Abstract: Considering the curse of dimensionality and low optimization efficiency caused by hyper-parameters in expensive constrained optimization problems,a new partial least squares Kriging model assisted efficient global optimization method was proposed.The efficiency of building Kriging model was improved by using the partial least squares kernel function,and two partial least squares weighted expectation infill criteria were involved to realize model adaptive adjustment and efficient global optimization.Test functions and engineering examples showed that the proposed method could decrease the calculation in hyper-parameter and improve the efficiency of solving expensive constrained optimization problems.Especially in high-dimensional problems,the proposed method could obtain superior solutions in terms of convergence speed,robustness and accuracy.

Key words: Kriging model, partial least squares kernel function, partial least squares expected improvement criterion, probability of feasibility, efficient global optimization method

摘要： 针对昂贵约束优化问题中因超参数过多引发的维数灾难及优化效率不高问题,提出一种新的偏最小二乘Kriging模型辅助的高效全局优化方法。该方法通过偏最小二乘核函数提升Kriging模型建模效率,构建两种偏最小二乘权期望填充准则实现模型的自适应调整及高效全局优化。测试函数及工程实例结果表明,所提方法可有效减少超参数计算量,提升昂贵约束优化问题求解效率。尤其在高维问题中,所提方法在解的收敛速度,稳健性及精度方面均具有优势。

关键词: Kriging模型, 偏最小二乘核函数, 偏最小二乘期望改进准则, 可行性概率, 高效全局优化方法