In European seismic prone countries most of the buildings have been constructed before the implementation of rigorous seismic and environmental regulations, therefore there is currently a pressing need to rehabilitate the existing built heritage by adopting efficient, sustainable and cheap retrofitting approaches. In this context, the paper focuses on 2D trussed perpendicular exoskeletons for retrofitting existing r.c. structures. In particular, starting from a case study of an existing building made of r.c., a performance-based optimization framework for the design is implemented through a real-coded Genetic algorithm, in order to determine the optimal number and position of exoskeletons around the building. Both 2D steel and timber exoskeletons are designed. The analysis of these retrofitting scenarios leads to valuable insights concerning the identification of the most efficient and sustainable consolidation approach, showing that timber exoskeletons are able to significantly reduce CO2 emissions and economic cost preserving structural safety of the existing building.