Intermittent random walks for an optimal search strategy: One-dimensional case

TL;DR

This paper investigates an optimal search strategy using intermittent random walks on a one-dimensional lattice, demonstrating how tuning the intermittency parameter significantly improves detection probability over pure random walks.

Contribution

It introduces a model of intermittent random walks for search strategies and identifies an optimal intermittency parameter that minimizes the probability of undetected targets.

Findings

Optimal intermittency parameter (N) reduces undetection probability.

Intermittent walks outperform pure random walks in detection efficiency.

Probability P_N is non-monotonic in , with a clear optimal value.

Abstract

We study the search kinetics of an immobile target by a concentration of randomly moving searchers. The object of the study is to optimize the probability of detection within the constraints of our model. The target is hidden on a one-dimensional lattice in the sense that searchers have no a priori information about where it is, and may detect it only upon encounter. The searchers perform random walks in discrete time n=0,1,2, ..., N, where N is the maximal time the search process is allowed to run. With probability \alpha the searchers step on a nearest-neighbour, and with probability (1-\alpha) they leave the lattice and stay off until they land back on the lattice at a fixed distance L away from the departure point. The random walk is thus intermittent. We calculate the probability P_N that the target remains undetected up to the maximal search time N, and seek to minimize this probability. We find that P_N is a non-monotonic function of \alpha, and show that there is an optimal choice \alpha_{opt}(N) of \alpha well within the intermittent regime, 0 < \alpha_{opt}(N) < 1, whereby P_N can be orders of magnitude smaller compared to the "pure" random walk cases \alpha =0 and \alpha = 1.