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Despite intensive studies during the last 30 years researchers are yet far from the "holy grail" of blind structure prediction of the three dimensional native state of a protein from its sequence of amino acids. We introduce here a Multimeme Algorithm which is robust across a range of protein structure models and instances. New benchmark sequences for the triangular lattice in the HP model and Functional Model Proteins in two and three dimensions are included here with their known optima. As there is no favourite protein model nor exact energy potentials to describe proteins, robustness accross a range of models must be present in any putative structure prediction algorithm. We demonstrate in this paper that while our algorithm present this feature it remains, in terms of cost, competitive with other techniques.