First Investigations on Noisy Model-Based Multi-objective Optimization

In many real-world applications concerning multi-objective optimization, the true objective functions are not observable. Instead, only noisy observations are available. In recent years, the interest in the effect of such noise in evolutionary multi-objective optimization (EMO) has increased and many specialized algorithms have been proposed. However, evolutionary algorithms are not suitable if the evaluation of the objectives is expensive and only a small budget is available. One popular solution is to use model-based multi-objective optimization (MBMO) techniques. In this paper, we present a first investigation on noisy MBMO. For this purpose we collect several noise handling strategies from the field of EMO and adapt them for MBMO algorithms. We compare the performance of those strategies in two benchmark situations: Firstly, we perform a purely artificial benchmark using homogeneous Gaussian noise. Secondly, we choose a setting from the field of machine learning, where the structure of the underlying noise is unknown.