Effective Generation of Feasible Solutions for Integer Programming via Guided Diffusion
Primary Area: optimization
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Keywords: Integer Programming, Diffusion Models
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Abstract: Feasible solutions are crucial for Integer Programming (IP) since they can substantially speed up the solving process. In many applications, similar IP instances often exhibit similar structures and shared solution distributions, which can be potentially modeled by deep learning methods. Unfortunately, existing deep-learning-based algorithms, such as Neural Diving \citep{nair2020solving}, fail to capture the full underlying distributions and can only generate \emph{partial} feasible solutions for a given IP instance. In this paper, we propose a novel framework that generates \emph{complete} feasible solutions \emph{end-to-end}. Our framework leverages contrastive learning to characterize the relationship between IP instances and solutions, and learns latent embeddings for both IP instances and their solutions. Further, the framework employs diffusion models to learn the distribution of solution embeddings conditioned on IP representations, with a dedicated guided sampling strategy that accounts for both constraints and objectives. We empirically evaluate our framework on four typical datasets of IP problems, and show that it effectively generates complete feasible solutions with a higher probability and a better quality for a given IP instance than the state-of-the-art.
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Submission Number: 3028
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