DIG-MILP: a Deep Instance Generator for Mixed-Integer Linear Programming with Feasibility Guarantee

TL;DR

DIG-MILP is a deep generative framework that creates realistic and feasible MILP instances from limited data, aiding solver tuning and machine learning model training.

Contribution

It introduces a VAE-based deep generative model that guarantees feasibility and boundedness of generated MILP instances using duality principles.

Findings

Generated instances closely match original data in solver solution times

DIG-MILP enhances machine learning model performance on MILP tasks

Supports data sharing without exposing original problem data

Abstract

Mixed-integer linear programming (MILP) stands as a notable NP-hard problem pivotal to numerous crucial industrial applications. The development of effective algorithms, the tuning of solvers, and the training of machine learning models for MILP resolution all hinge on access to extensive, diverse, and representative data. Yet compared to the abundant naturally occurring data in image and text realms, MILP is markedly data deficient, underscoring the vital role of synthetic MILP generation. We present DIG-MILP, a deep generative framework based on variational auto-encoder (VAE), adept at extracting deep-level structural features from highly limited MILP data and producing instances that closely mirror the target data. Notably, by leveraging the MILP duality, DIG-MILP guarantees a correct and complete generation space as well as ensures the boundedness and feasibility of the generated instances. Our empirical study highlights the novelty and quality of the instances generated by DIG-MILP through two distinct downstream tasks: (S1) Data sharing, where solver solution times correlate highly positive between original and DIG-MILP-generated instances, allowing data sharing for solver tuning without publishing the original data; (S2) Data Augmentation, wherein the DIG-MILP-generated instances bolster the generalization performance of machine learning models tasked with resolving MILP problems.