Accelerating CMA-ES in history matching problems using an ensemble of surrogates with generation-based management

Abstract

Because of the quasi-gradient update embedded in CMA-ES algorithm, it can outperform most of the population-based algorithms, from a convergence speed standpoint. However, due to the computationally expensive fitness function associated with history matching, the reduction of function (simulation) calls can be favourable. In this study, an ensemble of surrogates (proxies) with generation-based model-management is proposed to reduce the number of simulation calls efficaciously. Since the fitness function is highly nonlinear, an ensemble of surrogates (Gaussian process) is utilised. The likelihood term is divided into multiple functions, and each is represented via a separate surrogate. This improved the response surface fitting. In generation-based management, a stochastically selected measure (surrogate or reservoir-simulation) should be used to evaluate all the individuals of each generation. CMA-ES requires ranking of the individuals to select the parents. Therefore, the generation-based model-management fits well in CMA-ES, as surrogates are normally better in ranking the individuals than approximating the fitness. History matching for a real problem with 59 variables and PUNQ-S3 with eight variables was conducted via a standard CMA-ES and the proposed surrogate-assisted CMA-ES. The results showed that up to 65% and 50% less simulation calls for case#1 and case#2 were required.