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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.