Lévy flights in binary optimization

Lévy flights as an underlying mechanism for global optimization algorithms

In this paper we propose and advocate the use of the so called Lévy 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 appropriate to satisfy the need for algorithm, which is capable of generating trial steps of very different length in the search space. The required balance be...

Lévy flights and Lévy-Schrödinger semigroups

We analyze two different confining mechanisms for Lévy flights in the presence of external potentials. One of them is due to a conservative force in the corresponding Langevin equation. Another is implemented by Lévy-Schrödinger semigroups which induce so-called topological Lévy processes (Lévy flights with locally modified jump rates in the master equation). Given a stationary probability func...

Microscopic characterization of Lévy flights of light in atomic vapors

Lévy-Flights for Particle Swarm Optimisation Algorithms on Graphical Processing Units

Particle Swarm Optimisation (PSO) is a powerful algorithm for space search problems such as parametric optimisation. Particles with Lévy-Flights have a long-tailed probability of outlier jumps in the problem space that provide a good compromise between local space exploration and local minima avoidance. Generating many particles and their trajectories with Lévy-random deviates is computationall...

The Symmetric Stable Lévy Flights and the Feynman Path Integral

We determine the solution of the fractional spatial diffusion equation in n-dimensional Euclidean space for a “free” particle by computing the corresponding propagator. We employ both the Hamiltonian and Lagrangian approaches which produce exact results for the case of jumps governed by symmetric stable Lévy flights.