Multiclass problems with binary SVM classifiers are commonly treated as a decomposition in several binary sub-problems. An open question is how to properly tune all these sub-problems (SVM hyperparameters) in order to have the lowest error rate for a SVM multiclass scheme based on decomposition. In this paper, we propose a new approach to optimize the generalization capacity of such SVM multiclass schemes. This approach consists in a global selection of hyperparameters for sub-problems all together and it is denoted as multi-model selection. A multi-model selection can outperform the classical individual model selection used until now in the literature. An evolutionary algorithm (EA) is proposed to perform multi-model selection. Experimentations with our EA method show the benefits of our approach over the classical one.