Scaling Up Estimation of Distribution Algorithms for Continuous Optimization

Since estimation of distribution algorithms (EDAs) were proposed, many attempts have been made to improve EDAs´ performance in the context of global optimization. So far, the studies or applications of multivariate probabilistic model-based EDAs in continuous domain are still mostly restricted to low-dimensional problems. Traditional EDAs have difficulties in solving higher dimensional problems because of the curse of dimensionality and rapidly increasing computational costs. However, scaling up continuous EDAs for large-scale optimization is still necessary, which is supported by the distinctive feature of EDAs: because a probabilistic model is explicitly estimated, from the learned model one can discover useful properties of the problem. Besides obtaining a good solution, understanding of the problem structure can be of great benefit, especially for black box optimization. We propose a novel EDA framework with model complexity control (EDA-MCC) to scale up continuous EDAs. By employing weakly dependent variable identification and subspace modeling, EDA-MCC shows significantly better performance than traditional EDAs on high-dimensional problems. Moreover, the computational cost and the requirement of large population sizes can be reduced in EDA-MCC. In addition to being able to find a good solution, EDA-MCC can also provide useful problem structure characterizations. EDA-MCC is the first successful instance of multivariate model-based EDAs that can be effectively applied to a general class of up to 500-D problems. It also outperforms some newly developed algorithms designed specifically for large-scale optimization. In order to understand the strengths and weaknesses of EDA-MCC, we have carried out extensive computational studies. Our results have revealed when EDA-MCC is likely to outperform others and on what kind of benchmark functions.