Large Language Models (LLMs) are increasingly used for automated algorithm design. However the computational cost of evaluating the generated algorithms can be excessive.
We consider the common LLM-driven automated algorithm design (LLM4AD) setting in which a candidate algorithm is evaluated by aggregating its performance over a shared set of training instances. This instance-wise structure raises a natural question: must every candidate be evaluated on the entire instance set before deciding whether it remains competitive?
Taking inspiration from algorithm configuration, we introduce AdaEva, a drop-in adaptive partial-evaluation framework that progressively evaluates candidates on larger subsets of the same instance pool and eliminates unpromising candidates as evidence accumulates.
Importantly, AdaEva leaves the underlying LLM4AD procedure and per-instance evaluator unchanged and requires no prior knowledge about instance difficulty.
We instantiate this idea using successive halving (AdaEva-S) and statistical racing (AdaEva-R), and evaluate both mechanisms across three representative LLM4AD frameworks, multiple LLM backbones, and optimization domains spanning combinatorial and continuous black-box optimization.
Under matched evaluation budgets, AdaEva more reliably balances evaluation effort across candidates than fixed partial-evaluation strategies, yielding strong search efficiency and anytime performance together with improved held-out generalization across the evaluated settings.