arXiv:2607.21220v1 Announce Type: new Abstract: Expensive simulation-driven design is widely used in engineering to identify requirement-satisfying designs with as few high-fidelity simulations as possible. Most existing efforts address this challenge by improving optimization algorithms under fixed formulations, yet the formulation itself shapes the search landscape by defining the objectives and constraints optimized by the solver. Recent LLM-based automatic problem formulation methods generate formulations from natural-language requirements, but they mainly focus on design-intent alignment and overlook whether the formulation induces an efficient search process. To address this limitation, we propose SHA-PF, a search hardness-aware LLM-based problem formulation framework. We find that a formulation is more likely to guide efficient search when it prioritizes rare samples with greater progress potential. Based on this finding, SHA-PF defines a formulation search objective guided by s...