# Local Branching Relaxation Heuristics for Integer Linear Programs

arXiv: https://arxiv.org/abs/2212.08183 · HTML: https://mlsanity.com/paper/2212.08183/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 45 references that are in the map.
- First posted on arXiv 15 Dec 2022.

## Builds on (most cited first, 9 of 9)

- [Exact Combinatorial Optimization with Graph Convolutional Neural Networks](https://mlsanity.com/paper/1906.01629/) (2019)
- [Learning to Perform Local Rewriting for Combinatorial Optimization](https://mlsanity.com/paper/1810.00337/) (2018)
- [Neural Large Neighborhood Search for the Capacitated Vehicle Routing Problem](https://mlsanity.com/paper/1911.09539/) (2019)
- [Learning to Delegate for Large-scale Vehicle Routing](https://mlsanity.com/paper/2107.04139/) (2021)
- [Learning to branch with Tree MDPs](https://mlsanity.com/paper/2205.11107/) (2022)
- [Learning a Large Neighborhood Search Algorithm for Mixed Integer Programs](https://mlsanity.com/paper/2107.10201/) (2021)
- [Learning Large Neighborhood Search Policy for Integer Programming](https://mlsanity.com/paper/2111.03466/) (2021)
- [Learning Variable Ordering Heuristics for Solving Constraint Satisfaction Problems](https://mlsanity.com/paper/1912.10762/) (2019)
- [Revisiting local branching with a machine learning lens](https://mlsanity.com/paper/2112.02195/) (2021)

## Built on by (most cited first, 4 of 4)

- [Searching Large Neighborhoods for Integer Linear Programs with Contrastive Learning](https://mlsanity.com/paper/2302.01578/) (2023)
- [Balans: Multi-Armed Bandits-based Adaptive Large Neighborhood Search for Mixed-Integer Programming Problem](https://mlsanity.com/paper/2412.14382/) (2024)
- [Imbalances in Neurosymbolic Learning: Characterization and Mitigating Strategies](https://mlsanity.com/paper/2407.10000/) (2024)
- [On Improving Neurosymbolic Learning by Exploiting the Representation Space](https://mlsanity.com/paper/2602.07973/) (2026)

## Abstract (arXiv)

Large Neighborhood Search (LNS) is a popular heuristic algorithm for solving combinatorial optimization problems (COP). It starts with an initial solution to the problem and iteratively improves it by searching a large neighborhood around the current best solution. LNS relies on heuristics to select neighborhoods to search in. In this paper, we focus on designing effective and efficient heuristics in LNS for integer linear programs (ILP) since a wide range of COPs can be represented as ILPs. Local Branching (LB) is a heuristic that selects the neighborhood that leads to the largest improvement over the current solution in each iteration of LNS. LB is often slow since it needs to solve an ILP of the same size as input. Our proposed heuristics, LB-RELAX and its variants, use the linear programming relaxation of LB to select neighborhoods. Empirically, LB-RELAX and its variants compute as effective neighborhoods as LB but run faster. They achieve state-of-the-art anytime performance on several ILP benchmarks.