A genotype-phenotype-fitness assessment protocol for evolutionary self-assembly Wang tiles design

In a previous work we have reported on the evolutionary design optimisation of self-assembling Wang tiles capable of arranging themselves together into a target structure. Apart from the significant findings on how self-assembly is achieved, nothing has been yet said about the efficiency by which individuals were evolved. Specially in light that the mapping from genotype to phenotype and from this to fitness is clearly a complex, stochastic and non-linear relationship. One of the most common procedures would suggest running many experiments for different configurations followed by a fitness comparison, which is not only time-consuming but also inaccurate for such intricate mappings. In this paper we aim to report on a complementary dual assessment protocol to analyse whether our genetic algorithm, using morphological image analyses as fitness function, is an effective methodology. Thus, we present here fitness distance correlation to measure how effectively the fitness of an individual correlates to its genotypic distance to a known optimum, and introduce clustering as a mechanism to verify how the objective function can effectively differentiate between dissimilar phenotypes and classify similar ones for the purpose of selection.