The Influence of Noise on Multi-Parent Crossover for an Island Model GA

Many optimization problems tackled by evolutionary algorithms are not only computationally expensive, but also complicated with one or more sources of noise. One technique to deal with high computational overhead is parallelization. However, though the existing literature gives good insights about the expected behavior of parallelized evolutionary algorithms, we still lack an understanding of their performance in the presence of noise. This paper considers how parallelization might be leveraged together with multi-parent crossover in order to handle noisy problems. We present a rigorous running time analysis of an island model with weakly connected topology tasked with hill climbing in the presence of general additive noise. Our proofs yield insights into the relationship between the noise intensity and number of required parents. We translate this into positive and negative results for two kinds of multi-parent crossover operators. We then empirically analyze and extend this framework to investigate the trade-offs between noise impact, optimization time, and limits of computation power to deal with noise.