Why are global search algorithms not used in DoE? I'm reading about Design of Experiments via various textbooks (e.g. Montgomery's), and powerful global optimization methods (such as Ant Colony Optimization) are not used. They rely only on a basic sampling scheme in the search space; full factorial or otherwise, and then fit a linear model (perhaps with quadratic and interaction terms) of the experimental factors onto the response variable. Then they use that model to estimate optimal values for the inputs in order to maximize that response variable.
What is the purpose of limiting methods like this? Just deploying global search algorithms would result in a better optimization outcome.
EDIT:
I understand that optimization isn't the only (or main) purpose of DoE, but it's often part of the purpose. See for example chapter 11 of Montgomery's textbook titled Design and Analysis of Experiments, where optimization is the focus. I wanted to know why powerful search tools are not considered when optimization is a big part of the goal.

You refer chapter 11 of Montgomery's textbook, with the title "Response Surface Methods and Other Approaches to Process Optimization". So, interpreting your question as why response surface methods do not use global optimization methods.
Global optimization methods, as studied in optimization theory, is doing optimization on some known mathematical function. Implicitly, one is assuming that evaluation of function values at arbitrary points is cheap.
In contrast, Response Surface Methods tries to optimize some real-world system, often an industrial process. There is no known mathematical function representing the system, and "evaluation of values" is not cheap, it might imply running the process under non-standard conditions for some time (days? hours?), costs of changing process parameters, maybe even costs of destroyed or reduced production.
So this is very different from optimization of a known mathematical function, in reality, one is simultaneously trying to build a model of the system, and optimize it, under the restriction that evaluation is costly! That points to some analogy with active learning, see Motivations for experiment design in statistical learning?.
Another keyword is evolutionary operation  see Best DoE method to fit Gaussian Process Regressor
