We design, detail and test an approach to optimize a social welfare function over a surrogate model of a global multi-regional Computable General Equilibrium (CGE) model. Latin-Hypercube sampling generates random observations of policy instruments considered in the later optimization. The observations are individually solved in the CGE model and jointly define the data set on which a Multi-Layer Perceptron Neural Network is trained and validated in Python packages. The trained parameters of the Neural Network are passed to GAMS as an Algebraic Modelling language to optimize a welfare function over policy instruments, subject to the surrogate model and further topical constraints. The set-up and its implementation are to a large degree generic such that application to differently structured and detailed CGE models and considered policy instruments is straightforward. The main dis-advantage is that the generation of the observation sample is computing time intensive, on a modern laptop it required about 30 hours. The trained Neural Network replicates the simulation behavior of the CGE model quite accurately with all outputs predicted with a R2 > 99.998%. The representation as a Neural Network provides a set of relatively simple equations which can be solved very fast and implemented easily in different software packages. Besides optimization, such a surrogate model representing key input-output relations of a CGE model could hence also be integrated easily in some other modelling framework.