In the optimization process of the problem study, a hybrid strategy is used. This strategy combines different methods at different stages of the process in order to exploit the best features of each methodology. In this hybrid strategy, a balance between a global search process and the precision and efficiency of a local search procedure is required.

The use of reservoir simulators helps through the modelling of the behaviour of them. However, the simulation costs of a single simulation make the optimization process a difficult task to be considered. To avoid this problem a surrogate model is considered which is created by kriging from a set of solutions obtained using the simulator on sample points previously generated using the latinised centroidal Voronoi tessellation (LCVT) technique.

In the optimization process, the global search is driven by the genetic algorithm (GA), acting on a real model or on a surrogate model. This provides the region where the global optimal solution is located. Once such regions have been found, a local scheme can be used to converge to a precise optimum. The local search is driven by a sequential quadratic programming (SQP) when a real model is considered and by a sequential approximation optimization (SAO) when a surrogate model is considered.

With these algorithms, the combinations formulated are: the GA and SQP algorithms performed on the high fidelity model; the GA performed on the low fidelity model and the SQP algorithms performed on the high fidelity model; the GA and SAO algorithms performed on the low fidelity (surrogate) model.

All three hybrids converge to reported benchmark solution with fewer function simulation runs, except for the case which involves a high nonlinear objective function and also presents several constraints functions. These two aspects together make the problem too difficult to be solved by the evolutionary algorithms (EAs), in charge of the first stage of the optimization. It is important to emphasize that the solution provided by the reported benchmark (SAO algorithm) is a result found after a many tries in order to find a good solution, as typically when local search algorithms are used. The hybrid methodologies considered in this paper have the aim of avoiding the several initial points tries required for reservoir optimization problems.

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