Non-Markovian and Collective Search Strategies

Abstract: Agents searching for a target can improve their efficiency by memorizing where they have already been searching or by cooperating with other searchers and using strategies that benefit from collective effects. This chapter reviews such concepts: non-Markovian and collective search strategies. We start with the first passage properties of continuous non-Markovian processes and then proceed to the discrete random walker with 1-step and n-step memory. Next we discuss the auto-chemotactic walker, a random walker that produces a diffusive chemotactic cue from which the walker tries to avoid. Then ensembles of agents searching for a single target are discussed, whence the search efficiency may comprise in addition to the first passage time also metabolic costs. We consider the first passage properties of ensembles of chemotactic random walkers and then the pursuit problem, in which searchers (or hunters / predators) see the mobile target over a certain distance. Evasion strategies of single or many targets are also elucidated. Finally we review collective foraging strategies comprising many searchers and many immobile targets. We finish with an outlook on future research directions comprising yet unexplored search strategies of immune cells and in swarm robotics.