The Solvay Kitaev algorithm was discovered long before the Group Leaders Optimization algorithm and it has some nice theoretical properties. As far as I understand, both have exactly the same goals: given a finite dimensional unitary operator, they decompose the operator into basic quantum gates. I couldn't find any theoretical results about the time complexity or convergence time or error bounds for the GLOA as such. Does the latter (GLOA) have any practical advantage over the former at all, in terms of convergence time or anything?
P.S: For a detailed description of the GLOA, see: Understanding the Group Leaders Optimization Algorithm