AutoSG: LLM-Driven Solver Generation Solely from Task Prompts for Expensive Optimization

2026-05-25

AI Summary

This work addresses the lack of efficient, task-specific solvers for expensive optimization problems, a challenge exacerbated by existing large language model (LLM)-based code generation methods that often suffer from factual hallucinations, disruption of established local optima structures, and high evaluation costs. To overcome these limitations, we propose AutoSG, a fully automated framework that generates executable, customized optimization solvers from natural language task descriptions alone. AutoSG introduces three key innovations: retrieval-augmented generation to ground code in reliable scientific literature, a structure-preserving one-step self-refinement operator that integrates task-specific enhancements while maintaining critical optimization structures, and an instance-free LLM-as-a-Judge Elo scoring mechanism for efficient global solver ranking. Experiments demonstrate that AutoSG significantly outperforms both handcrafted and state-of-the-art LLM-generated solvers across diverse expensive optimization tasks.

Abstract

Expensive optimization tasks are ubiquitous in real-world applications, demanding highly specialized solvers. While LLM-driven automated solver generation shows promise, current paradigms face three critical issues when tackling expensive optimization: factual hallucinations due to deficient domain knowledge, the frequent dismantling of previously established locally optimal structures during refinement, and the prohibitive evaluation costs alongside restricted generalization caused by executing on training instances. To address these issues, we introduce AutoSG, a fully automated workflow directly translating natural language prompts into executable customized solvers. AutoSG features three core innovations: a retrieval-augmented solver generation module strictly grounding code in verified literature; a one-step self-refinement operator introducing task-specific improvements while preserving critical structural components; and an instance-free Elo-based LLM-as-a-Judge evaluation mechanism rapidly establishing global rankings. Extensive evaluations across diverse expensive optimization tasks confirm AutoSG significantly outperforms human-designed state-of-the-art frameworks and existing LLM-generated solvers.

Problem

• expensive optimization
• LLM-driven solver generation
• factual hallucination
• local optimal structure
• evaluation cost

Innovation

• retrieval-augmented generation
• self-refinement operator
• instance-free evaluation
• LLM-as-a-Judge
• solver generation