Handling discrete decisions in bilevel optimization via neural network embeddings

Bilevel optimization is an active area of research within the operations research community due to its ability to capture the interdependencies between two levels of decisions. This study introduces a metamodeling approach for addressing mixed-integer bilevel optimization problems, exploiting the approximation capabilities of neural networks. The proposed methodology employs neural network embeddings to approximate the optimal follower's response, bypassing the inner optimization problem by parametrizing it with continuous leader�s decisions. The use of Rectified Linear Unit (ReLU) activations allows the forward pass of the neural network to be represented as a set of mixed-integer linear constraints. Thereby, the bilevel structure is simplified into a single-level optimization model. A case study based on a two-echelon supply chain demonstrates the effectiveness of the approach, with solutions comparable to traditional bilevel optimization methods. The results suggest that neural network embeddings offer a promising alternative for tackling complex bilevel problems even when discrete decisions are involved and unveil the trade-off between prediction accuracy and computational demands. This methodology provides a versatile and efficient framework for solving mixed-integer bilevel optimization problems across diverse domains.