ID

E*

${\text{PERM}}_{{t}_{exp}}$

REMC_{
pm
}

REMC_{
m
}


Z4

3

3 (< 1 sec)

3 (< 1 sec)

3 (< 1 sec)

Z8

7

7 (< 1 sec)

7 (< 1 sec)

7 (< 1 sec)

Z12

11

11 (< 1 sec)

11 (< 1 sec)

11 (< 1 sec)

Z16

15

15 (3 sec)

15 (< 1 sec)

15 (< 1 sec)

Z20

19

19 (51 min)

19 (< 1 sec)

19 (< 1 sec)

Z24

23

23 (49 hrs†)

23 (< 1 sec)

23 (< 1 sec)

Z28

27

26

27 (< 1 sec)

27 (< 1 sec)

Z32

31

29

31 (< 1 sec)

31 (< 1 sec)

Z36

35

31

35 (1 sec)

35 (< 1 sec)

Z40

39

34

39 (2 sec)

39 (1 sec)

 The Zstructures proposed in [51] are easy for REMC to fold when compared with PERM. After Z24, PERM is unable to find the unique optimal conformation in any of the 100 independent runs conducted. When only one folding direction of PERM finds the optimal conformation, we report the mean runtime of that direction, denoting this in the table with a †. When best energies found by ${\text{PERM}}_{{t}_{1}}$ and ${\text{PERM}}_{{t}_{2}}$ differed (and neither find the optimal solution), the best energy by either is reported and the runtime is omitted. For every instance, 100 independent runs were conducted of 1 CPU hour each. In cases where not every run reached the same energy value after 1 hour, the expected runtime to reach the energy value shown in the table was calculated using the equation detailed by Parkes and Walser [54].