  We study the kinetics for the search of an immobile target by randomly moving
searchers that detect it only upon encounter. The searchers perform
intermittent random walks on a one-dimensional lattice. Each searcher can step
on a nearest neighbor site with probability "alpha", or go off lattice with
probability "1 - \alpha" to move in a random direction until it lands back on
the lattice at a fixed distance L away from the departure point. Considering
"alpha" and L as optimization parameters, we seek to enhance the chances of
successful detection by minimizing the probability P_N that the target remains
undetected up to the maximal search time N. We show that even in this simple
model a number of very efficient search strategies can lead to a decrease of
P_N by orders of magnitude upon appropriate choices of "alpha" and L. We
demonstrate that, in general, such optimal intermittent strategies are much
more efficient than Brownian searches and are as efficient as search algorithms
based on random walks with heavy-tailed Cauchy jump-length distributions. In
addition, such intermittent strategies appear to be more advantageous than
Levy-based ones in that they lead to more thorough exploration of visited
regions in space and thus lend themselves to parallelization of the search
processes.
