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On efficient global optimization via universal Kriging surrogate models

机译：通过通用Kriging代理模型的高效全局优化

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摘要

In this paper, we investigate the capability of the universal Kriging (UK) model for single-objective global optimization applied within an efficient global optimization (EGO) framework. We implemented this combined UK-EGO framework and studied four variants of the UK methods, that is, a UK with a first-order polynomial, a UK with a second-order polynomial, a blind Kriging (BK) implementation from the ooDACE toolbox, and a polynomial-chaos Kriging (PCK) implementation. The UK-EGO framework with automatic trend function selection derived from the BK and PCK models works by building a UK surrogate model and then performing optimizations via expected improvement criteria on the Kriging model with the lowest leave-one-out cross-validation error. Next, we studied and compared the UK-EGO variants and standard EGO using five synthetic test functions and one aerodynamic problem. Our results show that the proper choice for the trend function through automatic feature selection can improve the optimization performance of UK-EGO relative to EGO. From our results, we found that PCK-EGO was the best variant, as it had more robust performance as compared to the rest of the UK-EGO schemes; however, total-order expansion should be used to generate the candidate trend function set for high-dimensional problems. Note that, for some test functions, the UK with predetermined polynomial trend functions performed better than that of BK and PCK, indicating that the use of automatic trend function selection does not always lead to the best quality solutions. We also found that although some variants of UK are not as globally accurate as the ordinary Kriging (OK), they can still identify better-optimized solutions due to the addition of the trend function, which helps the optimizer locate the global optimum.
机译：在本文中，我们研究了在高效的全球优化（EGO）框架内应用的单目标全球优化的通用Kriging（英国）模型的能力。我们实施了这一联合的英国 - 自我框架，并研究了英国方法的四种变种，即英国，一个具有二阶多项式的一阶多项式，英国，来自OODACE工具箱的盲克里格汀（BK）实现，和多项式 - 混沌克里格（PCK）实施。来自BK和PCK模型的自动趋势功能选择的UK-EGO-EGO框架通过构建英国代理模型，然后通过Kriging模型上的预期改进标准进行优化，具有最低的休假交叉验证错误。接下来，我们使用五个合成试验功能和一个空气动力学问题进行了研究和比较了英国 - 自我变体和标准自我。 Our results show that the proper choice for the trend function through automatic feature selection can improve the optimization performance of UK-EGO relative to EGO.从我们的结果中，我们发现PCK-EGO是最好的变种，因为它与英国的其余部分相比具有更强大的性能;但是，总阶扩展应用于生成用于高维问题的候选趋势功能。注意，对于某些测试功能，具有预定多项式趋势函数的英国比BK和PCK更好地执行，表明使用自动趋势功能选择并不总是导致最佳质量解决方案。我们还发现，虽然英国的某些变体并不像普通的Kriging（OK）那样全球准确，但由于添加了趋势函数，它们仍然可以识别更好的优化解决方案，这有助于优化器定位全局最佳。

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