We consider the problem of optimizing black-box functions having sets of points as inputs (also referred to as clouds of points). Functions defined over sets are of common practical use and can be encountered when modeling turbine positions in wind farms, designs of experiments and designs of sensors or actuators networks, among others. In this work, we propose an evolutionary algorithm for functions defined over clouds of points. The clouds of points, with a possibly varying size, are represented as discrete uniform measures. In order to characterize the cross-over and mutation operators of the evolutionary algorithm, we rely on the Wasserstein barycenter [2]. The Wasserstein barycenter being a contracting operator, we introduce two types of mutations, namely the Boundary Mutation and the Random Mutation. The Boundary Mutation is devised to correct the contracting effect of the crossover. The Random Mutation plays its standard role of an unbiased and ergodic perturbation operator to counter premature convergence. The effects of the proposed operators on the evolutionary algorithm performance are studied on three families of test functions: wind farm proxies, the inertia of the points set and a Maximin design criterion. We implement the Wasserstein barycenter computation using the POT library [1]. These numerical tests allow us to asses the effect of the barycenter weights. Indeed, while for the crossover we adopt equal weights, several strategies to choose the weights (fixed versus random) are compared for the mutation. A second degree of freedom that is analyzed is the algorithmic arrangement of the calls to the operators. In this work, we consider and compare sequential and random calls to the various mutations. The performance of the algorithms involving Wasserstein barycenters are compared to a standard evolutionary search and a fully random search. The obtained results show the suitability of evolutionary operators involving optimal transport for the optimization of functions defined over sets of points, as near global optima are efficiently found for all three classes of problems (wind farm, inertia, design of experiment).