Alternating direction method and deep learning for discrete control with storage

Sophie Demassey (1) , Valentina Sessa (1) , Amirhossein Tavakoli (1, 2)

1 CMA - Centre de Mathématiques Appliquées
2 3iA Côte d’Azur - Interdisciplinary Institute for Artificial Intelligence

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.

Mots clés: Mixed Integer Nonlinear Programming; Variable splitting; Deep Learning; Mixed Integer Nonlinear Programming Variable splitting Deep Learning; Mixed Integer Nonlinear Programming

Domaines: Optimisation et contrôle [math.OC]; Apprentissage [cs.LG]; Recherche opérationnelle [math.OC]; Systèmes dynamiques [math.DS]

Sophie Demassey, Valentina Sessa, Amirhossein Tavakoli. Alternating direction method and deep learning for discrete control with storage. International Symposium on Combinatorial Optimization, ISCO 2024, May 2024, Tenerife, Spain. ⟨hal-04506597⟩