"The amount of PET required to deliver bottled beverages depends on numerous design and manufacturing factors (e.g., bottle capacity, the shape and texture associated with the brand, the oxidation rate of the contents, many parameters of the manufacturing technique). Because so many factors are involved, the mechanical design of plastic bottles is still, largely, a trial and error process18. No closed-form expression for the relationship between bottle weight and design attributes exists to our knowledge (most relevant academic studies rely on numerical methods). Thus, we opted for an empirical approach to quantify this relationship."
I'm sorry, what? There is absolutely no need to be doing this empirically. Apparently they could fill libraries with the gaps of what exists "to [their] knowledge." In fact, they do. They're called libraries.
The actual citation [18] they make states, "The problem is that the process continues to rely to some extent on trial and error." Not "largely" trial and error.
"The process" referring to the process of converting closed-form optimized solutions (they do exist! it's actually the entire purpose of that citation) into something that can be made consistently with blow molding. That entire reference is about the challenges of modeling blow molding, not packaging design, and how much progress there's been over the last 30 years in taking closed-form solutions from the drawing board to the manufacturing floor.
And the most efficient current designs were between 0.5 and 2.9L? Oh, so basically every PET plastic bottle? Real groundbreaking stuff, guys.