On a Parallelised Diffusion Induced Stochastic Algorithm with Pure Random Search Steps for Global Optimisation

Abstract

We propose a stochastic algorithm for global optimisation of a regular function, possibly unbounded, defined on a bounded set with regular boundary; a function that attains its extremum in the boundary of its domain of definition. The algorithm is determined by a diffusion process that is associated with the function by means of a strictly elliptic operator that ensures an adequate maximum principle. In order to preclude the algorithm to be trapped in a local extremum, we add a pure random search step to the algorithm. We show that an adequate procedure of parallelisation of the algorithm can increase the rate of convergence, thus superseding the main drawback of the addition of the pure random search step.

On the Special Issue “Limit Theorems of Probability Theory”

“…In [15], Manuel L. Esquível and Nadezhda P. Krasii describe the structure of the random matrices by deterministic matrices, forming the skeletons of the random matrices. The authors propose to use an algorithm of matrix substitutions with entries in a finite field of integers that modulo some prime number, akin to the algorithm of one dimensional automatic sequences.…”