OptimAI: Optimization from Natural Language Using LLM-Powered AI Agents

ICLR 2026 Conference Submission15716 Authors

Keywords: Optimization, Large Language Models, AI Agents

TL;DR: We present OptimAI, a multi-agent LLM framework that translates natural language optimization problems into executable code, achieving state-of-the-art results and demonstrating synergistic gains from heterogeneous model collaboration.

Abstract:

Optimization plays a vital role in scientific research and practical applications. However, formulating a concrete optimization problem described in natural language into a mathematical form and selecting a suitable solver to solve the problem requires substantial domain expertise.
We introduce OptimAI, a framework for solving Optimization problems described in natural language by leveraging LLM-powered AI agents, and achieve superior performance over current state-of-the-art methods.
Our framework is built upon the following key roles:
(1) a formulator that translates natural language problem descriptions into precise mathematical formulations;
(2) a planner that constructs a high-level solution strategy prior to execution; and
(3) a coder and a code critic capable of interacting with the environment and reflecting on outcomes to refine future actions.
Ablation studies confirm that all roles are essential; removing the planner or code critic results in $5.8\times$ and $3.1\times$ drops in productivity, respectively.
Furthermore, we introduce UCB-based debug scheduling to dynamically switch between alternative plans, yielding an additional $3.3\times$ productivity gain.
Our design emphasizes multi-agent collaboration, and our experiments confirm that combining diverse models leads to performance gains.
Our approach attains 88.1\% accuracy on the NLP4LP dataset and 82.3\% on the Optibench dataset, reducing error rates by 58\% and 52\%, respectively, over prior best results.

Primary Area: foundation or frontier models, including LLMs

Submission Number: 15716