SECTION 5
SOME EMPIRICAL RESULTS
5.1 Overview
This section reports the results of some computer simulations based upon the
genetic algorithm Markov chain model developed in Section 4. Their purpose is to help
fix some of the state space and asymptotic probability distribution ideas which are central
features of this work.
The results reported here are separated into four subsections. Section 5.2 concerns
enumeration of the state space, S'. Section 5.3 is devoted to generation of reward function
data, which are subsequently used in the two remaining subsections. Section 5.4 illus-
trates the behavior of some selected conditional probabilities as a function of the algo-
rithm control parameter, a. The results of the primary simulation task are reported in
Section 5.5. They concern computation of the three-operator stationary distribution at
extremely low (approaching zero) values of the mutation probability control parameter.
One of the significant theoretical results developed in subsequent sections is sug-
gested by the data presented in Section 5.5. It is that the zero mutation probability limit-
ing stationary distribution provides nonzero probability for all states corresponding to
uniform populations (i.e. one-operator absorbing states), including those which represent
suboptimal solutions. This result poses a complication for the attempt to extrapolate the
simulated annealing convergence theory onto the genetic algorithm, as discussed further
in section 5.5.
All simulation results included here were generated on the Cray Y-MP computer at
the Eglin AFB, Fl. Computer Science Directorate. The data presented in Section 5.5 con-
cerning the primary simulation task (the converged limiting stationary distribution