Title: Existence of optimal N-slinky-turn-spiral search paths for finding N-dimensional Brownian target

Authors: Mohamed Abd Allah El-Hadidy

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

Abstract: This paper presents more effective search technique for finding the N-dimensional Brownian target in N-dimensional space by using N-searchers. Each searcher moves along slinky-turn-spiral curve and starts its motion from the origin. An adaptive geometric features such as curvature and torsion of each searching path to meet the target is proposed. Rather than showing the existence of finite and optimal search paths, we find these optimal search paths which minimise the expected value of the first meeting time between one of the searchers and the target based on its geometric characteristics and features. A simulation study has been discussed to demonstrate the applicability of this technique.

Keywords: optimal search theory; geometric features; N-dimensional Brownian target; first meeting time.

DOI: 10.1504/IJMOR.2021.116313

International Journal of Mathematics in Operational Research, 2021 Vol.19 No.2, pp.180 - 203

Received: 16 Jan 2020
Accepted: 22 Feb 2020
Published online: 20 Jul 2021 *

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