  An efficient searcher needs to balance properly the tradeoff between the
exploration of new spatial areas and the exploitation of nearby resources, an
idea which is at the core of scale-free L\'evy search strategies. Here we study
multi-scale random walks as an approximation to the scale- free case and derive
the exact expressions for their mean-first passage times in a one-dimensional
finite domain. This allows us to provide a complete analytical description of
the dynamics driving the asymmetric regime, in which both nearby and faraway
targets are available to the searcher. For this regime, we prove that the
combination of only two movement scales can be enough to outperform both
balistic and L\'evy strategies. This two-scale strategy involves an optimal
discrimination between the nearby and faraway targets, which is only possible
by adjusting the range of values of the two movement scales to the typical
distances between encounters. So, this optimization necessarily requires some
prior information (albeit crude) about targets distances or distributions.
Furthermore, we found that the incorporation of additional (three, four, ...)
movement scales and its adjustment to target distances does not improve further
the search efficiency. This allows us to claim that optimal random search
strategies in the asymmetric regime actually arise through the informed
combination of only two walk scales (related to the exploitative and the
explorative scale, respectively), expanding on the well-known result that
optimal strategies in strictly uninformed scenarios are achieved through L\'evy
paths (or, equivalently, through a hierarchical combination of multiple
scales).
