Generalized Coordinated Search Problem for a Randomly Located Target

In this paper, we aim to obtain the investigation of the coordinated search problem, in which the velocities of each searcher are random variables. Our main goal is to find a randomly located target on the real line; this target may be a hole in an oil pipeline or a cut in a power cable below the sea surface. Currently, there are two searchers on the line, and instead of starting at the origin, they search from any point on the line. The first searcher searches the right part, and the second searcher searches the left part. We provide the most efficient coordinated search method, and we calculate the expected value of the time to detect the target. In addition, the conditions under which this expected value can be minimized were derived. The most important aspect of this method is that we have possession of the most effective method for search optimization.