Statistics of the Pareto front in Multi-objective Optimization under Uncertainties

Abstract In this paper we address an innovative approach to determine the mean and a confidence interval for a set of objects analogous to curves and surfaces. The approach is based on the determination of the most representative member of the family by minimizing a Hausdorff distance. This method is applied to the analysis of uncertain Pareto frontiers in multi-objective optimization (MOO). The determination of the Pareto front of deterministic MOO is carried by minimizing the hypervolume contained between the front and the utopia point. We give some examples and we apply the approach to a truss-like structure for which conflicting objective functions such as the structure mass and the maximum displacement are both to be minimized.