On Test Functions for Evolutionary Multi-objective Optimization

In order to evaluate the relative performance of optimization algorithms benchmark problems are frequently used. In the case of multi-objective optimization (MOO), we will show in this paper that most known benchmark problems belong to a constrained class of functions with piecewise linear Pareto fronts in the parameter space. We present a straightforward way to define benchmark problems with an arbitrary Pareto front both in the fitness and parameter spaces. Furthermore, we introduce a difficulty measure based on the mapping of probability density functions from parameter to fitness space. Finally, we evaluate two MOO algorithms for new benchmark problems.