Efficient search by optimized intermittent random walks

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.