LLM-Based Evaluation Planning for Heterogeneous Optimization

Nian Ran, Sebastian Brulin, Markus Olhofer, Mauricio A. Álvarez, Richard Allmendinger

Heterogeneous optimization problems require an optimizer to decide not only which candidate solutions to evaluate, but also which objectives and constraints should be evaluated under different costs and fidelities. Existing SOTA methods such as MFE-NSGA-III address this setting with manually designed selection metrics, but their behavior is largely determined by predefined heuristic rules and hyperparameters. In this work, we propose REP-HO, a reasoning-based evaluation planner that replaces the rule-based mixed-fidelity selection step with a large language model (LLM) planner. The LLM receives the same primitive optimization-state information as the heuristic planner, such as surrogate predictions, uncertainties, evaluation costs, and budget status. We first show that REP-HO achieves competitive performance compared to the human-designed metric-based method (MFE-NSGA-III). We then further enhance each decision with an adaptive nearest-neighbor summary, leading to better and more stable results. We evaluate REP-HO across five heterogeneous regimes covering cost imbalance, constraint difficulty, surrogate fidelity, budget level, and objective conflict. Across these regimes, one of…