Kriging模型的增量构造及其在全局优化中的应用

Incremental Kriging Model Rebuilding Method and its Application in Efficient Global Optimization

为了解决高效全局优化算法(EGO)中迭代次数增多时构建Kriging模型速度过慢,以及对于某些响应值变化范围较大的目标函数出现过早收敛的问题,提出了增量Kriging方法和基于此方法的改进EGO算法.增量方法利用已经得到的关联矩阵的逆矩阵和新增的数据点忽略关联系数优化的过程,直接进行一系列矩阵运算,得到新关联矩阵的逆矩阵,进而得到更新后的预测模型.改进的EGO算法使用上述的增量方法和更加严谨的停止规则,包括改善期望、自变量和响应值的停止准则.最后使用标准函数分别对增量方法和EGO算法进行测试,结果表明,增量方法可在损失少量精度的情况下大大缩短模型更新的时间,改进的EGO算法具有更高的效率和稳定性.

In efficient global optimization （EGO） algorithm, the time of rebuilding the Kriging model increases rapidly with the increasing of samples＇ size, and premature convergence may exist when the range of the objective function is too large. To conquer these problems, an incremental Kriging method （IKM） and the improved EGO algorithm are proposed. The inversion of the correlation matrix and the new data points are manipulated to get the coefficients of the Kriging model in IKM, while coefficients of correlation function are optimized and the inversion of new correlation matrix is directly calculated. Stopping criteria on expected improvement, response value and argument are used in the improved EGO algorithm. The experimental results demonstrate that IKM greatly reduces the time of modelling with little loss of accuracy and the improved EGO method has higher efficiency and better stability.