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.

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一种基于增量学习的快速克里金辅助进化算法

克里金模型，也称为高斯过程模型，广泛用于代理辅助进化算法 (SAEA)。然而，标准克里金模型的三次时间复杂度限制了它们在高维优化中的使用。为了解决这个问题，我们提出了一种用于高维代理辅助进化计算的增量克里金模型。主要思想是基于之前训练的模型的方程逐步更新克里金模型，而不是在新样本到来时从头开始构建模型，这样更新克里金模型的时间复杂度可以降低到二次方。所提出的增量学习方案非常适合在线 SAEA，因为它们会在每一代或几代中评估新样本。与标准克里金辅助进化算法相比，所提出的算法能够在测试问题上取得有竞争力的优化结果，并且明显快于标准克里金方法。与四种快速克里金辅助进化算法和四种最先进的 SAEA 相比，所提出的算法还显示出具有竞争力或更好的性能。这项工作提供了一种在高维代理辅助进化计算中使用克里金模型的快速方法。