There is an abundance of prior research on the optimization of production systems, but there is a research gap when it comes to optimizing which components should be included in a design, and how they should be connected. To overcome this gap, a novel approach is presented for topology optimization of production systems using a genetic algorithm (GA). This GA employs similarity-based mutation and recombination for the creation of offspring, and discrete-event simulation for fitness evaluation. To reduce computational cost, an extension to the GA is presented in which a neural network functions as a surrogate model for simulation. Three types of neural networks are compared, and the type most effective as a surrogate model is chosen based on its optimization performance and computational cost. Both the unassisted GA and neural network-assisted GA are applied to an industrial case study and a scalability case study. These show that both approaches are effective at finding the optimal solution in industrial settings, and both scale well as the number of potential solutions increases, with the neural network-assisted GA having the better scalability of the two.