Neur2BiLO: Neural Bilevel Optimization

TL;DR

Neur2BiLO introduces a neural network-based heuristic for bilevel optimization that efficiently approximates value functions, enabling fast and high-quality solutions for complex linear and non-linear problems with integer variables.

Contribution

It proposes a data-driven framework embedding neural networks into mixed-integer programs to solve bilevel problems more efficiently than traditional methods.

Findings

Achieves high-quality solutions rapidly across diverse bilevel problems.

Effective for both linear and non-linear objectives with mixed-integer variables.

Outperforms existing solvers in speed while maintaining solution quality.

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.