Soft robots diverge from traditional rigid robotics, offering unique advantages in adaptability, safety, and human-robot interaction. In some cases, soft robots can be powered by biohybrid actuators and the design process of these systems is far from straightforward. We analyse here two algorithms that may assist the design of these systems, namely, NEAT (NeuroEvolution of Augmented Topologies) and HyperNEAT (Hypercube-based NeuroEvolution of Augmented Topologies). These algorithms exploit the evolution of the structure of actuators encoded through neural networks. To evaluate these algorithms, we compare them with a similar approach using the Age Fitness Pareto Optimisation (AFPO) algorithm, with a focus on assessing the maximum displacement achieved by the discovered biohybrid morphologies. Additionally, we investigate the effects of optimisation against both the volume of these morphologies and the distance they can cover. To further accelerate the computational process, the proposed methodology is implemented in a client-server setting; so, the most demanding calculations can be executed on specialised and efficient hardware. The results indicate that the HyperNEAT-based approach excels in identifying morphologies with minimal volumes that still achieve satisfactory displacement targets.