Multiobjective Monotonicity Analysis: Pareto Set Dependency and Trade-Offs Causality in Configuration Design

Abstract

Multiobjective design optimization studies typically derive Pareto sets or use a scalar substitute function to capture design trade-offs, leaving it up to the designer’s intuition to use this information for design refinements and decision-making. Understanding the causality of trade-offs more deeply, beyond simple postoptimality parametric studies, would be particularly valuable in configuration design problems to guide configuration redesign. This article presents the method of multiobjective monotonicity analysis to identify root causes for the existence of trade-offs and the particular shape of Pareto sets. This analysis process involves reducing optimization models through constraint activity identification to a point where dependencies specific to the Pareto set and the constraints that cause them are revealed. The insights gained can then be used to target configuration design changes. We demonstrate the proposed approach in the preliminary design of a medical device for oral drug delivery.