Search Hardness-Aware LLM-Based Problem Formulation for Expensive Simulation-Driven Design

2026-07-23

AI Summary

This work addresses the inefficiency of existing large language model (LLM)-driven approaches to automated problem formulation, which often overlook the impact of problem phrasing on search efficiency, leading to excessive optimization costs in high-fidelity simulation scenarios. To overcome this limitation, the authors propose the SHA-PF framework, which uniquely incorporates search hardness into the problem formulation objective. By leveraging a search-hardness-aware mechanism, SHA-PF guides the LLM to generate, repair, and evolve problem formulations that prioritize high-potential rare samples, thereby shaping objective and constraint structures more conducive to efficient search. Integrating the generative and corrective capabilities of LLMs with evolutionary algorithms and a search-hardness-based scoring scheme, the framework bridges natural-language specifications and efficient optimization. Empirical results demonstrate that, across multi-objective benchmarks and five antenna design tasks, the generated formulations significantly reduce the number of simulations required to meet design specifications, outperforming current baselines.

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 search hardness, scoring each candidate formulation according to the priority. SHA-PF then searches the formulation space under this objective through LLM-based generation, repair, and evolutionary refinement. Experiments on the real-world multi-objective benchmark and five expensive antenna design benchmarks show that the formulations discovered by SHA-PF require significantly fewer evaluations to reach the design requirements than other baselines.

Problem

• simulation-driven design
• problem formulation
• search hardness
• large language models
• optimization

Innovation

• search hardness-aware
• LLM-based problem formulation
• expensive simulation-driven design
• formulation optimization
• sample prioritization