Exploiting Active Subspaces in Global Optimization: How Complex is your Problem?

When applying optimization method to a real-world problem, the possession of prior knowledge and preliminary analysis on the landscape of a global optimization problem can give us an insight into the complexity of the problem. This knowledge can better inform us in deciding what optimization method should be used to tackle the problem. However, this analysis becomes problematic when the dimensionality of the problem is high. This paper presents a framework to take a deeper look at the global optimization problem to be tackled: by analyzing the low-dimensional representation of the problem through discovering the active subspaces of the given problem. The virtue of this is that the problem's complexity can be visualized in a one or two-dimensional plot, thus allow one to get a better grip about the problem's difficulty. One could then have a better idea regarding the complexity of their problem to determine the choice of global optimizer or what surrogate-model type to be used. Furthermore, we also demonstrate how the active subspaces can be used to perform design exploration and analysis.