Autoresearch in Mixed-Integer Linear and Nonlinear Programming

2026-09-30

AI Summary

This study addresses the challenges of managing competing ideas and controlling long-cycle experimental trajectories in automated research for mixed-integer programming (MIP) by proposing the AutoMIP framework. This method is the first to integrate a persistent idea pool with an algorithmic tree search mechanism, leveraging an agent skill framework to enable the collaborative management of diverse research concepts and structured experimental exploration while continuously refining research directions and preserving valid hypotheses. Evaluated on the MIPLib and MINLPLib benchmarks, AutoMIP discovers numerous new optimal solutions and achieves success rates that significantly surpass those of existing automated research baselines.

Abstract

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.

Problem

• Autoresearch
• Mixed-Integer Linear Programming
• Mixed-Integer Nonlinear Programming
• Long-horizon experimental trajectories
• Operations Research

Innovation

• AutoMIP
• Idea Pooling
• Algorithm Tree Search
• Mixed-Integer Programming
• Autoresearch