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 post-optimality parametric studies, would be particularly valuable in configuration design problems to guide configuration redesign. This paper 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

A Novel Approach to Configuration Redesign: Using Multiobjective Monotonicity Analysis to Alter the Pareto Set

“…See [30,31] for an overview of the upper bound formulation (also known as ε-constraint), the underlying mathematics, and how to define limits for ε. As discussed in [28], this formulation has some computational limitations but its use here benefits the proposed analysis.…”

“…In [28], these principles were applied to derive the Multiobjective Monotonicity Analysis (MOMA) process for rigorous identification of the dependencies that cause trade-offs between objectives in problems of the form shown in Eqs. 6-9.…”

“…Using this basic insight, along with other theorems that ensure correct model reduction [28], MOMA allows identification of the conditions under which the bound objectives are active, i.e., the values of ε that affect the feasible domain of x, as illustrated in Fig. 1.…”

“…Furthermore, determining Fig. 1: MOMA allows the partial identification of the Pareto set, finding the values of ε where the bound objectives are active, semi-active, and inconsistent [28].…”

“…This article presents a systematic, analytical foundation for configuration redesign using Pareto-set Dependency Analysis [28]. This analysis relies on multiobjective monotonicity analysis to identify dependencies in the Pareto-set that cause trade-offs while also accounting for the constraints.…”