From Royal Road to Epistatic Road for Variable Length Evolution Algorithm

TL;DR

This paper introduces a flexible family of fitness landscapes for variable length representations in evolutionary algorithms, enabling analysis of neutrality and epistasis effects on algorithm performance.

Contribution

It proposes a novel tunable landscape model combining features of Royal Road and NK landscapes, filling a gap in theoretical frameworks for VLR in EAs.

Findings

Performance varies with neutrality and epistasis levels

Adaptive walks reveal landscape ruggedness

Correlation length correlates with algorithm success

Abstract

Although there are some real world applications where the use of variable length representation (VLR) in Evolutionary Algorithm is natural and suitable, an academic framework is lacking for such representations. In this work we propose a family of tunable fitness landscapes based on VLR of genotypes. The fitness landscapes we propose possess a tunable degree of both neutrality and epistasis; they are inspired, on the one hand by the Royal Road fitness landscapes, and the other hand by the NK fitness landscapes. So these landscapes offer a scale of continuity from Royal Road functions, with neutrality and no epistasis, to landscapes with a large amount of epistasis and no redundancy. To gain insight into these fitness landscapes, we first use standard tools such as adaptive walks and correlation length. Second, we evaluate the performances of evolutionary algorithms on these landscapes for various values of the neutral and the epistatic parameters; the results allow us to correlate the performances with the expected degrees of neutrality and epistasis.