This work considers the shape optimization of a crossflow plate heat exchanger air/water. The two objectives are to maximize the effectiveness while minimizing the total pressure drop. The shape variation concerns a trapezoidal rib mounted on the hot channels plates. A multiscale approach is presented, coupling CFD simulations and a NTU method. The optimization method is based on a genetic algorithm and kriging metamodels with adaptive sampling. Infill criteria are the maximum mean square error (MMSE) and multipoints expected improvement (q-EI). A clustering of the Pareto front individuals highlights a finite number of optimal shapes.