MOSKopt: A simulation-based data-driven digital twin optimizer with embedded uncertainty quantification

In this work, we present a new stochastic black-box optimizer—named MOSKopt—for optimization under uncertainty problems involving expensive-to-evaluate and arbitrarily complex simulation models subject to severe uncertainties and multiple design constraints. The optimizer relies on a novel surrogate-assisted, simulation-based, and data-driven optimization algorithm developed in our earlier work for multiple-constrained optimization of stochastic black-box systems using a stochastic Kriging (SK) type surrogate model, which has shown its promising potential in stochastic simulation optimization studies. MOSKopt replaces simulation replications with parallelized Monte Carlo simulations to characterize the resulting error distributions of the optimization objective and constraints in a more generalized way. In doing so, it broadly extends the applicability of SK-based frameworks to other optimization problems exposed to uncertain input data or model parameters—a commonly encountered paradigm in process simulations driving the digital twins. We benchmark the optimizer and its algorithms on three case studies with increasing complexity. The first two are benchmark test problems taken from simulation optimization literature, whereas the third optimizes the design and operations of a wastewater treatment plant (WWTP) subject to effluent quality constraints using a detailed plant-wide simulation model—the closest case to a digital twin—consisting of several high-fidelity bioprocess models (e.g., activated sludge and anaerobic digestion) calibrated for data obtained from full-scale wastewater treatment plants under uncertain influent scenarios. The results from case studies quantitatively demonstrate the superior efficacy of the MOSKopt algorithm over the literature methods not only in maintaining feasibility under multiple stochastic constraints but also in returning better objective function values. The results also show the potential of the MOSKopt’s entirely non-intrusive workflow, which makes it a suitable optimizer for applications involving digital twin projects with non-negligible uncertainties.