Supervised Large Neighbourhood Search for MIPs

TL;DR

This paper introduces a supervised machine learning approach integrated into Large Neighbourhood Search for MIPs, demonstrating significant performance improvements over traditional heuristics on benchmark datasets.

Contribution

It presents a novel ML-enhanced LNS method with minimal offline training, improving solution quality and efficiency for MIP problems compared to existing heuristics.

Findings

SLNS outperforms baseline heuristics on MIPLIB 2017

ML integration improves solution quality with minimal training

Techniques to enhance ML model accuracy and robustness

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.