Stationary probability density of stochastic search processes in global optimization

TL;DR

This paper introduces a method to analytically approximate the stationary probability densities of stochastic search processes, enabling identification of regions likely to contain global optima with computational efficiency.

Contribution

It presents a novel, linear-cost density estimation technique for stochastic search processes, facilitating better understanding of search space regions with high probability of containing global optima.

Findings

Efficient approximation of stationary densities for stochastic search processes.

Ability to identify high-probability regions for global optima.

Linear computational cost per iteration, scalable to large problems.

Abstract

A method for the construction of approximate analytical expressions for the stationary marginal densities of general stochastic search processes is proposed. By the marginal densities, regions of the search space that with high probability contain the global optima can be readily defined. The density estimation procedure involves a controlled number of linear operations, with a computational cost per iteration that grows linearly with problem size.