We consider the optimization of a computer model where each simulation either fails or returns a valid output performance. We first propose a new joint Gaussian process model for classification of the inputs (computation failure or success) and for regression of the performance function. We provide results that allow for a computationally efficient maximum likelihood estimation of the covariance parameters, with a stochastic approximation of the likelihood gradient. We then extend the classical improvement criterion to our setting of joint classification and regression. We provide an efficient computation procedure for the extended criterion and its gradient. We prove the almost sure convergence of the global optimization algorithm following from this extended criterion. We also study the practical performances of this algorithm, both on simulated data and on a real computer model in the context of automotive fan design.

我们考虑对计算机模型的优化，其中每个模拟都会失败或返回有效的输出性能。我们首先提出一个新的联合高斯过程模型，用于输入的分类（计算失败或成功）以及性能函数的回归。我们提供的结果允许对协方差参数进行计算有效的最大似然估计，并采用似然梯度的随机近似。然后，我们将经典改进标准扩展到联合分类和回归的设置。我们为扩展的标准及其梯度提供了一种有效的计算程序。根据这一扩展准则，我们证明了全局优化算法的几乎确定的收敛性。我们还研究了该算法的实际性能，