From Soliloquy to Agora: Memory-Enhanced LLM Agents with Decentralized Debate for Optimization Modeling

2026-04-28

AI Summary

Large language models (LLMs) struggle to reliably construct optimization models from natural language requirements, limiting their applicability in decision-making domains such as logistics and manufacturing. To address this, this work proposes Agora-Opt, a framework in which a multi-agent team independently generates end-to-end optimization formulations and coordinates through a result-driven, decentralized debate mechanism. The system incorporates a read-write memory bank that stores solver-validated artifacts and dispute-resolution experiences, enabling training-free, continual improvement. Agora-Opt is the first to integrate decentralized debate with reusable memory, overcoming reliance on a single model and supporting cross-LLM transfer and loosely coupled deployment—even recovering correct formulations when all initial proposals are erroneous. Experiments demonstrate that Agora-Opt significantly outperforms zero-shot LLMs, training-based approaches, and existing agent baselines on public benchmarks, while remaining robust across diverse backbone models and component variants.

Abstract

Optimization modeling underpins real-world decision-making in logistics, manufacturing, energy, and public services, but reliably solving such problems from natural-language requirements remains challenging for current large language models (LLMs). In this paper, we propose \emph{Agora-Opt}, a modular agentic framework for optimization modeling that combines decentralized debate with a read-write memory bank. Agora-Opt allows multiple agent teams to independently produce end-to-end solutions and reconcile them through an outcome-grounded debate protocol, while memory stores solver-verified artifacts and past disagreement resolutions to support training-free improvement over time. This design is flexible across both backbones and methods: it reduces base-model lock-in, transfers across different LLM families, and can be layered onto existing pipelines with minimal coupling. Across public benchmarks, Agora-Opt achieves the strongest overall performance among all compared methods, outperforming strong zero-shot LLMs, training-centric approaches, and prior agentic baselines. Further analyses show robust gains across backbone choices and component variants, and demonstrate that decentralized debate offers a structural advantage over centralized selection by enabling agents to refine candidate solutions through interaction and even recover correct formulations when all initial candidates are flawed. These results suggest that reliable optimization modeling benefits from combining collaborative cross-checking with reusable experience, and position Agora-Opt as a practical and extensible foundation for trustworthy optimization modeling assistance. Our code and data are available at https://github.com/CHIANGEL/Agora-Opt.

Problem

• optimization modeling
• large language models
• natural-language requirements
• decision-making
• reliable problem solving

Innovation

• decentralized debate
• memory-enhanced agents
• optimization modeling
• modular agentic framework
• training-free improvement