The (Pre-)Neanderthals were the first, you see:
When optimizing in multi-dimensional parameter spaces, local maximums are not as much of a problem as being misguided by maximums that are constrained on a lower dimensional subspace. Therefore, so called ‘walk-in’ methods are necessary. They must explore all directions of the high dimensional space. Apart from such details, we are more interested in complexity as such in order to allow complex reactions and properties/behaviors in the first place (before optimizing), and to further research how proxy-measures of complexity compare to performance.
Long Title: "Galactic Random-Genocide from Quantum-Relativistic Plenitude Principled Multiversial Many-Minds Ethics under the Doctrine of Diversity or Donald Trump"
Alternative Title: The 1 CC = 50 FF or FFF Theorem or One Concealed Carry saves Fifty Feely Faggots in a parallel universe under Donaldo Trumpovich.
Higher dimensional spaces allow configurations that are unexpected from lower dimensions. For example, four-dimensional topology escapes full classification. Since complexity is related to dimensionality, there is a certain “magic” to it. Increasing complexity is advantageous generally for adaptation. We can give examples from nanotechnology. With catalysts, starting with mono-metallic ones, the desired catalytic prowess increases almost geometrically with the number of different substances involved. Bimetallic catalysts multiply the catalytic rate constants of mono metallic compounds.
The properties of nano-structures depend on sizes and shapes. The synthesis of tailored nano-structures is thus important already for researching properties, not to mention optimizations toward applications. The ability to control the size, shape, and distribution of nano-particles in larger structures provides opportunities to systematically investigate, for example, catalytic and electro-optical properties and to discover new applications, whether in form of novel research techniques or medical devices.