A Neural Network-Based Distributional Constraint Learning Methodology for Mixed-Integer Stochastic Optimization
Bridging predictions and prescriptions is gaining attention within the OR community. One possible approach is the so-called Constraint Learning (CL) methodology, where trained machine learning models can be embedded as a set of constraints within mixed-integer optimization problems. In this work, we extend the traditional deterministic CL to account for decision dependent uncertainties. We propose a Distributional Constraint Learning (DCL) approach that makes use of a piece-wise linearizable neural network models to estimate the conditional distribution of a response variable, which depends on our decisions and exogeneous contextual information. Moreover, we formulate a stochastic optimization problem by sampling random values from the estimated conditional distribution. We test this methodology in a real-world power systems problem, where a Virtual Power Plant seeks to optimize its operation, subject to different forms of uncertainty, and with price-responsive consumers.
Palabras clave: stochastic optimization machine learning uncertainty mixed integer optimization power systems