Heat exchanger behaviour is a multi-scale issue where local scale enhancement mechanisms coexist with global scale distribution ones. The present work investigates a multi-objective shape optimization of a heat exchanger. The proposed method is sufficiently robust to address multi-scale issues and allows industrial applications. Heat exchanger performances are evaluated using computational fluid dynamics (CFD) simulations. A genetic algorithm coupled with a Kriging-based metamodelling are used as optimization tools. Clustering and Self-Organizing Maps (SOM) are used to analyse the optimization results. A metamodel builds an approximation of a simulator response (CFD) whose evaluation cost is reduced to be used together with genetic algorithm. An adaptive sampling is used to build cheap and precise approximations. The present optimization method is applied to a plate heat exchanger which constitutes a representative example of the aforementioned multi-scale aspects. The results show that the metamodelling is a paramount element of the method, ensuring the robustness and the versatility of the optimisation process. Additionally, it allows to build correlations of the local scale used to determine the global performances of the heat exchanger. The clustering and the SOM highlight a finite number of shapes, which represent a compromise among the antagonist objective functions, tailoring the method to an industrial context.