Real industrial studies often give rise to complex optimization problems involving mixed variables and time consuming simulators. To deal with these difficulties we propose the use of a Gaussian process regression surrogate with a suitable kernel able to capture simultaneously the output correlations with respect to continuous and categorical/discrete inputs without relaxation of the categorical variables. The surrogate is integrated into the Efficient Global Optimization method based on the maximization of the Expected Improvement criterion. This maximization is a Mixed Integer Non-Linear problem which is solved by means of an adequate optimizer: the Mesh Adaptive Direct Search, integrated into the NOMAD library. We introduce a random exploration of the categorical space with a data-based probability distribution and we illustrate the full strategy accuracy on a toy problem. Finally we compare our approach with other optimizers on a benchmark of functions.

实际的工业研究通常会引起复杂的优化问题，其中涉及混合变量和耗时的模拟器。为了解决这些困难，我们建议使用具有合适内核的高斯过程回归代理，该内核能够同时捕获关于连续和分类/离散输入的输出相关性，而无需放松分类变量。替代基于预期改进标准的最大化被集成到高效全局优化方法中。这种最大化是一个混合整数非线性问题，它可以通过适当的优化器来解决：将网格自适应直接搜索集成到NOMAD库中。我们介绍了基于数据的概率分布对分类空间的随机探索，并说明了玩具问题的完整策略准确性。最后，我们在功能基准上将我们的方法与其他优化器进行了比较。