Effect of model complexity for estimation of distribution algorithm in NK landscapes

Abstract

Evolutionary algorithms (EAs) have been widely proved to be effective in solving complex problems. Estimation of distribution algorithm (EDA) is an emerging EA, which manipulates probability models instead of genes for evolution EDA creates probability models based on the promising solution in the population and generates offspring by sampling from these models. The model complexity is a key factor in the performance of EDA. Complex models can express the relations among variables more accurately than simple models. However, for some problems with strong interaction among variables, building a model for all the relations becomes unrealistic and impractical due to its high computational cost and requirement for a large population size. This study aims to understand the behaviors of EDAs with different model complexities in NK landscapes. Specifically, this study compares the solution quality and convergence speed of univariate marginal distribution algorithm (UMDA), bivariate marginal distribution algorithm (BMDA), and estimation of Bayesian network (EBNA) in the NK landscapes with different parameter settings. The comparative results reveal that high complexity does not imply high performance: Simple model such as UMDA and BMDA can outperform complex mode like EBNA on the tested NK landscape problems. The results also show that BMDA achieves a stable high probability of generating the best solution and satisfactory solution quality; by contrast, the probability for EBNA drastically declines after some generations.