LLM-Based Evaluation Planning for Heterogeneous Optimization

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. Each decision is also conditioned on an adaptive nearest-neighbor summary of nearby high-fidelity infill points, and the same planner is instantiated with two open-weight backbones Qwen and Deepseek. 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 the two variants obtains the best mean ranking score in every regime, REP-HO(Deepseek) is first or second throughout, and the planner shows adaptive allocation behavior, such as prioritizing constraint evaluations under tighter budgets and reallocating constraint evaluation budget when surrogate reliability changes. These results suggest that LLMs can serve as flexible evaluation planners for heterogeneous optimization, offering a general alternative to fixed hand-designed metrics.