Multi-objective neuro-evolution: Should the main reproduction mechanism be crossover or mutation?

Given the fundamental difference between the selection and reproduction mechanisms of MO-CMA-ES and NSGA-II, it should be asked which kind of these mechanisms is better for the multi-objective evolution of neuro-controllers. This question, which has been recently raised and studied, is further investigated here. The numerical investigation is based on two multi-objective navigation problems, in conjunction with two types of networks. In all the studied cases it was found that MO-CMA-ES is better than NSGA-II. The reason for the superiority is explored. First, it is shown that the competing convention problem cannot serve as an explanation to the observed phenomenon. A method is suggested to investigate the convergence of the networks. Based on the proposed methodology, it is found that for the studied cases MO-CMA-ES has a much better convergence properties. The differences between the two algorithms, and the uniqueness of the considered neuro-evolution problems, lead to the following hypothesis. It is postulated that MO-CMA-ES is superior as a result of its ability to fine-tune the solutions by changing particular genes, each at a time.