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arXiv · 2610.33930

EnerGNN: Learning Optimization-Compatible Energy Functions for Exact Constrained Combinatorial Inference

Niki Triantafyllou·Maria M. Papathanasiou
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Abstract

Learning-based approaches to combinatorial optimization often predict solutions directly or use predictions to restrict search, while expressive energy-based models typically rely on approximate inference. We introduce EnerGNN, a framework that learns energy functions over complete binary configurations and minimizes them under explicit hard constraints through mixed integer programming (MIP). EnerGNN combines a graph neural network encoder with an optimization-compatible readout and a nonlinear energy head, enabling exact constrained inference over the learned energy. An optimality-aware contrastive loss trains the energy to reflect solution quality and constraint violations. Across Quadratic Knapsack, Combinatorial Auctions, and a personalized cell therapy supply chain problem, EnerGNN achieves near-optimal solutions with 100% feasibility. On the supply chain problem, it achieves a 0.05% mean primal gap and a 17.4$\times$ speedup over the monolithic MIP. The learned energy also generalizes to larger instances and supports zero-shot constraint injection, adapting to changing constraints without retraining while preserving feasibility.

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Niki Triantafyllou, Maria M. Papathanasiou. 2026-10-24. EnerGNN: Learning Optimization-Compatible Energy Functions for Exact Constrained Combinatorial Inference. https://arxiv.org/abs/2610.33930

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