In this paper we introduce robust and stochastically weighted sum approaches to deterministic and stochastic multi-objective optimization. The robust weighted sum approach minimizes the worst case weighted sum of objectives over a given weight region. We study the reformulations of the robust weighted sum problem under different definitions of deterministic weight regions. We next introduce a stochastic weighted sum approach to multi-objective optimization, where each of the objectives is stochastic. This approach treats trade-off weights as a random vector using which the weighted sum represents the impact of uncertain objectives. The concepts are explained with the help of numerical examples. The models are also extended to the use of a more general Lp-norm or Tchebycheff metric when constructing the weighted sum.
IEMS Dept. Northwestern Univ. 2010