Effects of noisy multiobjective test functions applied to evolutionary optimization algorithms

Abstract

In this paper we study the effects of noise in multiobjective optimization problems. We consider a test function, which may be affected by noise with different strength and frequency of occurrence. To simplify the analysis, the noise is applied to only one of the objective functions, i.e. one of the objective functions is affected by additional random influences. Three different evolutionary algorithms for multiobjective problems are analyzed in this way: the Covariance Matrix Adaption Evolution Strategy (CMA-ES), the Non-dominated Sorting Genetic Algorithm-II (NSGA-II), and the Particle Swarm Optimization (PSO). The results are presented and analyzed with respect to the resulting Pareto fronts and with respect to the distribution of variable values during the algorithm run. It can be observed that all three algorithms are basically able to derive suitable results. However, only PSO leads to a sparse Pareto front in case of noisy and non-noisy situations while CMA and NSGA-II perform similarly well. In some situations for NSGA-II and more clearly for CMA-ES specific patterns for the variable values (denoted as striae in this paper) can be observed which appear to be partly caused by the noise.