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arXiv · 2402.02552

Neur2BiLO: Neural Bilevel Optimization

Justin Dumouchelle·Esther Julien·Jannis Kurtz·Elias B. Khalil
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Abstract

Bilevel optimization deals with nested problems in which a leader takes the first decision to minimize their objective function while accounting for a follower's best-response reaction. Constrained bilevel problems with integer variables are particularly notorious for their hardness. While exact solvers have been proposed for mixed-integer linear bilevel optimization, they tend to scale poorly with problem size and are hard to generalize to the non-linear case. On the other hand, problem-specific algorithms (exact and heuristic) are limited in scope. Under a data-driven setting in which similar instances of a bilevel problem are solved routinely, our proposed framework, Neur2BiLO, embeds a neural network approximation of the leader's or follower's value function, trained via supervised regression, into an easy-to-solve mixed-integer program. Neur2BiLO serves as a heuristic that produces high-quality solutions extremely fast for four applications with linear and non-linear objectives and pure and mixed-integer variables.

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Justin Dumouchelle, Esther Julien, Jannis Kurtz, Elias B. Khalil. 2024-11-01. Neur2BiLO: Neural Bilevel Optimization. https://arxiv.org/abs/2402.02552

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