On strong homogeneity of two global optimization algorithms based on statistical models of multimodal objective functions

TL;DR

This paper investigates the implementation of global optimization algorithms based on statistical models, introducing the property of strong homogeneity and demonstrating that the P-algorithm and one-step Bayesian algorithm possess this property.

Contribution

It proposes a simple implementation of strongly homogeneous global optimization algorithms and proves that the P-algorithm and one-step Bayesian algorithm are strongly homogeneous.

Findings

P-algorithm is strongly homogeneous.

One-step Bayesian algorithm is strongly homogeneous.

A simple implementation of these algorithms is proposed.

Abstract

The implementation of global optimization algorithms, using the arithmetic of infinity, is considered. A relatively simple version of implementation is proposed for the algorithms that possess the introduced property of strong homogeneity. It is shown that the P-algorithm and the one-step Bayesian algorithm are strongly homogeneous.