# Automatic MILP Solver Configuration By Learning Problem Similarities

arXiv: https://arxiv.org/abs/2307.00670 · HTML: https://mlsanity.com/paper/2307.00670/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 67 references that are in the map.
- First posted on arXiv 2 Jul 2023.

## Builds on (most cited first, 25 of 25)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [FaceNet: A Unified Embedding for Face Recognition and Clustering](https://mlsanity.com/paper/1503.03832/) (2015)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [CosFace: Large Margin Cosine Loss for Deep Face Recognition](https://mlsanity.com/paper/1801.09414/) (2018)
- [Pointer Networks](https://mlsanity.com/paper/1506.03134/) (2015)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [Unsupervised Deep Embedding for Clustering Analysis](https://mlsanity.com/paper/1511.06335/) (2015)
- [Hyperband: A Novel Bandit-Based Approach to Hyperparameter Optimization](https://mlsanity.com/paper/1603.06560/) (2016)
- [Attention, Learn to Solve Routing Problems!](https://mlsanity.com/paper/1803.08475/) (2018)
- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018)
- [Neural Combinatorial Optimization with Reinforcement Learning](https://mlsanity.com/paper/1611.09940/) (2016)
- [Learning Combinatorial Optimization Algorithms over Graphs](https://mlsanity.com/paper/1704.01665/) (2017)
- [Understanding the Behaviour of Contrastive Loss](https://mlsanity.com/paper/2012.09740/) (2020)
- [Exact Combinatorial Optimization with Graph Convolutional Neural Networks](https://mlsanity.com/paper/1906.01629/) (2019)
- [Combinatorial optimization and reasoning with graph neural networks](https://mlsanity.com/paper/2102.09544/) (2021)
- [SMAC3: A Versatile Bayesian Optimization Package for Hyperparameter Optimization](https://mlsanity.com/paper/2109.09831/) (2021)
- [Combinatorial Optimization with Graph Convolutional Networks and Guided Tree Search](https://mlsanity.com/paper/1810.10659/) (2018)
- [Automated Algorithm Selection: Survey and Perspectives](https://mlsanity.com/paper/1811.11597/) (2018)
- [Evaluation of a Tree-based Pipeline Optimization Tool for Automating Data Science](https://mlsanity.com/paper/1603.06212/) (2016)
- [PyTorch Metric Learning](https://mlsanity.com/paper/2008.09164/) (2020)
- [Ecole: A Gym-like Library for Machine Learning in Combinatorial Optimization Solvers](https://mlsanity.com/paper/2011.06069/) (2020)
- [A Bi-Level Framework for Learning to Solve Combinatorial Optimization on Graphs](https://mlsanity.com/paper/2106.04927/) (2021)
- [Instance-wise algorithm configuration with graph neural networks](https://mlsanity.com/paper/2202.04910/) (2022)

## Built on by (most cited first, 5 of 5)

- [Rethinking the Capacity of Graph Neural Networks for Branching Strategy](https://mlsanity.com/paper/2402.07099/) (2024)
- [Learning to optimize: A tutorial for continuous and mixed-integer optimization](https://mlsanity.com/paper/2405.15251/) (2024)
- [Multi-task Representation Learning for Mixed Integer Linear Programming](https://mlsanity.com/paper/2412.14409/) (2024)
- [FORGE: Foundational Optimization Representations from Graph Embeddings](https://mlsanity.com/paper/2508.20330/) (2025)
- [BenLOC: A Benchmark for Learning to Configure MIP Optimizers](https://mlsanity.com/paper/2506.02752/) (2025)

## Abstract (arXiv)

A large number of real-world optimization problems can be formulated as Mixed Integer Linear Programs (MILP). MILP solvers expose numerous configuration parameters to control their internal algorithms. Solutions, and their associated costs or runtimes, are significantly affected by the choice of the configuration parameters, even when problem instances have the same number of decision variables and constraints. On one hand, using the default solver configuration leads to suboptimal solutions. On the other hand, searching and evaluating a large number of configurations for every problem instance is time-consuming and, in some cases, infeasible. In this study, we aim to predict configuration parameters for unseen problem instances that yield lower-cost solutions without the time overhead of searching-and-evaluating configurations at the solving time. Toward that goal, we first investigate the cost correlation of MILP problem instances that come from the same distribution when solved using different configurations. We show that instances that have similar costs using one solver configuration also have similar costs using another solver configuration in the same runtime environment. After that, we present a methodology based on Deep Metric Learning to learn MILP similarities that correlate with their final solutions' costs. At inference time, given a new problem instance, it is first projected into the learned metric space using the trained model, and configuration parameters are instantly predicted using previously-explored configurations from the nearest neighbor instance in the learned embedding space. Empirical results on real-world problem benchmarks show that our method predicts configuration parameters that improve solutions' costs by up to 38% compared to existing approaches.