  We consider a problem of finding a target located in a finite $d$-dimensional
domain, using $N$ independent random walkers, when partial information on the
target location is given as a probability distribution. When $N$ is large, the
first-passage time sensitively depends on the initial searcher distribution,
which invokes the question of what is the optimal searcher distribution that
minimizes the first-passage time. Here, we analytically derive the equation for
the optimal distribution and explore its limiting expressions. If the target
volume can be ignored, the optimal distribution is proportional to the target
distribution to the power of one-third. If we consider a target of a finite
volume and the probability of initial overlapping of searchers with the target
cannot be ignored in the large $N$ limit, the optimal distribution has a weak
dependence on the target distribution, given as a logarithm of the target
distribution. Using Langevin dynamics simulations, we numerically demonstrate
our predictions in one- and two-dimensions.
