Is MO-CMA-ES Superior to NSGA-II for the Evolution of Multi-objective Neuro-controllers?

In the last decade evolutionary multi-objective optimizers have been employed in studies concerning evolutionary robotics. In particular, the majority of such studies involve the evolution of neuro-controllers using either a genetic algorithm approach or an evolution strategies approach. Given the fundamental difference between these types of search mechanisms, a valid question is which kind of multi-objective optimizer is better for such applications. This question, which is dealt with here, is raised in view of the permutation problem that exists in evolutionary neural-networks. Two well-known Multi-objective Evolutionary Algorithms are used in the current comparison, namely MO-CMA-ES and NSGA-II. A multi-objective navigation problem is used for the testing, which is known to suffer from a local Pareto problem. For the employed simulation case MO-CMA-ES is better at finding a large sub-set of the approximated Pareto-optimal neuro-controllers, whereas NSGA-II is better at finding a complementary sub-set of the optimal controllers. This suggests that, if this phenomenon persists over a large range of case studies, then future studies should consider some modifications to such algorithms for the multi-objective evolution of neuro-controllers.