We are concerned with the efficiency of stochastic gradient estimation methods for large-scale nonlinear optimization in the presence of uncertainty. These methods aim to estimate an approximate gradient from a limited number of random input vector samples and corresponding objective function values. Ensemble methods usually employ Gaussian sampling to generate the input samples. It is known from the optimal design theory that the quality of sample-based approximations is affected by the distribution of the samples. We therefore evaluate six different sampling strategies to optimization of a high-dimensional analytical benchmark optimization problem, and, in a second example, to optimization of oil reservoir management strategies with and without geological uncertainty. The effectiveness of the sampling strategies is analyzed based on the quality of the estimated gradient, the final objective function value, the rate of the convergence, and the robustness of the gradient estimate. Based on the results, an improved version of the stochastic simplex approximate gradient method is proposed based on UE(s²) sampling designs for supersaturated cases that outperforms all alternative approaches. We additionally introduce two new strategies that outperform the UE(s²) designs previously suggested in the literature.

Since the early 2000's there has been a significant focus from many groups around the world towards the development and application of innovative technologies in order to improve reservoir management strategies and optimize field development plans. Benchmark studies are a very valuable way of evaluating and demonstrating the status and potential of developing technology. Numerical optimization is seen as a valuable technology for decision support in various stages of the life cycle of hydrocarbon fields. Its potential has been demonstrated in previous benchmark studies such as the 2008 Brugge study on Closed-Loop Reservoir Management albeit for primarily well control problems. Additionally since the Brugge benchmark exercise also involved history matching it was difficult to separate and thus draw significant conclusions about the performance of the optimization methods. Thus the OLYMPUS optimization benchmark challenge was setup and aimed at field development (FD) optimization under uncertainty. In this talk we will provide an overview of the OLYMPUS case and the optimization problems defined. In addition we aim to provide an anonymized overview of validated results from the participants for the OLYMPUS workshop which takes place the day after ECMOR.