AutoMIP improves solution finding in mixed-integer programming tasks
Autoresearch in Mixed-Integer Linear and Nonlinear Programming
Artificial Intelligence
Summary
Finding solutions to mixed-integer mathematical problems, which are very hard to solve, needs careful testing of different ideas over time. The authors developed AutoMIP, a method that keeps track of many possible solutions and experiments systematically, so it learns better ways to solve these problems. AutoMIP performs well on standard test sets and often finds better solutions than previous methods. This shows that organizing research ideas and experiments effectively can lead to improvements in solving complex optimization problems.
What this means in practice
- •For operations research teams: Improve solution quality and efficiency for complex scheduling or resource allocation problems using AutoMIP's organized experimental approach.
- •For industrial optimization engineers: Use AutoMIP to discover better algorithms for optimizing manufacturing or supply chain processes modeled as mixed-integer programs.
Authors
Yuwei Gu, Yaoxin Wu, Tong Guo, Wen Song, Zhiguang Cao
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.