A Quantile Neural Network Framework for Two-stage Stochastic Optimization

A. Alcántara Mata, C. Ruiz Mora, C. Tsay

Two-stage stochastic problems are often formulated using Sample Average Approximation (SAA), where uncertainty is modeled as a finite set of scenarios, resulting in a large monolithic problem. This models can be challenging to solve, and several problem-specific decomposition approaches have been proposed. An alternative approach is to approximate the expected second-stage objective value using a surrogate model, which can then be embedded in the first-stage problem to produce good heuristic solutions. In this work, we propose to instead model the distribution of the second-stage objective, specifically using a quantile neural network (QNN). Embedding this distributional approximation enables capturing uncertainty and is not limited to expected-value optimization. We discuss optimization formulations for embedding the QNN and demonstrate the effectiveness of the proposed framework using several computational case studies including a set of MIL optimization problems.

Keywords: Optimization under Uncertainty, Stochastic Programming, Neural Networks, Mixed-Integer Programming

Methods and Applications of OR III
June 13, 2025  11:00 AM
Sala de prensa (MR 13)

B. González Rodríguez, I. Gómez Casares, B. Ghaddar, J. González Díaz, B. Pateiro López

M. J. Cánovas Cánovas, J. Parra López

B. Llamazares Rodríguez