This paper considers the problem of planar multi-robot realizations of connectivity graphs. A realization is a set of planar positions for a team of robots with a connectivity graph that is identical to an a priori given connectivity graph with the additional constraint that it must be feasible. Feasibility means that that the robots must not be overlapping with each other. As the associated mathematical problem is known to be NP-hard, a stochastic approach based on genetic algorithms is proposed. First, a population set based on randomly generated planar and feasible multi-robot positions is generated. Next, a fitness function that measures the similarity of the graph of each member is constructed. Finally, new reproduction operators that enable the evolution of generations are introduced. An extensive statistical study with different number of robots demonstrates that the proposed algorithm can be used to obtain fairly complicated network topologies.