Deep learning enhanced mixed integer optimization: Learning to reduce
  model dimensionality
Niki Triantafyllou Maria M. Papathanasiou
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.