The final and fourth stage aims at additional improvement resorting to direct optimization of the best solution from the previous stages. MM has solid theoretical foundations and leads to efficient optimization schemes in multiple engineering disciplines. In the third stage, the precision of the proxy model is iteratively improved and the enhanced surrogate model is re-optimized via Manifold Mapping (MM), a method that combines models with different levels of accuracy. This fact is supported by the good performance in this type of optimization problems of techniques that rely strongly on linearity assumptions, such as Trajectory Piecewise Linearization, a procedure that is not always applicable due to its simulator-intrusive nature. GBCs can be especially suited to problems where nonlinearities are not strong, as is the case often for well-control optimization. This proxy is based on Generalized Barycentric Coordinates (GBCs), a generalization of the concept of barycentric coordinates used within a triangle. Thereafter, in the second stage, a fast-to-evaluate proxy model is constructed with the points considered in the experimental design. The first stage of PO consists in a global exploration of the search space using design of experiments. In this paper we present Progressive Optimization (PO), a simulator-nonintrusive four-stage methodology to accelerate optimal search substantially in well-control applications. However, in many practical situations the optimization algorithms used are still computationally expensive. Well-control management is nowadays frequently approached by means of mathematical optimization.
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