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It seems that both relax and backrub do localiezd sampling using the Metropolis criterion. Could any one tell me the differences between them? Thank you very much!
Backrub is pretty complex. Have you read any of the papers on Backrub in Rosetta (look for Smith and Kortemme)?
Relax is much simpler: it is many iterations of gradient minimization plus repacking, with varying weights on the fa_rep term to allow the structure to push over mild clashes to better minima.