Limitations of Pareto Front in Design Under Uncertainty and Their Reconciliation

Engineering design reconciles design constraints with decision maker (DM) preferences. The task of eliciting and encoding decision maker preferences is, however, extremely difficult. A Pareto front representing the locus of the nondominated designs is, therefore, often generated to help a decision maker select the best design. In this paper, we show that this method has a shortcoming when there is uncertainty in both the decision problem variables and in the model of decision maker's preferences. In this case, the Pareto front is inconsistent with multi-attribute utility (MAU) theory, unless the decision maker trades off attributes or some functions of them linearly. This is a strong restriction. To account for this, we propose a methodology that enables a decision maker to select the best design on a modified pareto front (MPF) which is acquired using envelopes of a set of certainty equivalent (CE) surfaces. The proposed method does not require separability of the multi-attribute utility function into single-attribute utilities, nor does it require the decision maker to trade the attributes (or any function of them) linearly. We demonstrate our approach on a simple optimization problem and in design of a reduction gear.