  Since Estimation of Distribution Algorithms (EDA) 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 continuous EDAs are still restricted to rather low dimensional
problems (smaller than 100D). Traditional EDAs have difficulties in solving
higher dimensional problems because of the curse of dimensionality and their
rapidly increasing computational cost. However, scaling up continuous EDAs for
higher dimensional optimization is still necessary, which is supported by the
distinctive feature of EDAs: Because a probabilistic model is explicitly
estimated, from the learnt model one can discover useful properties or features
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 EDAs. By using Weakly dependent variable Identification (WI) and Subspace
Modeling (SM), 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 produce a useful problem
structure characterization. EDA-MCC is the first successful instance of
multivariate model based EDAs that can be effectively applied a general class
of up to 500D problems. It also outperforms some newly developed algorithms
designed specifically for large scale optimization. In order to understand the
strength and weakness of EDA-MCC, we have carried out extensive computational
studies of EDA-MCC. Our results have revealed when EDA-MCC is likely to
outperform others on what kind of benchmark functions.
