A Natural Evolution Strategy for Multi-objective Optimization

Tobias Glasmachers, Tom Schaul, Jürgen Schmidhuber

Abstract: The recently introduced family of natural evolution strategies (NES), a novel stochastic descent method employing the natural gradient, is providing a more principled alternative to the well-known covariance matrix adaptation evolution strategy (CMA-ES). Until now, NES could only be used for single-objective optimization. This paper extends the approach to the multi-objective case, by first deriving a (1 + 1) hillclimber version of NES which is then used as the core component of a multi-objective optimization algorithm. We empirically evaluate the approach on a battery of benchmark functions and find it to be competitive with the state-of-the-art.