# SOLID: a Framework of Synergizing Optimization and LLMs for Intelligent Decision-Making

arXiv: https://arxiv.org/abs/2511.15202 · HTML: https://mlsanity.com/paper/2511.15202/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 32 references that are in the map.
- First posted on arXiv 19 Nov 2025.

## Builds on (most cited first, 19 of 19)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Large Language Models as Optimizers](https://mlsanity.com/paper/2309.03409/) (2023)
- [Reasoning with Language Model is Planning with World Model](https://mlsanity.com/paper/2305.14992/) (2023)
- [Promptbreeder: Self-Referential Self-Improvement Via Prompt Evolution](https://mlsanity.com/paper/2309.16797/) (2023)
- [ReEvo: Large Language Models as Hyper-Heuristics with Reflective Evolution](https://mlsanity.com/paper/2402.01145/) (2024)
- [MathPrompter: Mathematical Reasoning using Large Language Models](https://mlsanity.com/paper/2303.05398/) (2023)
- [Large Language Model Guided Tree-of-Thought](https://mlsanity.com/paper/2305.08291/) (2023)
- [OptiMUS: Scalable Optimization Modeling with (MI)LP Solvers and Large Language Models](https://mlsanity.com/paper/2402.10172/) (2024)
- [Global Convergence of ADMM in Nonconvex Nonsmooth Optimization](https://mlsanity.com/paper/1511.06324/) (2015)
- [AutoML-GPT: Automatic Machine Learning with GPT](https://mlsanity.com/paper/2305.02499/) (2023)
- [Towards Optimizing with Large Language Models](https://mlsanity.com/paper/2310.05204/) (2023)
- [Large Language Model-Based Evolutionary Optimizer: Reasoning with elitism](https://mlsanity.com/paper/2403.02054/) (2024)
- [From Large Language Models and Optimization to Decision Optimization CoPilot: A Research Manifesto](https://mlsanity.com/paper/2402.16269/) (2024)
- [Learning Optimal and Fair Policies for Online Allocation of Scarce Societal Resources from Data Collected in Deployment](https://mlsanity.com/paper/2311.13765/) (2023)
- [Performance of large language models in numerical vs. semantic medical knowledge: Benchmarking on evidence-based Q&As](https://mlsanity.com/paper/2406.03855/) (2024)

## Built on by (most cited first, 1 of 1)

- [LLM-Guided Transportation Hub Capacity Planning with Textual Business Inputs](https://mlsanity.com/paper/2607.03651/) (2026)

## Abstract (arXiv)

This paper introduces SOLID (Synergizing Optimization and Large Language Models for Intelligent Decision-Making), a novel framework that integrates mathematical optimization with the contextual capabilities of large language models (LLMs). SOLID facilitates iterative collaboration between optimization and LLMs agents through dual prices and deviation penalties. This interaction improves the quality of the decisions while maintaining modularity and data privacy. The framework retains theoretical convergence guarantees under convexity assumptions, providing insight into the design of LLMs prompt. To evaluate SOLID, we applied it to a stock portfolio investment case with historical prices and financial news as inputs. Empirical results demonstrate convergence under various scenarios and indicate improved annualized returns compared to a baseline optimizer-only method, validating the synergy of the two agents. SOLID offers a promising framework for advancing automated and intelligent decision-making across diverse domains.