Data Mining (113 page)

Opposite mapping, from the binary code to the real value of the argument, is also unique:

and it will be used only for checking the intermediate results of optimization. For example, if we want to transform the value x = 11 into a binary string, the corresponding code will be 01011. On the other hand, code 11001 represents the decimal value x = 25.

13.3.2 Initial Population

The initialization process is very simple: We randomly create a population of chromosomes (binary codes) with the given length. Suppose that we decide that the parameter for the number of strings in the population is equal to four. Then one possible randomly selected population of chromosomes is

13.3.3 Evaluation

The evaluation function for binary vectors representing chromosomes is equivalent to the initial function f(x) where the given chromosome represents the binary code for the real value x. As noted earlier, the evaluation function plays the role of the environment, rating potential solutions in terms of their fitness. For our example, four chromosomes CR
₁
to CR
₄
correspond to values for input variable x:

Consequently, the evaluation function would rate them as follows:

The results of evaluating the chromosomes initially generated may be given in a tabular form, and they are represented in Table
13.2
. The expected reproduction column shows “the evaluated quality” of chromosomes in the initial population. Chromosomes CR
₂
and CR
₄
are more likely to be reproduced in the next generation than CR
₁
and CR
₃
.