Parametric Pareto Set Learning for Expensive Multi-Objective Optimization

TL;DR

This paper introduces PPSL-MOBO, a novel framework that efficiently learns to predict Pareto-optimal solutions across varying parameters in expensive multi-objective optimization problems, reducing computational costs significantly.

Contribution

It proposes a parametric learning approach using hypernetworks and Gaussian processes to unify and accelerate multi-objective optimization across parameters.

Findings

Effective on modular design problems with shared components.

Successfully handles dynamic objectives evolving over time.

Reduces the need for costly re-optimization for new parameters.

Abstract

Parametric multi-objective optimization (PMO) addresses the challenge of solving an infinite family of multi-objective optimization problems, where optimal solutions must adapt to varying parameters. Traditional methods require re-execution for each parameter configuration, leading to prohibitive costs when objective evaluations are computationally expensive. To address this issue, we propose Parametric Pareto Set Learning with multi-objective Bayesian Optimization (PPSL-MOBO), a novel framework that learns a unified mapping from both preferences and parameters to Pareto-optimal solutions. PPSL-MOBO leverages a hypernetwork with Low-Rank Adaptation (LoRA) to efficiently capture parametric variations, while integrating Gaussian process surrogates and hypervolume-based acquisition to minimize expensive function evaluations. We demonstrate PPSL-MOBO's effectiveness on two challenging applications: multi-objective optimization with shared components, where certain design variables must be identical across solution families due to modular constraints, and dynamic multi-objective optimization, where objectives evolve over time. Unlike existing methods that cannot directly solve PMO problems in a unified manner, PPSL-MOBO learns a single model that generalizes across the entire parameter space. By enabling instant inference of Pareto sets for new parameter values without retraining, PPSL-MOBO provides an efficient solution for expensive PMO problems.