*Given a random algorithm, does varying non-zero probabilities of
accepting an uphill move work better than never taking an uphill
move?*

Here, in some sense, we are comparing hillclimbing and simulated annealing. To answer this question we use the same 50% lateral move probability, and 40 million hillclimbing attempts followed by a minimization step.

Figures 4.2 through 4.4 show us
the answer is `not necessarily'. For example, hillclimbing (**rldhc**)
without minimization was significantly different than **sa1/m** and
**sigmet1/m** in every dataset: Hillclimbing can beat some simulated
annealing schedules. Furthermore, we cannot say our best ranked
simulated annealing schedule was statistically different than these
hillclimbing results. In fact, in the Fall 1998 dataset -- the only
dataset where the mean rank order (Figure 4.4) did
not match the average score sorted order (Figure 4.7)
-- the **rldhc** average score was the lowest.

Sometimes, with a good annealing schedule, we can escape local minimal
traps that catch hillclimbers, and arrive closer to the global optimal
solution, though how close we cannot say. As we see in the next
section, accepting lateral moves is essential to finding a good
solution in our domain. With a sufficient number of attempts, random
lateral descent hillclimbing (**rldhc**) produced results comparable to
simulated annealing.