Fitness Landscape Analysis of Genetic Programming Search Spaces with Local Optima Networks

Abstract

Fitness landscape analysis (FLA) refers to a set of techniques to characterise optimisation problems. This paper presents an FLA of three types of genetic programming (GP) benchmarks: parity, symbolic regression, and artificial ant. We applied a modern graph-based FLA tool called Local Optima Networks and several classical FLA metrics (fitness distance correlation, neutrality, and ruggedness measures) to study the tree-based GP search spaces. Our analysis shows that the search spaces for all problems contain many local optima and are highly deceptive. The parity problems are highly rugged and neutral. Conversely, the problems of symbolic regression are less rugged and neutral. Finally, the artificial ant problem is highly rugged but less neutral. Our results indicate that a mutation in deep nodes makes finding the global optimum difficult.