Levy Flights, Non-local Search and Simulated Annealing

TL;DR

This paper introduces a novel stochastic optimization method combining Levy flights with simulated annealing, enabling efficient non-local search for the global minimum in complex potential landscapes.

Contribution

It proposes a new approach using Levy flights with variable stability index in simulated annealing to improve convergence speed in non-convex stochastic optimization.

Findings

Fast convergence to the ground state due to polynomial temperature decrease

Effective non-local search enabled by Levy flights with large jumps

Applicable to complex, unknown potential landscapes

Abstract

We solve a problem of non-convex stochastic optimisation with help of simulated annealing of Levy flights of a variable stability index. The search of the ground state of an unknown potential is non-local due to big jumps of the Levy flights process. The convergence to the ground state is fast due to a polynomial decrease rate of the temperature.