# Learning to Schedule Heuristics in Branch-and-Bound

arXiv: https://arxiv.org/abs/2103.10294 · HTML: https://mlsanity.com/paper/2103.10294/

## Key facts

- Cited by 46 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 27 references that are in the map.
- First posted on arXiv 18 Mar 2021.

## Builds on (most cited first, 5 of 5)

- [Exact Combinatorial Optimization with Graph Convolutional Neural Networks](https://mlsanity.com/paper/1906.01629/) (2019)
- [Solving Mixed Integer Programs Using Neural Networks](https://mlsanity.com/paper/2012.13349/) (2020)
- [ParamILS: An Automatic Algorithm Configuration Framework](https://mlsanity.com/paper/1401.3492/) (2014)
- [Learning to Branch](https://mlsanity.com/paper/1803.10150/) (2018)
- [Solver Scheduling via Answer Set Programming](https://mlsanity.com/paper/1401.1024/) (2014)

## Built on by (most cited first, 30 of 46)

- [DeepACO: Neural-enhanced Ant Systems for Combinatorial Optimization](https://mlsanity.com/paper/2309.14032/) (2023)
- [MIP-GNN: A Data-Driven Framework for Guiding Combinatorial Solvers](https://mlsanity.com/paper/2205.14210/) (2022)
- [Learning to branch with Tree MDPs](https://mlsanity.com/paper/2205.11107/) (2022)
- [Searching Large Neighborhoods for Integer Linear Programs with Contrastive Learning](https://mlsanity.com/paper/2302.01578/) (2023)
- [Learning to Compare Nodes in Branch and Bound with Graph Neural Networks](https://mlsanity.com/paper/2210.16934/) (2022)
- [Towards Foundation Models for Mixed Integer Linear Programming](https://mlsanity.com/paper/2410.08288/) (2024)
- [Exploring the Power of Graph Neural Networks in Solving Linear Optimization Problems](https://mlsanity.com/paper/2310.10603/) (2023)
- [Machine Learning Augmented Branch and Bound for Mixed Integer Linear Programming](https://mlsanity.com/paper/2402.05501/) (2024)
- [Machine Learning for Cutting Planes in Integer Programming: A Survey](https://mlsanity.com/paper/2302.09166/) (2023)
- [Apollo-MILP: An Alternating Prediction-Correction Neural Solving Framework for Mixed-Integer Linear Programming](https://mlsanity.com/paper/2503.01129/) (2025)
- [Distributional MIPLIB: a Multi-Domain Library for Advancing ML-Guided MILP Methods](https://mlsanity.com/paper/2406.06954/) (2024)
- [Learning to Configure Separators in Branch-and-Cut](https://mlsanity.com/paper/2311.05650/) (2023)
- [Improved Sample Complexity Bounds for Branch-and-Cut](https://mlsanity.com/paper/2111.11207/) (2021)
- [Promoting Generalization for Exact Solvers via Adversarial Instance Augmentation](https://mlsanity.com/paper/2310.14161/) (2023)
- [FrontierCO: Real-World and Large-Scale Evaluation of Machine Learning Solvers for Combinatorial Optimization](https://mlsanity.com/paper/2505.16952/) (2025)
- [Learning To Dive In Branch And Bound](https://mlsanity.com/paper/2301.09943/) (2023)
- [SORREL: Suboptimal-Demonstration-Guided Reinforcement Learning for Learning to Branch](https://mlsanity.com/paper/2412.15534/) (2024)
- [Learning to Optimize for Mixed-Integer Non-linear Programming with Feasibility Guarantees](https://mlsanity.com/paper/2410.11061/) (2024)
- [Accelerate Presolve in Large-Scale Linear Programming via Reinforcement Learning](https://mlsanity.com/paper/2310.11845/) (2023)
- [Multi-task Representation Learning for Mixed Integer Linear Programming](https://mlsanity.com/paper/2412.14409/) (2024)
- [Online Learning for Scheduling MIP Heuristics](https://mlsanity.com/paper/2304.03755/) (2023)
- [Learning Backdoors for Mixed Integer Linear Programs with Contrastive Learning](https://mlsanity.com/paper/2401.10467/) (2024)
- [A Neural Separation Algorithm for the Rounded Capacity Inequalities](https://mlsanity.com/paper/2306.17283/) (2023)
- [Learning to Remove Cuts in Integer Linear Programming](https://mlsanity.com/paper/2406.18781/) (2024)
- [Balans: Multi-Armed Bandits-based Adaptive Large Neighborhood Search for Mixed-Integer Programming Problem](https://mlsanity.com/paper/2412.14382/) (2024)
- [PROPEL: Supervised and Reinforcement Learning for Large-Scale Supply Chain Planning](https://mlsanity.com/paper/2504.07383/) (2025)
- [Search Strategy Generation for Branch and Bound Using Genetic Programming](https://mlsanity.com/paper/2412.09444/) (2024)
- [Beyond Local Selection: Global Cut Selection for Enhanced Mixed-Integer Programming](https://mlsanity.com/paper/2503.15847/) (2025)
- [CLCR: Contrastive Learning-based Constraint Reordering for Efficient MILP Solving](https://mlsanity.com/paper/2504.03688/) (2025)
- [Revisiting local branching with a machine learning lens](https://mlsanity.com/paper/2112.02195/) (2021)

## Abstract (arXiv)

Primal heuristics play a crucial role in exact solvers for Mixed Integer Programming (MIP). While solvers are guaranteed to find optimal solutions given sufficient time, real-world applications typically require finding good solutions early on in the search to enable fast decision-making. While much of MIP research focuses on designing effective heuristics, the question of how to manage multiple MIP heuristics in a solver has not received equal attention. Generally, solvers follow hard-coded rules derived from empirical testing on broad sets of instances. Since the performance of heuristics is instance-dependent, using these general rules for a particular problem might not yield the best performance. In this work, we propose the first data-driven framework for scheduling heuristics in an exact MIP solver. By learning from data describing the performance of primal heuristics, we obtain a problem-specific schedule of heuristics that collectively find many solutions at minimal cost. We provide a formal description of the problem and propose an efficient algorithm for computing such a schedule. Compared to the default settings of a state-of-the-art academic MIP solver, we are able to reduce the average primal integral by up to 49% on a class of challenging instances.