This work presents recent advances within the AlgoRithms for Global Optimization of coNstrAined grey-box compUTational problems (ARGONAUT) framework, developed for optimization of systems which lack analytical forms and derivatives. A new parallel version of ARGONAUT (p-ARGONAUT) is introduced to solve high dimensional problems with a large number of constraints. This development is motivated by a challenging case study, namely the operation of an oilfield using water-flooding. The objective of this case study is the maximization of the Net Present Value over a five-year time horizon by manipulating the well pressures, while satisfying a set of complicating constraints related to water-cut limitations and water handling and storage. Dimensionality reduction is performed via the parametrization of the pressure control domain, which is then followed by global optimization of the constrained grey-box system. Results are presented for multiple case studies and the performance of p-ARGONAUT is compared to existing derivative-free optimization methods. Published by Elsevier Ltd.