Interactive Multiobjective Optimization Under Uncertainty

Uncertainty presents unique difficulties in multiobjective optimization problems, because decision makers are faced with risky situations requiring analysis of multiple outcomes in differing states of nature. Very few direct choice (interactive) multiobjective methods are capable of addressing problems with probabilistic outcomes. We thus propose a general multiobjective algorithm which accommodates uncertainty. The method is appropriate for use in a multiple criteria framework with a discrete number of states of nature. Without loss of generality, and in the interest of simplicity of exposition, our method is explored and developed in the context of a bicriterion optimization problem using a two stage mathematical programming model. Simulation and behavioral experiments are conducted which verify that the method is viable for problems with greater dimensionality.