On population diversity measures of the evolutionary algorithms used in history matching

In history matching, the aim is to generate multiple good-enough history-matched models with a limited number of simulations which will be used to efficiently predict reservoir performance. History matching is the process of the conditioning reservoir model to the observation data; is mathematically ill-posed, inverse problem and has no unique solution and several good solutions may occur.

Numerous evolutionary algorithms are applied to history matching which operate differently in terms of population diversity in the search space throughout the evolution. Even different flavours of an algorithm behave differently and different values of an algorithm’s control parameters result in different levels of diversity. These behaviours vary from explorative to exploitative.

The need to measure population diversity arises from two bases. On the one hand maintaining population diversity in evolutionary algorithms is essential to detect and sample good history-matched ensemble models in parameter search space. On the other hand, since the objective function evaluations in history matching are computationally expensive, algorithms with fewer total number of reservoir simulations in result of a better convergence are much more favourable. Maintaining population’s diversity is crucial for sampling algorithm to avoid premature convergence toward local optima and achieve a better match quality.

In this paper, we introduce and use two measures of the population diversity in both genotypic and phenotypic space to monitor and compare performance of the algorithms. These measures include an entropy-based diversity from the genotypic measures and a moment of inertia based diversity from the phenotypic measures.

The approach has been illustrated on a synthetic reservoir simulation model, PUNQ-S3, as well as on a real North Sea model with multiple wells. We demonstrate that introduced population diversity measures provide efficient criteria for tuning the control parameters of the population-based evolutionary algorithms as well as performance comparison of the different algorithms used in history matching.