Related papers: Global optimization using L\'evy flights
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…
The Unmanned Aerial Vehicle (UAV) path planning problem is a complex optimization problem in the field of robotics. In this paper, we investigate the possible utilization of this problem in benchmarking global optimization methods. We…
L\'evy walks are continuous time random walks with spatio-temporal coupling of jump lengths and waiting times, often used to model superdiffusive spreading processes such as animals searching for food, tracer motion in weakly chaotic…
Levy flights and subdiffusive processes and their properties are discussed. We derive the space- and time-fractional transport equations, and consider their solutions in external potentials. An extensive list of references is included.
We introduce a strategy of navigation in undirected networks, including regular, random, and complex networks, that is inspired by L\'evy random walks, generalizing previous navigation rules. We obtained exact expressions for the stationary…
We introduce a formalism of fractional diffusion on networks based on a fractional Laplacian matrix that can be constructed directly from the eigenvalues and eigenvectors of the Laplacian matrix. This fractional approach allows random walks…
Efficiency of an optimization process is largely determined by the search algorithm and its fundamental characteristics. In a given optimization, a single type of algorithm is used in most applications. In this paper, we will investigate…
The aim of global optimization is to find the global optimum of arbitrary classes of functions, possibly highly multimodal ones. In this paper we focus on the subproblem of global optimization for differentiable functions and we propose an…
Building upon the knowledge of the distribution of the first positive position reached by a random walker starting from the origin, one can derive new results on the statistics of the gap between the largest and second-largest positions of…
The global optimization have the very extensive applications in econometrics, science and engineering. However, the global optimization for non-convex objective functions is particularly difficult since most of the existing global…
A Levy walk is a non-Markovian stochastic process in which the elementary steps of the walker consist of motion with constant speed in randomly chosen directions and for a random period of time. The time of flight is chosen from a…
The paper considers a distributed algorithm for global minimization of a nonconvex function. The algorithm is a first-order consensus + innovations type algorithm that incorporates decaying additive Gaussian noise for annealing, converging…
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…
Among Markovian processes, the hallmark of L\'evy flights is superdiffusion, or faster-than-Brownian dynamics. Here we show that L\'evy laws, as well as Gaussians, can also be the limit distributions of processes with long range memory that…
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…
The advancement of artificial intelligence has cast a new light on the development of optimization algorithm. This paper proposes to learn a two-phase (including a minimization phase and an escaping phase) global optimization algorithm for…
The paper proposes a new algorithm for solving global univariate optimization problems. The algorithm does not require convexity of the target function. For a broad variety of target functions after performing (if necessary) several…
An efficient search algorithm is very crucial in robotic area, especially for exploration missions, where the target availability is unknown and the condition of the environment is highly unpredictable. In a very large environment, it is…
Continuous time random walks combining diffusive and ballistic regimes are introduced to describe a class of L\'evy walks on lattices. By including exponentially-distributed waiting times separating the successive jump events of a walker,…
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…