(one-operator absorbing states) have nonzero probability. Consequently, only the final
probabilities for the uniform population states are displayed in Figures 5-7 through 5-16,
with each such state indexed by the decimal integer value corresponding to the solution
represented.
Table 5-5 summarizes the Cray Y-MP computer resources expended in generating
these data. Tabulated there are the number of vector multiplications (of dimension N')
required to attain the termination condition and the CPU time utilized. The CPU time is
in seconds, rounded to the nearest integer. The tabulated data are collected from the log
files generated in the computer runs which produced the stationary distribution data for
Figures 5-7 through 5-16.
The limiting distribution entropy results in Figures 5-17 and 5-18 are computed
from the converged stationary distributions. The results are recorded in bits and are
plotted as a function of population size.
A very significant result suggested by the limiting stationary distribution data is that
the a -> 0' value of the stationary distribution is nonzero for all possible uniform states.
This behavior, which is confirmed by theoretical results developed in Section 7, pre-
cludes extrapolation of the simulated annealing global optimality convergence result onto
the genetic algorithm. However, as suggested by the data plotted in Figures 5-17 and
5-18, it may be possible to approach the desired limiting behavior as closely as required
by adjusting the population size parameter. Those figures indicate that for sufficiently
large values of the population size parameter, the limiting distribution is dominated by
optimal solutions, and that the limiting distribution entropy decreases monotonically with
increasing population size. Results developed in Section 9 reinforce this premise.