Fuzzy Optimal Search Plan forN-Dimensional Randomly Moving Target

Abstract

This paper presents a search model that finds [Formula: see text]-dimensional randomly moving target in which any information of the target position is not available to the searchers. There exist [Formula: see text]-searchers, starting the searching process from the origin. Rather than finding the conditions that make the expected value of the first meeting time between one of the searchers and the target is finite, this work shows the existence of the fuzzy optimal search plan that minimizes the expected value of the first meeting time. The effectiveness of this method is illustrated by using an example with numerical results.

Existence of cooperative search technique to find a Brownian target

“…Besides that, they found the optimal search plan that minimizes this expected value. For different kinds of search plans on the line, plan, and space, the reader can see, El-Hadidy et al [11][12][13][14][15][16][17][18][19][20], Kagan and Ben-Gal [21], Guerrier and Holcman [22], Palyulin et al [23], Radmard and Croft [24], Stone et al [25], and Jia et al [26].…”

Minimizing the expected search time of finding the hidden object by maximizing the discount effort reward search

“…Earlier, many interesting methods to track the stochastically moving object have been presented by Dai et al [12] and Deilami et al [13]. Besides that, Mohamed et al [14,15], Mohamed and El-Hadidy [16], Mohamed and El-Hadidy [17], Beltagy and El-Hadidy [18], Abou-Gabal and El-Hadidy [19], Mohamed et al [20], Kassem and El-Hadidy [21], El-Hadidy and El-Bagoury [22], El-Hadidy [23][24][25][26][27][28][29][30][31], El-Hadidy and Alzulaibani [6,7], and El-Hadidy et al [32] provided many different mathematical treatments of this issue in both cases stochastically moving and hidden objects.…”

Existence of a finite multiplicative search plan with random distances and velocities to find a d-dimensional Brownian target

“…On the plane, Mohamed and El-Hadidy [8,9] and El-Hadidy [10] presented more interesting search strategies with deterministic distance and regular fixed velocity to find the two-dimensional randomly moving targets. On the space, El-Hadidy and colleagues [11][12][13][14][15][16] studied different techniques with deterministic distances and velocities by using multiple searchers. The main objective of these earlier works is to obtain the conditions that make the first meeting time between one of the searchers and the moving target finite.…”