It’s a fun/NP-hard problem, this take on it ended up being useful: https://github.com/stephaniemhutson/BoxPackingAPI/blob/maste...

https://medium.com/the-chain/solving-the-box-selection-algor...

You are right there is a field of optimization dedicated to solving this problem to guaranteed optimality.

However, Multi dimensional bin packing problems are the some of the hardest non linear optimization problems.

Early in my generative art, I spent a lot of time packing various small shapes together, it was a fun process to figure out how to maximize the coverage without leaving large gaps. For example, a piece with almost every shape I was using: https://digcon.art/details.html?key=river-in-the-woods

Depends on the shape. Irregular shape packing and optimisation is still being advanced. Newer approaches are using ai. Lots of GitHub repositories with different approaches.

Or he wrote a constraint satisfaction resolver maybe

Communications theory is largely about how to pack circles/spheres efficiently in multiple dimensions. So arguably pretty much all of the modern society is based on efficient packing.

One I can think of is circles-in-circles where you are bundling wires or optical fibre cores into cables. (And probably for tensile cables used in bridges and so on)

Bin packing everywhere! Truck loading?

Minimizing maximum to minimum ratio for structural stability.