Triangula uses a modified genetic algorithm which I wrote about on the wiki here [1]. The reason I didn't use simulated annealing is because I ran some tests and found it was generally less effective for my case.
Do you have a specific initialization scheme? The example gif goes very fast but it seems to find very fit individuals in the first generation which seems too good to be random.
Actually, the initialization is completely random. The reason why it might seem too optimal is because the algorithm chooses the colors most similar to the image when rendering the triangles.
[1] https://github.com/RH12503/Triangula/wiki/Explanation-of-the...