Cutting stock optimization

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algorithm

Hi all,
I am dealing with cutting stock problem with a twist.
I have pieces to cut in a beam of fixed length, but the pieces have angle cuts, with many angles.

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I am using a First Fit Decreasing which work fine.
I am already rotating pieces to nest angles.

Now, I am on the problem of reordering pieces to minimize waste between pieces. Can have up to 50 pieces in a single beam, but usually 10-20 pieces.

What I have tried:

Tried nothing yet, just started to think about the problem.

How would you proceed ? What would be your algorithm ?

[Update]
I have been working on the problem all WE.
So my problem is at column generation level. Since I use FFD heuristic, I have partial columns and I need to know if I can add another piece to the column.
The difficulty is that the position and orientation of each pieces matters.
My approach so far is more geometric:
- I consider that each piece is a chain.
- I get the 2 chains with the largest angle and replace them with a new bigger chain by putting the 2 largest angles back to back. The resulting chain is put back in the pool of chains.
I repeat until there is 1 last chain in pool.
Still some cases that don't work as expected, but look promising.