Scale-invariance of ruggedness measures in fractal fitness landscapes

TL;DR

This paper investigates the fractal and rugged properties of fitness landscapes generated by chaotic maps, revealing that ruggedness measures like correlation length and information content are scale-invariant and self-similar.

Contribution

It demonstrates the scale-invariance of ruggedness measures in fractal fitness landscapes created by chaos, providing insights into landscape analysis.

Findings

Ruggedness measures are scale-invariant.

Fitness landscapes exhibit fractal and self-similar properties.

Four different chaotic maps produce similar ruggedness characteristics.

Abstract

The paper deals with using chaos to direct trajectories to targets and analyzes ruggedness and fractality of the resulting fitness landscapes. The targeting problem is formulated as a dynamic fitness landscape and four different chaotic maps generating such a landscape are studied. By using a computational approach, we analyze properties of the landscapes and quantify their fractal and rugged characteristics. In particular, it is shown that ruggedness measures such as correlation length and information content are scale-invariant and self-similar.