Multi-objective optimisation in the presence of uncertainty

There has been only limited discussion on the effect of uncertainty and noise in multi-objective optimization problems and how to deal with it. We address this problem by assessing the probability of dominance and maintaining an archive of solutions which are, with some known probability, mutually non-dominating. We examine methods for estimating the probability of dominance. These depend crucially on estimating the effective noise variance and we introduce a novel method of learning the variance during optimization. Probabilistic domination contours are presented as a method for conveying the confidence that may be placed in objectives that are optimized in the presence of uncertainty