This work presents an innovative computationally-efficient methodology for the synthesis of reflectarrays through the System-by-Design (SbD) paradigm. The proposed approach integrates different analysis and synthesis functional blocks in order to yield effective solutions while reducing the computational burden of the design procedure. Towards this end, a fast surrogate model is used to predict the electromagnetic response of each candidate solution, while a global optimizer is used to effectively explore the search space and synthesize a reduced-complexity reflectarray surface layout satisfying specific radiation features.