# A learning-based mathematical programming formulation for the automatic configuration of optimization solvers

arXiv: https://arxiv.org/abs/2401.04237 · HTML: https://mlsanity.com/paper/2401.04237/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 42 references that are in the map.
- First posted on arXiv 8 Jan 2024.

## Builds on (most cited first, 3 of 3)

- [ParamILS: An Automatic Algorithm Configuration Framework](https://mlsanity.com/paper/1401.3492/) (2014)
- [Pitfalls and Best Practices in Algorithm Configuration](https://mlsanity.com/paper/1705.06058/) (2017)
- [Optimal Decision Trees for the Algorithm Selection Problem: Integer Programming Based Approaches](https://mlsanity.com/paper/1907.02211/) (2019)

## Built on by (most cited first, 2 of 2)

- [BenLOC: A Benchmark for Learning to Configure MIP Optimizers](https://mlsanity.com/paper/2506.02752/) (2025)
- [GRIMIP: A General Framework for Instance-Specific Configuration of MIP Solvers Using LLMs](https://mlsanity.com/paper/2606.23299/) (2026)

## Abstract (arXiv)

We propose a methodology, based on machine learning and optimization, for selecting a solver configuration for a given instance. First, we employ a set of solved instances and configurations in order to learn a performance function of the solver. Secondly, we formulate a mixed-integer nonlinear program where the objective/constraints explicitly encode the learnt information, and which we solve, upon the arrival of an unknown instance, to find the best solver configuration for that instance, based on the performance function. The main novelty of our approach lies in the fact that the configuration set search problem is formulated as a mathematical program, which allows us to a) enforce hard dependence and compatibility constraints on the configurations, and b) solve it efficiently with off-the-shelf optimization tools.