The field of neuroevolution has achieved much attention in recent years from both academia and industry. Numerous papers have reported its successful applications in different fields ranging from medical domain to autonomous systems. However, it is not clear which evolutionary optimization techniques lead to the best results. In this paper, multilayer perceptron (MLP) neural networks (NNs) are trained and optimized using four advanced bio-inspired evolutionary algorithms (EA). The algorithms are Multi-Verse Optimizer (MVO), Moth-flame optimization (MFO), Cuckoo Search (CS) and Particle Swarm Optimization (PSO). Each algorithm is equipped with two operators: evolutionary population dynamics and mutation, which impact on exploration and exploitation. Optimized MLPs are then used for the navigation of an autonomous robot. Accuracy and area under the curve metrics are used for the evaluation and comparison metrics. Moreover, two well-regarded gradient descent algorithms including Back propagation (BP) and Levenberg Marquardt (LM) are utilized to validate the results obtained by evolutionary-based MLP trainers. It is observed that MLPs developed using MFO are the most robust ones among MLPs trained using other evolutionary and gradient descent algorithms.