Related papers: Optimization of random search processes in the pre…
We study the efficiency of search processes based on Levy flights (LFs) with power-law distributed jump lengths in the presence of an external drift. While LFs turn out to be efficient search processes when relative to the starting point…
Optimal random foraging strategy has gained increasing concentrations. It is shown that L\'evy flight is more efficient compared with the Brownian motion when the targets are sparse. However, standard L\'evy flight generally cannot be…
Efficiency of search for randomly distributed targets is a prominent problem in many branches of the sciences. For the stochastic process of L\'evy walks, a specific range of optimal efficiencies was suggested under variation of search…
In many random search processes of interest in chemistry, biology or during rescue operations, an entity must find a specific target site before the latter becomes inactive, no longer available for reaction or lost. We present exact results…
The L\'evy flight foraging hypothesis asserts that biological organisms have evolved to employ (truncated) L\'evy flight searches due to such strategies being more efficient than those based on Brownian motion. However, we provide here a…
L\'{e}vy flights is a random walk where the step-lengths have a probability distribution that is heavy-tailed. It has been shown that L\'{e}vy flights can maximize the efficiency of resource searching in uncertain environments, and also…
A combined dynamics consisting of Brownian motion and L\'evy flights is exhibited by a variety of biological systems performing search processes. Assessing the search reliability of ever locating the target and the search efficiency of…
The search for hidden targets is a fundamental problem in many areas of science, engineering, and other fields. Studies of search processes often adopt a probabilistic framework, in which a searcher randomly explores a spatial domain for a…
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…
We investigated the relationships between search efficiency, movement strategy, and non-local communication in the biological context of animal foraging. We considered situations where the members of a population of foragers perform either…
We study analytically an intermittent search process in one dimension. There is an immobile target at the origin and a searcher undergoes a discrete time jump process starting at $x_0\geq0$, where successive jumps are drawn independently…
L\'evy Flights are paradigmatic generalised random walk processes, in which the independent stationary increments---the "jump lengths"---are drawn from an $\alpha$-stable jump length distribution with long-tailed, power-law asymptote. As a…
In this paper we propose and advocate the use of the so called L\'evy flights as a driving mechanism for a class of stochastic optimization computations. This proposal, for some reasons overlooked until now, is - in author's opinion - very…
This paper studies a class of enhanced diffusion processes in which random walkers perform L\'evy flights and apply it for global optimization. L\'evy flights offer controlled balance between exploitation and exploration. We develop four…
We consider a forager diffusing via a fractional heat equation and we introduce several efficiency functionals whose optimality is discussed in relation to the L\'evy exponent of the evolution equation. Several biological scenarios, such as…
We consider a stationary prey in a given region of space and we aim at detecting optimal foraging strategies. On the one hand, when the prey is uniformly distributed, the best possible strategy for the forager is to be stationary and…
It is widely accepted that inverse square L\'evy walks are optimal search strategies because they maximize the encounter rate with sparse, randomly distributed, replenishable targets when the search restarts in the vicinity of the…
Search strategies based on random walk processes with long-tailed jump length distributions (Levy walks) on the one hand and intermittent behavior switching between local search and ballistic relocation phases on the other, have been…
We address the generic problem of random search for a point-like target on a line. Using the measures of search reliability and efficiency to quantify the random search quality, we compare Brownian search with L\'evy search based on…
Levy flights are known to be optimal search strategies in the particular case of revisitable targets. In the relevant situation of non revisitable targets, we propose an alternative model of bidimensional search processes, which explicitly…