What is the technical name that describes this research approach?

Is there a term that best describes a research scenario in which you have tremendous variability among independent variables and instead of choosing very specific independent variables to test, you more or less test random combinations or variables until you discover significant correlation? For example, in testing the effectiveness of the design of a web page on whether or not people make purchases, there are a wide range of possible variations in color, text, layout, etc.

You could thoughtfully recombine 1000’s of these elements to see what works best, or you could have software automate the random presentation while testing click through and purchases, etc.

I’m familiar with the terms “trial and error” and “shotgun” but is there a statistical model/theory/paradigm/whatever that says something like…

Whenever there is X degree of variability or imprecision among independent variables or the interaction between independent and dependent variables, then a “trial and error/shotgun/fishing expedition” approach is advisable.

Am I making sense?