Alternating direction method and deep learning for discrete control with storage
Résumé
This paper deals with scheduling the operations in systems with storage modeled as a mixed integer nonlinear program (MINLP). Due to time interdependency induced by storage, discrete control, and nonlinear operational conditions, computing even a feasible solution may require an unaffordable computational burden.
We exploit a property common to a broad class of these problems to devise a decomposition algorithm related to alternating direction methods, which progressively adjusts the operations to the storage state profile.
We also design a deep learning model to predict the continuous storage states to start the algorithm instead of the discrete decisions, as commonly done in the literature. This enables search diversification through a multi-start mechanism and prediction using scaling in the absence of a training set.
Numerical experiments on the pump scheduling problem in water networks show the effectiveness of this hybrid learning/decomposition algorithm in computing near-optimal strict-feasible solutions in more reasonable times than other approaches.
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