A Fast Kriging-Assisted Evolutionary Algorithm Based on Incremental Learning

Kriging models, also known as Gaussian process models, are widely used in surrogate-assisted evolutionary algorithms (SAEAs). However, the cubic time complexity of the standard Kriging models limits their usage in high-dimensional optimization. To tackle this problem, we propose an incremental Kriging model for high-dimensional surrogate-assisted evolutionary computation. The main idea is to update the Kriging model incrementally based on the equations of the previously trained model instead of building the model from scratch when new samples arrive, so that the time complexity of updating the Kriging models can be reduced to quadratic. The proposed incremental learning scheme is very suitable for online SAEAs since they evaluate new samples in each one or several generations. The proposed algorithm is able to achieve competitive optimization results on the test problems compared with the standard Kriging-assisted evolutionary algorithm and is significantly faster than the standard Kriging approach. The proposed algorithm also shows competitive or better performances compared with four fast Kriging-assisted evolutionary algorithms and four state-of-the-art SAEAs. This work provides a fast way of employing Kriging models in high-dimensional surrogate-assisted evolutionary computation.