Illustration and comparison of difficult structures for PERM and ACO-HPPFP-3 in 2D. Left side: Lowest energy conformation of a biological sequence (B50-7, 45 amino acids, energy -17) that is harder for PERM (t1 = 271, t2 = 299, t
= 284 CPU seconds) than for ACO-HPPFP-3 (t
= 130 CPU seconds; cut-off time 1 CPU hour). Right side: Lowest energy conformation of a biological sequence (B50-5, 53 amino acids, energy -22) that is much harder for ACO-HPPFP-3 than for PERM; within a cut-off time of 1 CPU hour, both ACO-HPPFP-3 and PERM reached this energy in 10 out of 10 runs in t
= 820 and t1 = 5, t2 = 118, t
= 9 CPU seconds on average, respectively.