Next: 3 Experimental Investigation
Up: 2 Regression Problems and
Previous: 2 Regression Problems and
Contents
To better understand the distribution of fitness values that a
selection method is presented with, and the ability of the population
to represent solutions for each problem instance, we use the measure of
entropy based on fitness, described in detail in Chapter 4.
Again, the entropy measure represents the chaos of the system with
respect to the distribution of fitness values amongst the
population [Rosca, 1995a].
An increase in entropy reflects the system (population's fitness
values) moving into a state of more chaos (more different fitness
values). This measure also gives us a sense of how the fitness values are
distributed over the fitness classes, from a uniform distribution
over all fitness classes to the other extreme of the entire
population belonging to only one fitness class.
Measuring the genetic diversity of populations is difficult, as there
are many aspects of tree shapes and contents that could be measured.
In this study, a measure is used based on the edit distance between
two trees, introduced and used in Chapter 4 as edit distance One,
and in Chapter 5 as the nonweighted edit distance.
This measure is used to understand how structurally similar populations become and
to give
insight into the search process.
Figure 6.1:
The Binomial3 problem and the generated polynomial functions of degree 3 (upper right), 7 (bottom left) and 11 (bottom right). The inset for degree 7 and 11 shows the same xrange and smaller yrange between [0.005:0.005], where it is relatively easy for genetic programming to find a close fit, but difficult to finetune the approximation.

Next: 3 Experimental Investigation
Up: 2 Regression Problems and
Previous: 2 Regression Problems and
Contents
S Gustafson
20040520