Graphic statics provide a visual understanding of the relation between a structures’ shape and its efforts, a valuable quality in the field of structural conception. When combined to a shape grammar, the graphical method has proven to be a very powerful tool in the process of structural form-finding [Lee, 2015]. The shape-grammar based graphic statics tool (SGBGS- tool) presented by J. Lee generates truss networks for a given set of initial conditions by applying a chosen set of grammar-rules to the systems’ virtual equilibrium forces. For this approach to result in a truss that is structurally feasible however, the designer needs either a part of luck or some patience: while all resulting topologies are statically stable, only a few are interesting in terms of costs and constructability. An engineer whom would be given the task to apply the method manually would surely notice that in some specific situations, applying rule X results in unfortunate designs. Likewise, in some situations, given the structures’ outline, one would be more inclined to apply rule Y or Z than rule X. One might also consider to combine features of two available shapes. The SGBGS-method could greatly benefit from this “trial and error” approach, producing network topologies in a less-time consuming manner and with a more satisfying geometry – based on preferences determined by the user (i.e. fewer elements, lighter overall weight …). The aim of this project was to study the possibility of applying an evolutionary algorithm to the mentioned SGBGS-method, combining the wide shape-freedom enabled by the use of shape grammar to the fitness-based survival process of natural selection. A method supporting cross-overs of GDGS-geometries is proposed and implemented in an evolutionary algorithm to allow for an informed navigation of the design space. Additionally, the project considers the development of several possible fitness functions to influence the selection process of the algorithm. The resulting exploration approach aims at providing a creatively satisfying yet efficient way of generating truss networks – in terms of shape, statics and computation time.