Generative Reliability-Based Design Optimization Using In-Context Learning Capabilities of Large Language Models

TL;DR

This work introduces LLM-RBDO, a generative reliability-based design optimization framework that couples in-context learning of large language models with Kriging-based reliability analysis to efficiently generate feasible design points under uncertainty. The optimization is formulated as $\min\_{\mathbf{d}} Cost(\mathbf{d})$ subject to $\Pr(G_i(\mathbf{x},\mathbf{d})<0) \le 1-\Phi(\beta_{t_i})$, with design bounds and random variables, while a Kriging surrogate accelerates reliability evaluation. A structured prompt design and a penalty-based constraint encoding enable the LLM to iteratively propose design points in a clear JSON format, with convergence governed by predefined criteria and adaptive generation around promising regions. Case studies in a 2D mathematical problem and a high-dimensional vehicle side-crash design demonstrate competitive convergence to a genetic algorithm in low dimensions and near-optimal results in high dimensions, highlighting both the potential and current limitations of LLM-driven design under uncertainty.

Abstract

Large Language Models (LLMs) have demonstrated remarkable in-context learning capabilities, enabling flexible utilization of limited historical information to play pivotal roles in reasoning, problem-solving, and complex pattern recognition tasks. Inspired by the successful applications of LLMs in multiple domains, this paper proposes a generative design method by leveraging the in-context learning capabilities of LLMs with the iterative search mechanisms of metaheuristic algorithms for solving reliability-based design optimization problems. In detail, reliability analysis is performed by engaging the LLMs and Kriging surrogate modeling to overcome the computational burden. By dynamically providing critical information of design points to the LLMs with prompt engineering, the method enables rapid generation of high-quality design alternatives that satisfy reliability constraints while achieving performance optimization. With the Deepseek-V3 model, three case studies are used to demonstrated the performance of the proposed approach. Experimental results indicate that the proposed LLM-RBDO method successfully identifies feasible solutions that meet reliability constraints while achieving a comparable convergence rate compared to traditional genetic algorithms.

Figures (11)

• Figure 1: LLM Architecture and Prompt Engineering
• Figure 2: Example of LLM-RBDO Prompt
• Figure 3: Overall Flowchart of LLM-RBDO
• Figure 4: Contour of the Limit State Function and Candidate Initial Design Points
• Figure 5: Iterative Process of Optimal Cost Function Value in LLM-RBDO (Case Study 1)