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This paper presents the cooperation between two searchers at the origin to find a Random Walk moving target on the real line. No information is not available about the target’s position all the time. 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, we show the existence of the optimal search strategy which minimizes this first meeting time. The effectiveness of this model is illustrated using a numerical example.

In this paper, we present a complex cooperative search technique for finding the Random Walking microorganism cells on one of [Formula: see text]-intersect real lines at the origin. We have 2[Formula: see text] unit speed searchers starting together from the origin. Furthermore, proving the existence of a finite search plan, we are discussing the existence of optimality for this search plan which minimizes the expected value of the first meeting time between one of the searchers and the microorganism cells.

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We consider the coordinated search problem ,where the lost target is located on one of the two intersection lines excipt the point of intersection of the lines ,and the the point of intersection lines is the origin .We have four searchers who start together from the origin , where every two searchers aim to detect the lost target on their line .The position of the target is a random variable , which has unsymmetric distribution. In this paper we will find the expected value of the first meeting time for the searchers to return to starting point (the origin) after one of them has found the target and the optimal search plan to find it. We show that the previous studies are special cases from our studies.

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