In this paper we have proposed a basic agent-based model based on evolutionary dynamics for investigating innovation initiation process. In our model we suppose each agent will represent a firm which is interacting with other firms through a given network structure. We consider a two-hit process for presenting a potentially successful innovation in this model and therefore at each time step each firm can be in on of three different stages which are respectively, Ordinary, Innovative, and Successful. We design different experiments in order to investigate how different interaction networks may affect the process of presenting a successful innovation to the market. In this experiments, we use five different network structures, i.e. Erdős and Rényi, Ring Lattice, Small World, Scale-Free and Distance-Based networks. According to the results of the simulations, for less frequent innovations like radical innovation, local structures are showing a better performance comparing to Scale-Free and Erdős and Rényi networks. Although as we move toward more frequent innovations, like incremental innovations, difference between network structures becomes less and non-local structures show relatively better performance.