  We explore the case of a group of random walkers looking for a target
randomly located in space, such that the number of walkers is not constant but
new ones can join the search, or those that are active can abandon it, with
constant rates $r_b$ and $r_d$, respectively. Exact analytical solutions are
provided both for the fastest-first-passage time and for the collective search
time required to reach the target, in the seminal case of Brownian walkers with
$r_d=0$. We prove that even for such a simplified situation there exists an
optimal rate $r_b$ at which walkers should join the search to minimize the
collective effort required to reach the target. We discuss how these results
open a new line to understand the optimal regulation of cooperative random
searches, e.g. for the case of biological foraging in social species.
