Optimizing expensive black-box systems with limited data is an extremely challenging problem. As a resolution, we present a new surrogate optimization approach by addressing two gaps in prior research -- unimportant input variables and inefficient treatment of uncertainty associated with the black-box output. We first design a new flexible non-interpolating parsimonious surrogate model using a partitioning-based multivariate adaptive regression splines approach, Tree Knot MARS (TK-MARS). The proposed model is specifically designed for optimization by capturing the structure of the function, bending at near-optimal locations, and is capable of screening unimportant input variables. Furthermore, we develop a novel replication approach called Smart-Replication, to overcome the uncertainty associated with the black-box output. The Smart-Replication approach identifies promising input points to replicate and avoids unnecessary evaluations of other data points. Smart-Replication is agnostic to the choice of a surrogate and can adapt itself to an unknown noise level. Finally to demonstrate the effectiveness of our proposed approaches we consider different complex global optimization test functions from the surrogate optimization literature. The results indicate that TK-MARS outperforms original MARS within a surrogate optimization algorithm and successfully detects important variables. The results also show that although non-interpolating surrogates can mitigate uncertainty, replication is still beneficial for optimizing highly complex black-box functions. The robustness and the quality of the final optimum solution found through Smart-Replication are competitive with that using no replications in environments with low levels of noise and using a fixed number of replications in highly noisy environments.
翻译:优化昂贵且数据有限的黑匣子系统是一个极具挑战性的问题。作为一个解决方案,我们提出了一种新的替代优化方法,解决了先前研究中的两个缺口 -- -- 与黑盒输出相关的不重要的投入变量和对不确定性的处理效率低下。我们首先设计了一个新的灵活的、非内插的、有讽刺色彩的代谢模型,使用基于分区的多变适应性回归样条法,Tree Knot MARS(TK-MARS) 。拟议模型是专门为优化而设计的,其方法是捕捉功能结构,在接近最佳的地点弯曲,并能够筛选非重要的投入变量变量变量。此外,我们开发了名为“智能复制”的新型复制方法,以克服与黑盒输出相关的不确定性。“智能复制”方法确定了有希望的输入点,以便复制和避免对其他数据点进行不必要的评估。“智能复制”是用来选择一个隐蔽器,并且能够适应一个未知的噪音水平。最后复制方法的实效是,我们考虑从化黑盒优化文献文献中的不同复杂的全球优化测试功能。此外,我们开发了一个叫做智能复制的“智能复制”的复制功能的复制方法,其结果显示,通过高额和高额的升级的变压的变压的变压,它能能是用来在高的压式的。