In the high-cost simulation-driven design domain, translating ambiguous design requirements into a mathematical optimization formulation is a bottleneck for optimizing product performance. This process is time-consuming and heavily reliant on expert knowledge. While large language models (LLMs) offer potential for automating this task, existing approaches either suffer from poor formalization that fails to accurately align with the design intent or rely on solver feedback for data filtering, which is unavailable due to the high simulation costs. To address this challenge, we propose automated problem formulation (APF), a solver-independent framework that utilizes LLMs to convert engineers’ natural language requirements into executable optimization models. The core of this framework is an innovative pipeline for automatically generating high-quality data, which overcomes the difficulty of constructing suitable fine-tuning datasets in the absence of high-cost solver feedback with the help of data generation and test instance annotation. The generated high-quality dataset is used to perform supervised fine-tuning on LLMs, significantly enhancing their ability to generate accurate and executable optimization problem formulations. Experimental results on antenna design demonstrate that APF significantly outperforms the existing methods in both the accuracy of requirement formalization and the quality of resulting radiation efficiency curves in meeting the design goals.

Large Language Models (LLMs) have been extensively used across diverse domains, including virtual assistants, automated code generation, and scientific research. However, they remain vulnerable to jailbreak attacks, which manipulate the models into generating harmful responses despite safety alignment. Recent studies have shown that current safety-aligned LLMs undergo shallow safety alignment. In this work, we conduct an in-depth investigation into the underlying mechanism of this phenomenon and reveal that it manifests through learned ”safety trigger tokens” that activate the model’s safety patterns when paired with the specific input. Through both analysis and empirical verification, we further demonstrate the high similarity of the safety trigger tokens across different harmful inputs. Accordingly, we propose D-STT, a simple yet effective defense algorithm that identifies and explicitly decodes safety trigger tokens of the given safety-aligned LLM to activate the model’s learned safety patterns. In this process, the safety trigger is constrained to a single token, which effectively preserves model usability by introducing minimal intervention in the decoding process. Extensive experiments across diverse jailbreak attacks and benign prompts demonstrate that D-STT substantially reduces output harmfulness while preserving model usability and incurring negligible response time overhead, demonstrating highly competitive and consistent performance across diverse models compared to ten baseline methods.