Integrating deep learning models and multiparametric programming

Abstract

Deep learning models are a class of approximate models that are proven to have strong predictive capabilities for representing complex phenomena. The introduction of deep learning models into an optimization formulation provides a means to reduce the problem complexity and maintain model accuracy. Recently it has been shown that deep learning models in the form of neural networks with rectified linear units can be exactly recast as a mixed-integer linear programming formulation. However, developing the optimal solution of problems involving mixed-integer decisions in online applications remains challenging. Multiparametric programming alleviates the online computational burden of solving an optimization problem involving bounded uncertain parameters. In this work, a strategy is presented to integrate deep learning and multiparametric programming. This integration yields a unified methodology for developing accurate surrogate models based on deep learning and their offline, explicit optimal solution. The proposed strategy is demonstrated on the optimal operation of a chemostat.