# Autoresearch in Mixed-Integer Linear and Nonlinear Programming

arXiv: https://arxiv.org/abs/2609.39360 · HTML: https://mlsanity.com/paper/2609.39360/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 37 of its 50 references that are in the map.
- First posted on arXiv 30 Sep 2026.

## Builds on (most cited first, 30 of 37)

- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [A-MEM: Agentic Memory for LLM Agents](https://mlsanity.com/paper/2502.12110/) (2025)
- [ExpeL: LLM Agents Are Experiential Learners](https://mlsanity.com/paper/2308.10144/) (2023)
- [Language Agent Tree Search Unifies Reasoning Acting and Planning in Language Models](https://mlsanity.com/paper/2310.04406/) (2023)
- [RAPTOR: Recursive Abstractive Processing for Tree-Organized Retrieval](https://mlsanity.com/paper/2401.18059/) (2024)
- [ReEvo: Large Language Models as Hyper-Heuristics with Reflective Evolution](https://mlsanity.com/paper/2402.01145/) (2024)
- [Evolution of Heuristics: Towards Efficient Automatic Algorithm Design Using Large Language Model](https://mlsanity.com/paper/2401.02051/) (2024)
- [NL4Opt Competition: Formulating Optimization Problems Based on Their Natural Language Descriptions](https://mlsanity.com/paper/2303.08233/) (2023)
- [ORLM: A Customizable Framework in Training Large Models for Automated Optimization Modeling](https://mlsanity.com/paper/2405.17743/) (2024)
- [Reinforcement Learning for Integer Programming: Learning to Cut](https://mlsanity.com/paper/1906.04859/) (2019)
- [OptiMUS: Scalable Optimization Modeling with (MI)LP Solvers and Large Language Models](https://mlsanity.com/paper/2402.10172/) (2024)
- [Monte Carlo Tree Search for Comprehensive Exploration in LLM-Based Automatic Heuristic Design](https://mlsanity.com/paper/2501.08603/) (2025)
- [HiAgent: Hierarchical Working Memory Management for Solving Long-Horizon Agent Tasks with Large Language Model](https://mlsanity.com/paper/2408.09559/) (2024)
- [LLMOPT: Learning to Define and Solve General Optimization Problems from Scratch](https://mlsanity.com/paper/2410.13213/) (2024)
- [Towards Scientific Intelligence: A Survey of LLM-based Scientific Agents](https://mlsanity.com/paper/2503.24047/) (2025)
- [Agent KB: Leveraging Cross-Domain Experience for Agentic Problem Solving](https://mlsanity.com/paper/2507.06229/) (2025)
- [From Automation to Autonomy: A Survey on Large Language Models in Scientific Discovery](https://mlsanity.com/paper/2505.13259/) (2025)
- [MemoryArena: Benchmarking Agent Memory in Interdependent Multi-Session Agentic Tasks](https://mlsanity.com/paper/2602.16313/) (2026)
- [From Isolated Conversations to Hierarchical Schemas: Dynamic Tree Memory Representation for LLMs](https://mlsanity.com/paper/2410.14052/) (2024)
- [Agentic AI for Scientific Discovery: A Survey of Progress, Challenges, and Future Directions](https://mlsanity.com/paper/2503.08979/) (2025)
- [Learning To Cut By Looking Ahead: Cutting Plane Selection via Imitation Learning](https://mlsanity.com/paper/2206.13414/) (2022)
- [CORAL: Towards Autonomous Multi-Agent Evolution for Open-Ended Discovery](https://mlsanity.com/paper/2604.01658/) (2026)
- [A GNN-Guided Predict-and-Search Framework for Mixed-Integer Linear Programming](https://mlsanity.com/paper/2302.05636/) (2023)
- [LLM4AD: A Platform for Algorithm Design with Large Language Model](https://mlsanity.com/paper/2412.17287/) (2024)
- [EvoX: A Distributed GPU-accelerated Framework for Scalable Evolutionary Computation](https://mlsanity.com/paper/2301.12457/) (2023)
- [Apollo-MILP: An Alternating Prediction-Correction Neural Solving Framework for Mixed-Integer Linear Programming](https://mlsanity.com/paper/2503.01129/) (2025)
- [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)
- [Learning to Cut via Hierarchical Sequence/Set Model for Efficient Mixed-Integer Programming](https://mlsanity.com/paper/2404.12638/) (2024)

## Abstract (arXiv)

Despite recent progress in autoresearch, applying it to practical operations research problems, typically formulated as NP-hard mixed-integer linear or nonlinear programs (MILPs or MINLPs), remains challenging because effective research requires systematically managing competing ideas and long-horizon experimental trajectories. We introduce AutoMIP, a reusable agent skill for organizing long-horizon autoresearch in mixed-integer programming through idea pooling and algorithm tree search. AutoMIP maintains a persistent pool of complementary candidate ideas while organizing executable experiments into an algorithm tree, enabling the agent to preserve unexplored hypotheses, refine promising algorithms, and switch to alternative methodological directions based on historical states. On MILP and MINLP benchmark cohorts, AutoMIP achieves the highest final success rates among the evaluated autoresearch frameworks. On MIPLib, AutoMIP discovers new best solutions for 31 of 60 instances, surpassing existing autoresearch frameworks. On MINLPLib, it achieves new best solutions for 52 of 60 instances. Ablation studies further demonstrate the complementary contributions of idea pooling and algorithm tree search, highlighting the importance of jointly maintaining diverse research ideas and structured experimental trajectories for long-horizon autoresearch.