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Table 3 Performance comparison of various algorithms for the 3D HP Protein Folding Problem. Comparison of the solution quality obtained in 3D by the hydrophobic zipper (HZ) algorithm [23], the constraint-based hydrophobic core construction method (CHCC) [26], the core-directed chain growth algorithm (CG) [25], the contact interactions (CI) algorithm [24], the pruned-enriched Rosenbluth method (PERM) and ACO-HPPFP-3. For CI, only the best energies obtained are shown. For HZ, CHCC and CG, the reported CPU times are taken from [25]; these are the expected times for finding optimal solutions on a Sparc 1 workstation. In the case of HZ, the reported CPU times are based on an extrapolation from the measured times required for finding suboptimal conformations with the energy values listed here. The CPU times for PERM and ACO-HPPFP-3 were determined on our reference 2.4 GHz Pentium IV machine based on 50 – 100 runs per instance. The energy values shown in bold face correspond to currently best known solution qualities.

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

ID E HZ CHCC CG CI PERM t1 PERM t2 PERM t exp ACO
S2-1 -32 -31(4 hrs) -32 (30 min) -32 (9.4 min) -32 -32 (0.1 min) -32 (0.5 min) -32 (0.2 min) -32 (30 min)
S2-2 -34 -32 (18 hrs) -34 (2.3 min) -34 (35 min) -33 -34 (0.3 min) -34 (48 min) -34 (0.6 min) -34 (420 min)
S2-3 -34 -31 (23 hrs) -34 (30 min) -34 (62 min) -32 -34 (0.1 min) -34 (4 days) -34 (0.2 min) -34 (120 min)
S2-4 -33 -30 (19 days) -33 (71 min) -33 (29 min) -32 -33 (2 min) -33 (4 min) -33 (3 min) -33 (300 min)
S2-5 -32 -30 (1.3 days) -32 (32 min) -32 (12 min) -32 -32 (0.5 min) -32 (19 min) -32 (1 min) -32 (15 min)
S2-6 -32 -29 (2.1 days) -32 (80 min) -32 (460 min) -30 -32 (0.5 min) -32 (0.1 min) -32 (0.2 min) -32 (720 min)
S2-7 -32 -29 (2.5 days) -32 (110 min) -32 (64 min) -30 -32 (0.5 min) -32 (2 days) -32 (1 min) -32 (720 min)
S2-8 -31 -29 (4 hrs) -31 (530 min) -31 (38 min) -30 -31 (0.3 min) -31 (8 min) -31 (0.6 min) -31 (120 min)
S2-9 -34 -31(4.5 hrs) -34 (8.3 min) -33 -32 -34 (5 min) -34 (10 min) -34 (7 min) -34 (450 min)
S2-10 -33 -33 (1.1 hr) -33 (4.8 min) -33(1.1 min) -32 -33 (0.01 min) -33 (0.01 min) -33 (0.01 min) -33 (60 min)