Supervised Large Neighbourhood Search for MIPs
Charly Robinson La Rocca, Jean-François Cordeau, Emma Frejinger
TL;DR
This work studies how supervised learning can accelerate MIPs by embedding predictions into Large Neighbourhood Search (LNS) destroy operators. It introduces a modular LNS matheuristic and a Supervised LNS (SLNS) using per-variable predictions, plus probing and sampling data collection with lightweight models to minimize offline training. Experimental results on MIPLIB 2017 and Locomotive Assignment Problem (LAP) show that ML-enhanced LNS can outperform state-of-the-art solvers in some settings and that random LNS remains a strong baseline, while biased SLNS configurations can yield improvements when predictions are informative. The findings highlight a promising, solver-agnostic pathway for incorporating ML into LNS, while also emphasizing the need for larger, diverse datasets and instance-adaptive learning strategies for robust generalization.
Abstract
Large Neighbourhood Search (LNS) is a powerful heuristic framework for solving Mixed-Integer Programming (MIP) problems. However, designing effective variable selection strategies in LNS remains challenging, especially for diverse sets of problems. In this paper, we propose an approach that integrates Machine Learning (ML) within the destroy operator of LNS for MIPs with a focus on minimal offline training. We implement a modular LNS matheuristic as a test bench to compare different LNS heuristics, including our ML-enhanced LNS. Experimental results on the MIPLIB 2017 dataset demonstrate that the matheuristic can significantly improve the performance of state-of-the-art solvers like Gurobi and SCIP. We conduct analyses on noisy oracles to explore the impact of prediction accuracy on solution quality. Additionally, we develop techniques to enhance the ML model through loss adjustments and sampling routines. Our findings suggest that while random LNS remains competitive, our Supervised LNS (SLNS) outperforms other baselines and helps set the foundation for future research on ML for LNS methods that are both efficient and general.