MIPGen: Learning to Generate Scalable MIP Instances

Tianxing Yang, Huigen Ye, Hua Xu, Hongyan Wang

Primary Area: optimization

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Keywords: Mixed-Integer Programming, Generator

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TL;DR: This paper introduces MIPGen, a novel generative framework designed to generate MIP problems autonomously.

Abstract: Large-scale Mixed-Integer Programming (MIP) problems have been efficiently addressed using Machine Learning (ML)-based frameworks to obtain high-quality solutions. When addressing real-world MIP problems, ML-based frameworks often face challenges in acquiring sufficient isomorphic instances for practical training. This underscores the need for generators that can autonomously produce isomorphic MIP problems from existing instances. This paper introduces MIPGen, a novel generative framework for autonomous MIP instance generation. Our key contribution lies in the three-stage problem generation in MIPGen: 1) Instances Classification, which learns and clusters the embeddings of a bipartite graph representation of the problem; 2) Node Splitting and Merging, which splits the bipartite graph and tries to reconstruct it; 3) Scalable Problem Construction, which concatenates tree structures to get larger problems. We demonstrate that the instances generated by MIPGen are highly similar to the original problem instances and can effectively enhance the solution effect of the ML-based framework. Further experiments show that the scaled-up generated instances still retain the problem's structural properties, validating the proposed framework's effectiveness.

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Submission Number: 2681