Multi-attribute decision making and multi-objective optimization complement each other. Often, while making design decisions involving multiple attributes, a Pareto front is generated using a multi-objective optimizer. The end user then chooses the optimal design from the Pareto front based on his/her preferences. This seemingly simple methodology requires sufficient modification if uncertainty is present. We explore two kinds of uncertainties in this paper: uncertainty in the decision variables which we call inherent design problem (IDP) uncertainty and that in knowledge of the preferences of the decision maker which we refer to as preference assessment (PA) uncertainty. From a purely utility theory perspective a rational decision maker maximizes his or her expected multi attribute utility. We show how this is inherently inconsistent with providing the decision maker with alternatives on the Pareto Front unless the decision maker trades off attributes or some function thereof linearly. In this paper we propose a methodology, rooted in a set of axioms that can be used in conjunction with a modified Pareto Front to select the best design. We present our findings on a simple optimization problem involving two attributes.
Definition of terms
Inherent Design Problem (IDP) Uncertainty- Inherent design problem uncertainty because of variability in decision variables and/or noise in objective function evaluation.
Preference Assessment (PA) Uncertainty- Uncertainty in the knowledge of the decision maker's utility function because of imperfect assessment.