Estimating Decision Uncertainty from Preference Uncertainty: Application to Ground Vehicle Design

TL;DR

This paper introduces a probabilistic framework to quantify how uncertainty in preferences affects the stability and variability of optimal vehicle designs in multi-objective optimization.

Contribution

It develops a novel method to propagate preference uncertainty to decision uncertainty and applies sensitivity analysis to understand variability sources.

Findings

Preference uncertainty leads to probabilistic distributions over optimal designs.

Sensitivity analysis identifies key variables influencing decision variability.

Case studies demonstrate the framework's ability to assess design stability under preference variability.

Abstract

Engineering design problems are often modeled as multi-objective optimization tasks in which a scalarized utility function selects an optimal design from the Pareto set. In practice, preferences are imperfectly known, so uncertainty in the preference model leads to uncertainty in the resulting optimal design. This paper proposes a probabilistic framework that treats preference parameters as random variables and examines how preference uncertainty propagates to decision uncertainty. A random preference vector induces a probability distribution over optimal designs, allowing us to identify which regions of the Pareto front are most likely to be selected and to assess recommendation stability under preference variability. To explain the sources of this variability, we apply variance-based global sensitivity analysis to the induced optimal solutions, using Sobol' indices and Shapley values to quantify the contributions of individual design variables and their dependencies. We further summarize the overall dispersion of the optimal-design distribution using the Fr\'echet variance, which provides a scalar measure of decision stability under a given preference model. Two vehicle design case studies demonstrate how problem structure can lead to discrete versus continuous decision distributions and show how the proposed quantities support preference-aware design analysis.