In this paper we investigate the protein sequence design (PSD) problem (also known as the inverse protein folding problem) under the Canonical model 4 on 2D and 3D lattices [12, 25]. The Canonical model is specified by (i) a geometric representation of a target protein structure with amino acid residues via its contact graph, (ii) a binary folding code in which the amino acids are classified as hydrophobic (H) or polar (P), (iii) an energy function Φ defined in terms of the target structure that should favor sequences with a dense hydrophobic core and penalize those with many solvent-exposed hydrophobic residues (in the Canonical model, the energy function Φ gives an H-H residue contact in the contact graph a value of −1 and all other contacts a value of 0), and (iv) to prevent the solution from being a biologically meaningless all H sequence, the number of H residues in the sequence S is limited by fixing an upper bound λ on the ratio between H and P amino acids. The sequence...