Methods for the analysis of evolutionary algorithms

Abstract

Analyzing evolutionary algorithms is often surprisingly difficult. It can be challenging even for very simple evolutionary algorithms on very simple functions. This is due to the fact that evolutionary algorithms are a class of randomized search heuristics mimicking natural evolution that have been designed to search effectively for good solutions in a vast search space without any thought about analysis. The directed random sampling of the search space they perform gives rise to complex and hard to analyze random processes that can be described as complex Markov chains as we have discussed in Sect. 3.1. This motivates us to start our analysis with evolutionary algorithms that are as simple as possible and consider fitness functions that are as simple as possible. We do not claim that such evolutionary algorithms are actually applied in practice or that example problems bear much resemblance to real optimization problems.