Existence of a periodic search strategy for a parabolic spiral target motion in the plane

Journal of Taibah University for Science

Alzulaibani

2019

Self Cite

We present the existence of a finite search plan to find Brownian target on the d-space by using d-searchers. Each searcher moves continuously in both directions of the origin (starting point) of the line (field of its search) with random distances and velocities. We express theses distances and velocities with independent random variables with known probability density functions (PDFs). We present more analysis about the density of the random distances in our model by using Fourier-Laplace representation. This analysis will provide us with the conditions that make the expected value of the first meeting time between the target and one of the searchers finite.

Section: Example 31mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Journal of Taibah University for Science

Alzulaibani

2019

Self Cite

“…More recently, the search problem for a moving target through a finite set of cells with a multiple search speed option has been investigated by Hong et al (2009). Also, some different kinds of search plans have been studied by El-Hadidy (2015a, 2015b, 2015c, Mohamed and El-Hadidy (2013a, 2013b, 2013c, Mohamed et al (2012), Beltagy and El-Hadidy (2013), El-Hadidy and Abou-Gabal (2014), Kassem and El-Hadidy (2014), El-Hadidy and El-Bagoury (2014) and El-Hadidy and Kassem (2015).…”

Section: Literature Reviewmentioning

confidence: 99%

M-states search problem for a lost target with multiple sensors

Teamah

Kassem

2017

IJMOR

This paper considers the discrete search problem for a single lost target by using multiple sensors. The lost target either located in one of a finite set of different states (cells) or moved through them according to random process with discrete time and discrete state space. A search effort at each fixed number of time intervals is a random variable with a given distribution. The probability that the target in a certain state j at a certain time i and the detection function is supposed to be known to the searchers. We seek for the optimal distribution of the effort that minimises the probability of undetection the target over the set of possible different states. Our aim is to deduce an explicit formula for the random distribution of the random variable effort. An algorithm is constructed for obtaining this optimal solution. The effectiveness of this method is illustrated using some examples with numerical results.Keywords: optimal search effort; probability of undetection; nonlinear stochastic programming problem; discrete search problem; deterministic nonlinear stochastic programming problem.

“…The target has symmetric or asymmetric distribution and with less information about this target available to the searchers. More recently, Mohamed and El-Hadidy [26] studied this problem when the target moves with parabolic spiral in the plane and starts its motion from a random point. Also, Mohamed and El-Hadidy [27] disscussed this problem in the plane when the target moves randomly with conditionally deterministic motion.…”

Section: Introductionmentioning

confidence: 99%

Optimal Multiplicative Generalized Linear Search Plan for a Discrete Random Walker

Mohamed

Journal of Optimization

2013

Self Cite

This paper formulates a search model that gives the optimal search plan for the problem of finding a discrete random walk target in minimum time. The target moves through one of n-disjoint real lines in R : we have n-searchers starting the searching process for the target from any point rather than the origin. We find the conditions that make the expected value of the first meeting time between one of the searchers and the target finite. Furthermore, we show the existence of the optimal search plan that minimizes the expected value of the first meeting time and find it. The effectiveness of this model is illustrated using numerical example.