Which algorithm to choose for 2D packing?

Question

Mathematics

Hello. Please help me choose an algorithm for this case of two-dimensional packing:
There are rectangular objects that need to be placed in a polygonal area. An example of such an area (shaded in the picture):

I want to use this algorithm to solve the subproblem of three-dimensional packing of a container (in layers). Help me please.

Answer 1

Read the forum and success story here:
https://www.kaggle.com/c/packing-santas-sleigh

Answer 2

Google "backpacking problem"

Answer 3

Google "bin packing problem" or "Bin packing problem".
https://en.wikipedia.org/wiki/Bin_packing_problem
I was looking for a solution for my problems, here are some links.
Not a bad implementation of the BPP solution in Excel.
Directly in Excel, you can set all the parameters (number and sizes of boxes and elements) and get a ready-made solution and even a visualization of the result.
verolog.deis.unibo.it/bpp-spreadsheet-solver
Article on Habré, description of algorithms, there is an example of implementation.
https://habrahabr.ru/post/136225/
Most of all I was approached by the solutions of this author.
The best combination is runtime/result.
clb.demon.fi/projects/rectangle-bin-packing
clb.demon.fi/projects/more-rectangle-bin-packing
clb.demon.fi/projects/even-more-rectangle-bin-packing
Implementation:
https://github.com/juj/RectangleBinPack
I used the last ones, reworking them to fit my needs.
I came to such that I use several algorithms at once,
changing them during execution, and randomly changing the parameters for selecting elements for packing.