Deep learning enhanced mixed integer optimization: Learning to reduce model dimensionality

This work introduces a framework to address the computational complexity inherent in Mixed-Integer Programming (MIP) models by harnessing the potential of deep learning. We compare the effectiveness of (a) feed-forward neural networks (ANN) and (b) convolutional neural networks (CNN) in approximating the active dimensions within MIP problems. We utilize multi-label classification to account for more than one active dimension. To enhance the framework's performance, we employ Bayesian optimization for hyperparameter tuning, aiming to maximize sample-level accuracy. The primary objective is to train the neural networks to predict all active dimensions accurately, thereby maximizing the occurrence of global optimum solutions. We apply this framework to a flow-based facility location allocation Mixed-Integer Linear Programming (MILP) formulation that describes long-term investment planning and medium-term tactical planning in a personalized medicine supply chain for cell therapy manufacturing and distribution.