What kind of algorithm would solve this problem: shortest routing between 3D cubes

Question

I have these in 3D space:

1. Green points where blue routes begin
2. Black hole/sphere where all blue routes end ⚫
3. Red cubes that must not have any collision with blue routes
4. Blue routes beginning from green points, ending at black hole, and avoiding red cubes

I intend to:

• Compute the shortest total blue routes. The objective is the minimum total blue routes.
• Assume the red cubes are triangle meshes in 3D space.
• Share segments between the routes as much as possible. Since any share is counted only once.

I wonder what family of mathematical algorithms I'm looking for. It should be optimization. But I need more details to actually implement it. It would be great too if some repositories on GitHub are introduced. Any programming language is fine.