A Distance Metric for Mixed Integer Programming Instances
Gwen Maudet, Gr\'egoire Danoy

TL;DR
This paper introduces the first mathematical distance metric for MILP instances, enabling better comparison and classification of problem instances, which improves solver guidance and instance set analysis.
Contribution
It proposes a novel, formulation-based distance metric for MILP instances, extending to instance-level comparison and outperforming existing methods in class identification.
Findings
The metric accurately identifies MILP instance classes.
The greedy variant is nearly as accurate as the exact version but much faster.
The method outperforms state-of-the-art non-learned approaches in class grouping tasks.
Abstract
Mixed-integer linear programming (MILP) is a powerful tool for addressing a wide range of real-world problems, but it lacks a clear structure for comparing instances. A reliable similarity metric could establish meaningful relationships between instances, enabling more effective evaluation of instance set heterogeneity and providing better guidance to solvers, particularly when machine learning is involved. Existing similarity metrics often lack precision in identifying instance classes or rely heavily on labeled data, which limits their applicability and generalization. To bridge this gap, this paper introduces the first mathematical distance metric for MILP instances, derived directly from their mathematical formulations. By discretizing right-hand sides, weights, and variables into classes, the proposed metric draws inspiration from the Earth mover's distance to quantify mismatches…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Optimization Algorithms Research · Data Management and Algorithms · Optimization and Search Problems
MethodsSparse Evolutionary Training
