Skip to main content

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]. H i and P i indicate a string of i consecutive H's and P's, respectively; likewise, (s) i indicates an i-fold repetition of string s.

From: An ant colony optimisation algorithm for the 2D and 3D hydrophobic polar protein folding problem

ID Length E* Protein Sequence
2D HP
S1-1 20 -9 (HP) 2 PH 2 PHP 2 HPH 2 P 2 HPH
S1-2 24 -9 H2(P2H)7H
S1-3 25 -8 P2HP2(H2P4)3H2
S1-4 36 -14 P 3 H 2 P 2 H 2 P 5 H 7 P 2 H 2 P 4 H 2 P 2 HP 2
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 P 2 H 3 PH 8 P 3 H 10 PHP 3 H 12 P 4 H 6 PH 2 PHP
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 P 6 HPH 2 P 5 H 3 PH 5 PH 2 P 4 H 2 P 2 H 2 PH 5 PH 10 PH 2 PH 7 p 11 H 7 P 2 HPH 3 P 6 HPH 2
3D HP
S2-1 48 -32 HPH 2 P 2 H 4 PH 3 P 2 H 2 P 2 HPH 2 PHPH 2 P 2 H 2 P 3 HP 8 H 2
S2-2 48 -34 H 4 PH 2 PH 5 P 2 HP 2 H 2 P 2 HP 6 HP 2 HP 3 HP 2 H 2 P 2 H 3 PH
S2-3 48 -34 PHPH2PH6P2HPHP2HPH2(PH)2P3H(P2H2)2P2H P HP2HP
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