From Fixed Archives to New Operating Conditions: Offline Parametric Multi-Objective Optimization

Many engineering systems must operate under varying conditions, such as turbines facing different wind speeds or vehicles carrying different payloads, and the designs that are best for one condition are rarely best for another. Because cost, safety, and performance must be balanced at once, each condition poses its own multi-objective problem with its own Pareto set, and repeating the optimization for every new condition is too slow for timely deployment. In practice, substantial historical evaluation data are often available, which motivates reusing them offline to reconstruct trade-off solutions for previously unobserved conditions without new evaluations. The challenge in this offline parametric multi-objective optimization (Offline PMOO) setting is to generalize to unseen conditions and to recover diverse trade-offs without exploiting model errors in regions with sparse data, which neither current offline optimization nor parametric multi-objective methods address. We therefore formalize Offline PMOO and construct a benchmark of 27 tasks, ranging from synthetic test functions to engineering applications. After investigating the limitations of task-conditioned surrogate models in this regime, we propose a generative refinement strategy, instantiated via Parametric Scalarized Diffusion (PSD) and Parametric Pareto Flow Matching (PPFM), which learns a conditional prior from archived elite designs and uses surrogate models purely to steer refinement, so that candidates do not drift into unsupported regions. PPFM and PSD rank first and second on the synthetic and shared-component engineering suites. Our evaluation also maps the limits of learned solvers: surrogate-only models are preferable on a conditional simulator suite, and zero-learning archive reuse suffices for many-objective problems where Pareto dominance loses its discriminative power.