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.

深度学习模型是一类近似模型，已被证明具有代表复杂现象的强大预测能力。将深度学习模型引入优化公式提供了一种降低问题复杂性并保持模型准确性的方法。最近显示，深度神经网络模型具有经过校正的线性单元的神经网络形式，可以作为混合整数线性规划公式进行精确重铸。但是，开发在线应用程序中涉及混合整数决策的问题的最佳解决方案仍然具有挑战性。多参数编程减轻了解决涉及有界不确定参数的优化问题的在线计算负担。在这项工作中，提出了一种整合深度学习和多参数编程的策略。这种集成产生了一个统一的方法，用于基于深度学习及其离线显式最佳解决方案来开发精确的替代模型。所建议的策略在化学稳定器的最佳操作上得到了证明。