Title: Spiral with line segment directory for a helix search path to find a randomly located target in the space

Authors: Mohamed Abd Allah El-Hadidy

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

Abstract: In this paper we present more interesting search plan in the space to find a lost hanging black box in the water from a view point of computational stochastic geometry. The space is divided into cubic cells with knowing side length. There exist one searcher moves on helix path along spiral with line segment directory. Depending on the target has known trivariate known distribution, we focus on the optimal geometry features such as curvature and torsion of the helix search path which minimise the expected value of detecting the target. Assuming trivariate standard normal distribution we present numerical example to show the applicability of this model.

Keywords: computational stochastic geometry; search theory; trivariate standard normal distribution.

DOI: 10.1504/IJOR.2021.113502

International Journal of Operational Research, 2021 Vol.40 No.2, pp.185 - 199

Received: 25 Oct 2017
Accepted: 26 May 2018
Published online: 09 Mar 2021 *

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