We propose a simple but effective multi-source domain generalization technique based on deep neural networks by incorporating optimized normalization layers that are specific to individual domains. Our approach employs multiple normalization methods while learning separate affine parameters per domain. For each domain, the activations are normalized by a weighted average of multiple normalization statistics. The normalization statistics are kept track of separately for each normalization type if necessary. Specifically, we employ batch and instance normalizations in our implementation to identify the best combination of these two normalization methods in each domain. The optimized normalization layers are effective to enhance the generalizability of the learned model. We demonstrate the state-of-the-art accuracy of our algorithm in the standard domain generalization benchmarks, as well as viability to further tasks such as multi-source domain adaptation and domain generalization in the presence of label noise.