Study of the Influence of the Number Normalization Scheme Used in Two Chaotic Pseudo Random Number Generators Used as the Source of Randomness in Differential Evolution

TL;DR

This study investigates how different normalization schemes of chaotic pseudo random number generators influence the convergence speed of differential evolution algorithms, highlighting the impact of normalization method and probability distribution.

Contribution

It introduces the use of Gingerbread man and Tinkerbell chaotic maps with various normalization methods in differential evolution, analyzing their effects on algorithm performance.

Findings

Normalization method affects convergence speed.

Arctangent and straightforward normalization improve performance.

Chaotic PRNGs can enhance differential evolution efficiency.

Abstract

In many publications, authors showed that chaotic pseudo random number generators (PRNGs) may improve performance of the evolutionary algorithms. In this paper, we use two chaotic maps Gingerbread man and Tinkerbell as the chaotic PRNGs instead of the classical PRNG in the differential evolution. Numbers generated by this maps are normalized to the unit interval by three different methods -- operation modulo, straightforward number normalization where we know minimal and maximal generated number and arctangent of the two variables $x$ and $y$, where numbers $x$ and $y$ are generated by the Gingerbread man map and Tinkerbell map. The first goal of this paper is to show whether the differential evolution convergence speed might be affected by the way how we normalize number generated by the chaotic map. The second goal is to find out the influence of the probability distribution function of the selected chaotic PRNGs. The results mentioned below showed that the selected normalization method may improve differential evolution convergence speed, especially in the case of arctangent and straightforward number normalization, where we know the minimal and maximal generated numbers.