Autoresearch in Mixed-Integer Programming via Idea Pooling and Algorithm Tree Search

Despite recent progress in autoresearch, applying it to practical operations research problems, which are typically formulated as NP-hard mixed-integer linear or nonlinear programs (MILPs or MINLPs), requires more systematic and efficient research capabilities to manage competing ideas and experimental trajectories. We introduce AutoMIP, a reusable agent skill for organizing long-horizon autoresearch in MIPs through idea pooling and algorithm tree search. AutoMIP maintains a persistent pool of complementary candidate ideas, and organizes executable experiments in an algorithm tree, allowing the agent to preserve untried hypotheses, refine promising algorithms, and switch to new methodological directions from historical states. AutoMIP achieves the highest final success rate for MILP or MINLP benchmark cohorts. In MIPLib, AutoMIP reaches new best solutions for 31 out of 60 instances, more than current autoresearch frameworks; In MINLPLib, AutoMIP is more advantageous with a success rate of 52 out of 60. The complementary effects of idea pooling and algorithm tree search are evidenced by the ablation study.