Table 2.

Performance comparison of various algorithms for the 2D HP Protein Folding Problem. Comparison of the solution quality obtained in 2D by the evolutionary algorithm of Unger and Moult (EA) [14], the evolutionary Monte Carlo algorithm of Liang and Wong (EMC) [19], the multi-self-overlap ensemble algorithm of Chickenji et al. (MSOE) [17], the pruned-enriched Rosenbluth method (PERM) and ACO-HPPFP-3. For EA and EMC, the reported energy values are the lowest among five independent runs, and the values in parentheses are the numbers of valid conformations scanned before the lowest energy values were found. Missing entries indicate cases where the respective method has not been tested on a given instance. The CPU times reported in parentheses for MSOE have been determined on a 500 MHz CPU, and those for PERM and ACO-HPPFP-3 are based on 100 – 200 runs per instance on our reference 2.4 GHz Pentium IV machine. The energy values shown in bold face correspond to currently best known solution qualities.

ID	E	GA	EMC	MSOE	PERM t1	PERM t2	PERM texp	ACO
S1-1	-9	-9 (30 492)	-9 (9 374)		-9 (< 1 sec)	-9 (< 1 sec)	-9 (< 1 sec)	-9 (< 1 sec)
S1-2	-9	-9 (30 491)	-9 (6 929)		-9 (< 1 sec)	-9 (< 1 sec)	-9 (< 1 sec)	-9 (< 1 sec)
S1-3	-8	-8 (20 400)	-8 (7 202)		-8 (6 sec)	-8 (< 1 sec)	-8 (2 sec)	-8 (< 1 sec)
S1-4	-14	-14 (301 339)	-14 (12 447)		-14 (< 1 sec)	-14 (< 1 sec)	-14 (< 1 sec)	-14 (4 sec)
S1-5	-23	-23 (126 547)	-23 (165 791)		-23 (3 min)	-23 (< 1 sec)	-23 (2 sec)	-23 (1 min)
S1-6	-21	-21 (592 887)	-21 (74 613)		-21 (3 sec)	-21 (3 sec)	-21 (3 sec)	-21 (15 sec)
S1-7	-36	-34 (208 781)	-35 (203 729)		-36 (7 sec)	-36 (3 sec)	-36 (4 sec)	-36 (20 min)
S1-8	-42	-37 (187 393)	-39 (564 809)	-39	-42 (78 hrs)	-42 (78 hrs)	-42 (78 hrs)	-42 (1.5 hrs)
S1-9	-53		-52 (44 029)		-53 (64 sec)	-53 (60 sec)	-53 (1 min)	-53 (20% of runs 1 days)
S1-10	-50			-50 (50 hrs)	-50 (50% of runs 1 hrs)	-50 (20 min)	-50	-49 (12 hrs)
S1-11	-48			-47	-48 (9 min)	-48 (7 min)	-48 (8 min)	-47 (10 hrs)