Adaptive Basis Function Selection Enhanced Multisurrogate-Assisted Evolutionary Algorithm for Production Optimization

Surrogate-assisted evolutionary algorithms (SAEAs) have become a popular approach for solving reservoir production optimization problems. The radial- basis-function network (RBFN) is a robust surrogate model technology suitable for reservoir development with numerous wells and a long production lifetime. There are several types of basis functions for constructing RBFN models. However, existing research shows that selecting the basis function with competitive performance for the current optimization problem is challenging without prior knowledge. In conventional SAEAs, the basis function is often predetermined, but its prediction accuracy for the problem at hand cannot be guaranteed. Furthermore, canonical SAEAs usually employ only one surrogate model for the entire optimization process. However, relying on a single surrogate model for optimization increases the probability of search direction misdirection due to prediction deviations. In this paper, a novel method named adaptive basis function selection enhanced multisurrogate-assisted evolutionary algorithm (ABMSEA) is introduced for production optimization. This method mainly includes two innovations. First, by training and testing different types of basis functions, the one with the best prediction performance is adaptively selected. Second, the ensemble model is constructed using the bootstrap sampling method, comprising multiple global surrogate models based on the selected best basis function. To search for a set of solutions that perform well on multiple surrogates, we employ an efficient multiobjective optimization (MOO) algorithm called nondominated sorting genetic algorithm II (NSGA- II). This algorithm uses the surrogates themselves as objective functions, aiming to find solutions that yield favorable results across multiple surrogates. The proposed method improves the efficiency of production optimization while enhancing global search capabilities. To evaluate the effectiveness of ABMSEA, we conduct tests on four 100D benchmark functions, a three-channel model, and an egg model. The obtained results are compared with those obtained from differential evolution (DE) and three other surrogate-model -based methods. The experimental results demonstrate that ABMSEA exhibits an accurate selection of competitive basis functions for the current optimization period while maintaining high optimization efficiency and avoiding local optima. Consequently, our method enables optimal well control, leading to the attainment of the highest net present value (NPV).