Title: Optimal multiplicative generalised coordinated search technique to find a d-dimensional random walker

Authors: Mohamed Abd Allah El-Hadidy; Ajab Abdullah Alfreedi; Alaa Awad Alzulaibani

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 and Statistics Department, Faculty of Science, Taibah University, Yanbu, Saudi Arabia

Abstract: This paper presents a new interesting search model that minimises the expected value of the total detection cost of the d-dimensional random walk target with maximum probability. This technique is called a generalised coordinated linear search technique with multiple searchers. The target may be in one of the d-directions (dimensions) inside the space. We study this technique from a probabilistic and optimisation point of view where each direction is considered as a cylinder and it is searched by two searchers. They start the searching process from any point rather than the origin. The target's initial position is a random variable vector with a known probability distribution. We show the existence of a finite search plan by using the analytical methods. To minimise the expected value of the first meeting time between one of the searchers and the target, we should discuss the existence of the optimality conditions for this search plan and then find the optimal search plan. A numerical example illustrates the effectiveness of this technique.

Keywords: coordinated search technique; optimality conditions; d-dimensional random walk target.

DOI: 10.1504/IJOR.2021.117686

International Journal of Operational Research, 2021 Vol.42 No.1, pp.1 - 33

Received: 11 Oct 2018
Accepted: 17 Apr 2019
Published online: 21 Sep 2021 *

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