# LLaMoCo: Instruction Tuning of Large Language Models for Optimization Code Generation

arXiv: https://arxiv.org/abs/2403.01131 · HTML: https://mlsanity.com/paper/2403.01131/

## Key facts

- Cited by 45 papers in the map (data through 14 Oct 2026).
- Builds on 69 of its 150 references that are in the map.
- First posted on arXiv 2 Mar 2024.

## Builds on (most cited first, 30 of 69)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Scaling Instruction-Finetuned Language Models](https://mlsanity.com/paper/2210.11416/) (2022)
- [A Survey of Large Language Models](https://mlsanity.com/paper/2303.18223/) (2023)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [HuggingFace's Transformers: State-of-the-art Natural Language Processing](https://mlsanity.com/paper/1910.03771/) (2019)
- [Fine-Tuning Language Models from Human Preferences](https://mlsanity.com/paper/1909.08593/) (2019)
- [Code Llama: Open Foundation Models for Code](https://mlsanity.com/paper/2308.12950/) (2023)
- [Large Language Models Encode Clinical Knowledge](https://mlsanity.com/paper/2212.13138/) (2022)
- [Mixtral of Experts](https://mlsanity.com/paper/2401.04088/) (2024)
- [Multitask Prompted Training Enables Zero-Shot Task Generalization](https://mlsanity.com/paper/2110.08207/) (2021)
- [Competition-Level Code Generation with AlphaCode](https://mlsanity.com/paper/2203.07814/) (2022)
- [Rethinking the Role of Demonstrations: What Makes In-Context Learning Work?](https://mlsanity.com/paper/2202.12837/) (2022)
- [LIMA: Less Is More for Alignment](https://mlsanity.com/paper/2305.11206/) (2023)
- [CodeGen: An Open Large Language Model for Code with Multi-Turn Program Synthesis](https://mlsanity.com/paper/2203.13474/) (2022)
- [Large Language Models as Optimizers](https://mlsanity.com/paper/2309.03409/) (2023)
- [StarCoder: may the source be with you!](https://mlsanity.com/paper/2305.06161/) (2023)
- [InCoder: A Generative Model for Code Infilling and Synthesis](https://mlsanity.com/paper/2204.05999/) (2022)
- [DS-1000: A Natural and Reliable Benchmark for Data Science Code Generation](https://mlsanity.com/paper/2211.11501/) (2022)

## Built on by (most cited first, 30 of 45)

- [A Survey on Large Language Models for Code Generation](https://mlsanity.com/paper/2406.00515/) (2024)
- [LLMOPT: Learning to Define and Solve General Optimization Problems from Scratch](https://mlsanity.com/paper/2410.13213/) (2024)
- [Trace is the Next AutoDiff: Generative Optimization with Rich Feedback, Execution Traces, and LLMs](https://mlsanity.com/paper/2406.16218/) (2024)
- [A Systematic Survey on Large Language Models for Algorithm Design](https://mlsanity.com/paper/2410.14716/) (2024)
- [Large Language Models for Code Generation: A Comprehensive Survey of Challenges, Techniques, Evaluation, and Applications](https://mlsanity.com/paper/2503.01245/) (2025)
- [Toward Automated Algorithm Design: A Survey and Practical Guide to Meta-Black-Box-Optimization](https://mlsanity.com/paper/2411.00625/) (2024)
- [ConfigX: Modular Configuration for Evolutionary Algorithms via Multitask Reinforcement Learning](https://mlsanity.com/paper/2412.07507/) (2024)
- [Planning of Heuristics: Strategic Planning on Large Language Models with Monte Carlo Tree Search for Automating Heuristic Optimization](https://mlsanity.com/paper/2502.11422/) (2025)
- [Pretrained Optimization Model for Zero-Shot Black Box Optimization](https://mlsanity.com/paper/2405.03728/) (2024)
- [Reinforcement Learning-based Self-adaptive Differential Evolution through Automated Landscape Feature Learning](https://mlsanity.com/paper/2503.18061/) (2025)
- [A Systematic Survey on Large Language Models for Evolutionary Optimization: From Modeling to Solving](https://mlsanity.com/paper/2509.08269/) (2025)
- [SolverLLM: Leveraging Test-Time Scaling for Optimization Problem via LLM-Guided Search](https://mlsanity.com/paper/2510.16916/) (2025)
- [MetaBox-v2: A Unified Benchmark Platform for Meta-Black-Box Optimization](https://mlsanity.com/paper/2505.17745/) (2025)
- [LLASP: Fine-tuning Large Language Models for Answer Set Programming](https://mlsanity.com/paper/2407.18723/) (2024)
- [Privacy-preserved LLM Cascade via CoT-enhanced Policy Learning](https://mlsanity.com/paper/2410.08014/) (2024)
- [Metaheuristics and Large Language Models Join Forces: Toward an Integrated Optimization Approach](https://mlsanity.com/paper/2405.18272/) (2024)
- [Towards Universal Offline Black-Box Optimization via Learning Language Model Embeddings](https://mlsanity.com/paper/2506.07109/) (2025)
- [Instance Generation for Meta-Black-Box Optimization through Latent Space Reverse Engineering](https://mlsanity.com/paper/2509.15810/) (2025)
- [Large Language Models in Operations Research: Methods, Applications, and Challenges](https://mlsanity.com/paper/2509.18180/) (2025)
- [DesignX: Human-Competitive Algorithm Designer for Black-Box Optimization](https://mlsanity.com/paper/2505.17866/) (2025)
- [An Agentic Framework with LLMs for Solving Complex Vehicle Routing Problems](https://mlsanity.com/paper/2510.16701/) (2025)
- [Opt-Verifier: Unleashing the Power of LLMs for Optimization Modeling via Dual-Side Verification](https://mlsanity.com/paper/2605.29556/) (2026)
- [Language Models as Efficient Reward Function Searchers for Custom-Environment Multi-Objective Reinforcement](https://mlsanity.com/paper/2409.02428/) (2024)
- [PerfCoder: Large Language Models for Interpretable Code Performance Optimization](https://mlsanity.com/paper/2512.14018/) (2025)
- [TIDE: Tuning-Integrated Dynamic Evolution for LLM-Based Automated Heuristic Design](https://mlsanity.com/paper/2601.21239/) (2026)
- [Beyond the Node: Clade-level Selection for Efficient MCTS in Automatic Heuristic Design](https://mlsanity.com/paper/2602.00549/) (2026)
- [ORPilot: A Production-Oriented Agentic LLM-for-OR Tool for Optimization Modeling](https://mlsanity.com/paper/2605.02728/) (2026)
- [OptSkills: Learning Generalizable Optimization Skills from Problem Archetypes via Cluster-Based Distillation](https://mlsanity.com/paper/2605.29829/) (2026)
- [OptiHive: Ensemble Selection for LLM-Based Optimization via Statistical Modeling](https://mlsanity.com/paper/2508.02503/) (2025)
- [A Stochastic Differential Equation Framework for Multi-Objective LLM Interactions: Dynamical Systems Analysis with Code Generation Applications](https://mlsanity.com/paper/2510.10739/) (2025)

## Abstract (arXiv)

Recent research explores optimization using large language models (LLMs) by either iteratively seeking next-step solutions from LLMs or directly prompting LLMs for an optimizer. However, these approaches exhibit inherent limitations, including low operational efficiency, high sensitivity to prompt design, and a lack of domain-specific knowledge. We introduce LLaMoCo, the first instruction-tuning framework designed to adapt LLMs for solving optimization problems in a code-to-code manner. Specifically, we establish a comprehensive instruction set containing well-described problem prompts and effective optimization codes. We then develop a novel two-phase learning strategy that incorporates a contrastive learning-based warm-up procedure before the instruction-tuning phase to enhance the convergence behavior during model fine-tuning. The experiment results demonstrate that a CodeGen (350M) model fine-tuned by our LLaMoCo achieves superior optimization performance compared to GPT-4 Turbo and the other competitors across both synthetic and realistic problem sets. The fine-tuned model and the usage instructions are available at https://anonymous.4open.science/r/LLaMoCo-722A.