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Related papers: Global optimization using L\'evy flights

200 papers

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…

Optimization and Control · Mathematics 2025-08-20 Serena Dipierro , Giovanni Giacomin , Enrico Valdinoci

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…

Neural and Evolutionary Computing · Computer Science 2025-01-27 Mhd Ali Shehadeh , Jakub Kudela

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…

Statistical Mechanics · Physics 2019-03-27 Bartłomiej Dybiec , Karol Capała , Aleksei Chechkin , Ralf Metzler

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.

Statistical Mechanics · Physics 2007-06-26 Ralf Metzler , Aleksei V. Chechkin , Joseph Klafter

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…

Statistical Mechanics · Physics 2012-11-22 A. P. Riascos , José L. Mateos

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…

Statistical Mechanics · Physics 2015-06-23 A. P. Riascos , José L. Mateos

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…

Optimization and Control · Mathematics 2012-03-30 Xin-She Yang , Suash Deb

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…

Neural and Evolutionary Computing · Computer Science 2018-06-18 Louis Faury , Flavian Vasile , Clément Calauzènes , Olivier Fercoq

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…

Statistical Mechanics · Physics 2025-09-04 Claude Godrèche , Jean-Marc Luck

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…

Optimization and Control · Mathematics 2015-07-17 Da-Zheng Feng , Han-Zhe Feng , Hai-Qin Zhang

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…

Statistical Mechanics · Physics 2013-08-27 Abhishek Dhar , Keiji Saito

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…

Optimization and Control · Mathematics 2019-07-23 Brian Swenson , Soummya Kar , H. Vincent Poor , José M. F. Moura

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…

Statistical Mechanics · Physics 2020-08-26 A. Padash , A. V. Chechkin , B. Dybiec , I. Pavlyukevich , B. Shokri , R. Metzler

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…

Statistical Mechanics · Physics 2016-02-10 Denis Boyer , Inti Pineda

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…

Statistical Mechanics · Physics 2007-09-17 Michael A. Lomholt , Tal Koren , Ralf Metzler , Joseph Klafter

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…

Machine Learning · Computer Science 2020-03-11 Haotian Zhang , Jianyong Sun , Zongben Xu

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…

Optimization and Control · Mathematics 2016-01-26 Sergey Nikitin

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…

Robotics · Computer Science 2011-08-30 Donny K. Sutantyo , Serge Kernbach , Valentin A. Nepomnyashchikh , Paul Levi

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,…

Statistical Mechanics · Physics 2014-12-02 Giampaolo Cristadoro , Thomas Gilbert , Marco Lenci , David P. Sanders

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…

Statistical Mechanics · Physics 2024-04-12 J. C. Tzou , Leo Tzou