Table 1.
2D and 3D HP standard benchmark instances. Benchmark instances for the 2D and 3D HP Protein Folding Problem used in this study with optimal or best known energy values E*. Most instances for 2D and 3D HP can also be found in [44]; Sequence S1-9 (2D) is taken from [45], and the last two instances (2D) are from [21]. Hi and Pi indicate a string of i consecutive H's and P's, respectively; likewise, (s)i indicates an i-fold repetition of string s.
| ID | Length | E* | Protein Sequence |
| 2D HP | |||
| S1-1 | 20 | -9 | (HP)2PH2PHP2HPH2P2HPH |
| S1-2 | 24 | -9 | H2(P2H)7H |
| S1-3 | 25 | -8 | P2HP2(H2P4)3H2 |
| S1-4 | 36 | -14 | P3H2P2H2P5H7P2H2P4H2P2HP2 |
| S1-5 | 48 | -23 | P2H(P2H2)2P5H10P6(H2P2)2HP2H5 |
| S1-6 | 50 | -21 | H2(PH)3PH4PH(P3H)2P4H(P3H)2PHPH4(HP)3H2 |
| S1-7 | 60 | -36 | P2H3PH8P3H10PHP3H12P4H6PH2PHP |
| S1-8 | 64 | -42 | H12(PH)2(P2H2)2P2HP2H2PPH2P2HP2(H2P2)2(HP)2H12 |
| S1-9 | 85 | -53 | H4P4H12P6(H12P3)3HP2(H2P2)2HPH |
| S1-10 | 100 | -50 | P3H2P2H4P2H3(PH2)2PH4P8H6P2H6P9HPH2PH11P2H3PH2PHP2HPH3P6H3 |
| S1-11 | 100 | -48 | P6HPH2P5H3PH5PH2P4H2P2H2PH5PH10PH2PH7p11H7P2HPH3P6HPH2 |
| 3D HP | |||
| S2-1 | 48 | -32 | HPH2P2H4PH3P2H2P2HPH2PHPH2P2H2P3HP8H2 |
| S2-2 | 48 | -34 | H4PH2PH5P2HP2H2P2HP6HP2HP3HP2H2P2H3PH |
| S2-3 | 48 | -34 | PHPH2PH6P2HPHP2HPH2(PH)2P3H(P2H2)2P2HPHP2HP |
| S2-4 | 48 | -33 | PHPH2P2HPH3P2H2PH2P3H5P2HPH2(PH)2P4HP2(HP)2 |
| S2-5 | 48 | -32 | P2HP3HPH4P2H4PH2PH3P2(HP)2HP2HP6H2PH2PH |
| S2-6 | 48 | -32 | H3P3H2PH(PH2)3PHP7HPHP2HP3HP2H6PH |
| S2-7 | 48 | -32 | PHP4HPH3PHPH4PH2PH2P3HPHP3H3(P2H2)2P3H |
| S2-8 | 48 | -31 | PH2PH3PH4P2H3P6HPH2P2H2PHP3H2(PH)2PH2P3 |
| S2-9 | 48 | -34 | (PH)2P4(HP)2HP2HPH6P2H3PHP2HPH2P2HPH3P4H |
| S2-10 | 48 | -33 | PH2P6H2P3H3PHP2HPH2(P2H)2P2H2P2H7P2H2 |