DOI: 10.1504/IJMOR.2021.112929

International Journal of Mathematics in Operational Research, 2021 Vol.18 No.2, pp.210 - 235

Received: 03 Aug 2019
Accepted: 25 Dec 2019
Published online: 10 Feb 2021 *

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