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

2026-04-29

AI Summary

This work addresses the challenge of decision uncertainty in engineering design arising from incomplete preference information, which complicates the assessment of solution robustness and recommendation stability. The authors propose a probabilistic framework that models preference parameters as random variables to analyze how their uncertainty propagates to optimal design decisions and to characterize the probability distribution over regions of the Pareto front being selected. For the first time in preference-driven optimization, variance-based global sensitivity analysis and Fréchet variance are integrated with Sobol’ indices and Shapley values to quantify the contributions of design variables to decision uncertainty and to measure overall decision stability. Applied to a ground vehicle design case, the approach reveals how problem structure induces either discrete or continuous decision distributions, thereby enabling robust design recommendations under preference uncertainty.

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 Fréchet 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.

Problem

• preference uncertainty
• decision uncertainty
• multi-objective optimization
• Pareto front
• design stability

Innovation

• preference uncertainty
• decision uncertainty
• global sensitivity analysis
• Fréchet variance
• Pareto optimality