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Jun 3, 2014 at 18:12 comment added D.W. @fli, not really. If simulated annealing doesn't work, and neither SAT nor ILP work out well, I suppose you could look into tabu search -- though I don't really have any reason to expect it to work well, and it's more of a "well, I guess if you don't have any other idea what else to try..." sort of suggestion. Sorry I don't have better ideas for you. Trying an implementation before accepting this answer is definitely a good idea; that's the best way to find out whether it'll work or whether it's useless. Good luck!
Jun 3, 2014 at 12:14 comment added fli Thanks @D.W. I think I have a better understanding of my problem now. I would like to pick the spanning trees (so that there are a minimal amount of edges and every state will have the same amount of edges) such that the variance in the degree of all nodes is maximised. As I have a defined objective function, simulated annealing still looks like a good candidate for solving this, but with my better defined problem, is there anything else you would recommend to try? Nevertheless, I'm going to try an implementation before I accept this answer. Thanks!
Jun 3, 2014 at 6:04 history answered D.W. CC BY-SA 3.0