Piecewise linear trees as surrogate models for system design and planning under high-frequency temporal variability

The design and planning of systems subject to high-frequency time-varying conditions (e.g., prices, resource supplies, and customer demand) requires the solution of multi-period optimization problems, which have to account for operational aspects that are often described by complex nonlinear models. Accordingly, to overcome the computational challenges associated with the solution of the above problems, we present a framework to build computationally efficient and yet accurate optimization models. We also propose a general method to use trained piecewise linear (PWL) trees as surrogate models to approximate nonlinearities in relatively high dimensions and embed these trees onto mathematical optimization models. We show that, for some datasets, embedding PWL trees leads to models that result in a better balance between accuracy and computational performance when compared with approaches based on other machine-learning surrogate models. We showcase the applicability of the proposed framework via a case study on maintenance optimization of building cooling systems.