Parametric Pareto Set Learning for Expensive Multi-Objective Optimization

• URL: http://arxiv.org/abs/2511.05815v1
• Date: Sat, 08 Nov 2025 03:05:28 GMT
• Title: Parametric Pareto Set Learning for Expensive Multi-Objective Optimization
• Authors: Ji Cheng, Bo Xue, Qingfu Zhang,
• Abstract summary: Parametric multi-objective optimization (PMO) addresses the challenge of solving an infinite family of multi-objective optimization problems.<n>Traditional methods require re-execution for each parameter configuration, leading to prohibitive costs when objective evaluations are computationally expensive.
• Score: 16.780031024741223
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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