Abstract
Finding an optimal well placement scenario is a complex and computationally intensive problem. The major computational cost is associated with the numerical reservoir simulation which should be executed for the fitness evaluation of each scenario. For such problems, a robust optimization algorithm is required. Population-based algorithms are powerful, but computationally demanding, optimizers. Surrogate-assisted algorithms have been developed to reduce the CPU-time of these optimizers, by substituting the original fitness function (OF), partially or completely, with an approximation function (AF), often known as proxy or surrogate.
in these algorithms, a model management strategy should be implemented to use the OF effectively and minimally, during the optimization process, fn this study, a self-adaptive model management strategy is developed, in which two surrogates are required. The first surrogate approximates the fitness function landscape, and the second one estimates the fidelity of the first surrogate over the search space (uncertainty map). According to the estimated uncertainty, the probability of using the OF is calculated for each individual, and then the algorithm stochastically decides to use the OF or AF. A heuristic fuzzy rule is applied to define the range of probability values in each evolution-cycle, based on the average fidelity of the second surrogate. The proposed technique is installed on a genetic algorithm, and two artificial neural networks are used as the proxies, which are trained online.
The robustness of the proposed algorithm is analyzed using a semi-synthetic reservoir model, PUNQ-S3. The outcomes are compared with the results achieved by two common algorithms, a typical (unassisted) genetic algorithm, and an offline-learning surrogate-assisted genetic algorithm. The comparison indicates that the proposed method can reduce the computational costs up to 48%. This surrogate-assisted algorithm may enhance the applicability of population-based algorithms in well placement optimization problems, by reducing the associated computational costs.
