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When applying optimization method to a real-world problem, the possession ofprior knowledge and preliminary analysis on the landscape of a globaloptimization problem can give us an insight into the complexity of the problem.This knowledge can better inform us in deciding what optimization method shouldbe used to tackle the problem. However, this analysis becomes problematic whenthe dimensionality of the problem is high. This paper presents a framework totake a deeper look at the global optimization problem to be tackled: byanalyzing the low-dimensional representation of the problem through discoveringthe active subspaces of the given problem. The virtue of this is that theproblem's complexity can be visualized in a one or two-dimensional plot, thusallow one to get a better grip about the problem's difficulty. One could thenhave a better idea regarding the complexity of their problem to determine thechoice of global optimizer or what surrogate-model type to be used.Furthermore, we also demonstrate how the active subspaces can be used toperform design exploration and analysis.

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