Autoresearch in Mixed-Integer Linear and Nonlinear Programming

Frontier LLMs are increasingly used to automate scientific research through iterative search. We distinguish idea-driven search from solution-driven search and identify three core challenges: organizing evolving research ideas, selecting promising directions, and maintaining alignment between ideas and their implementations. To address these challenges, we introduce the Agentic Idea Manager (AIM), a fully autonomous framework for managing and exploring research directions in idea-driven automated research. Inspired by Bayesian optimization, AIM uses an Agentic Surrogate and an Agentic Acquisition mechanism to organize discovered ideas and guide their selection. A Solution Auditor maintains idea-solution integrity, while a Resource Planner adaptively allocates the remaining experimental budget across parallel search branches. Experiments on 10 AutoLab benchmark tasks show that AIM surpasses the strongest baseline by 1.6 percentage points on System Optimization tasks and 4.9 percentage points on long-horizon Model Development & CUDA tasks. Notably, AIM reaches the best baseline performance up to 3.1x faster in wall-clock time. We further provide a theoretical analysis of when searching over ideas becomes beneficial. Our analysis shows that explicit idea-level allocation makes semantic coverage directly controllable, and that broader coverage becomes increasingly valuable when competitive research directions are sparse among many plausible alternatives. Project Page: https://imhgchoi.github.io/agentic-idea-manager/

Auto Research uses language-model agents to propose, implement, and evaluate machine-learning changes in a closed loop, but is usually judged by its terminal pipeline. A terminal score cannot reveal which technical decision produced a gain or distinguish a reusable discovery from a change adapted to development feedback. We introduce intervention-centered Auto Research, which validates research decisions rather than only final artifacts and makes their reliability measurable. Feature, Model, Representation, and Data axes are searched independently with inner five-fold feedback. Each axis winner is frozen before an outer-holdout matrix compares all alternatives on evidence the loop never sees. Across 701 agent-executed attempts spanning ten Matbench endpoints, outer evidence confirms the selected intervention on nine of ten endpoints and preserves 89.3% of non-tied intervention orderings. It also rejects an aggregate Representation gain that inner feedback endorsed. The resulting matrix reveals an information-dependent hierarchy. Composition-only tasks support several routes to improvement, whereas structure-informed tasks favor local geometry features and complementary tree ensembles. A subsequent compatibility test combines already frozen Feature and Model code without further search or tuning and raises mean outer-holdout improvement from 19.0% to 26.3%. By validating decisions rather than only artifacts, this design turns adaptive search into reusable evidence wherever agents propose executable alternatives against a fixed evaluator.

Mixed-integer programming (MIP) research is both mathematically sophisticated and engineering-intensive: testing an algorithmic hypothesis within a branch-and-cut solver requires substantial implementation, debugging, tuning, and large-scale benchmarking. We propose an agentic MIP research framework that shortens this feedback loop by embedding LLM agents into a solver-aware harness for generating, verifying, and evaluating plugins for the open-source solver SCIP. Propagation methods play a central role in accelerating MIP solving by exploiting global constraints. We instantiate our framework on the semantic lifting of MIP formulations into global constraints and the automatic construction of propagation-only SCIP constraint handlers. On the MIPLIB 2017 benchmark set, the framework successfully recovers global constraint structures from constraint programming and generates executable constraint detectors and propagation-only constraint handlers. Furthermore, the framework naturally extends to in-context learning within a sandboxed environment, enabling agents not only to tune and debug generated constraint handlers on real instances, but also to explore global constraint patterns in MIP problems and discover novel propagation strategies not yet implemented in SCIP. This framework allows us to systematically distinguish meaningful algorithmic improvements from low-value or overly costly candidates: the novel propagation methods successfully solved five additional instances within the explored benchmark. Overall, this framework demonstrates that LLM agents can autonomously navigate the complex MIP research loop, paving the way for a more automated solver development process.