Figure 18 shows the progress of a SA search on the two-dimensional Rosenbrock function, . Although one would not ordinarily choose to use SA on a problem which is amenable to solution by more efficient methods, it is interesting to do so for purposes of comparison. Each of the solutions accepted in a 1000 trial search is shown (marked by symbols). The algorithm employed the adaptive step size selection scheme of equations (67) and (68). It is apparent that the search is wide-ranging but ultimately concentrates in the neighborhood of the optimum.
Figure 19 shows the progress in reducing the objective function for the same search. Initially, when the annealing temperature is high, some large increases in are accepted and some areas far from the optimum are explored. As execution continues and falls, fewer uphill excursions are tolerated (and those that are tolerated are of smaller magnitude). The last 40% of the run is spent searching around the optimum. This performance is typical of the SA algorithm.
The code used in this example is mo_sa.f. It uses the input data available in file mo_sa_in.dat. Both of these files may be viewed with an html browser.
To view copies of these files, click on their names here: mo_sa.f, mo_sa_in.dat)