Next: Newt: An Implementation
Up: Genetic Algorithm
Previous: Mutation
As before, the population is a set of (profile, fitness) tuples. For
the present purposes, assume that the profiles in the population are
ordered in the decreasing order of their fitness. So let,
When a new generation of the population is created, the fit members of
the population are retained and the unfit ones are eliminated. Let
be the retention rate, namely the proportion of population
members that will be retained in the new generation. The vacancies are
proportional to (1 - ). Let 
be the crossover rate, namely
the proportion of vacancies filled in by crossovers. The remaining
vacancies are filled in by mutations. The new generation can then be
described as follows:
where
where 
is the size of population 
and 
and 
are random
numbers between 
and 
. The probability that (or )
being some number 
is proportional to 
i.e. the
fitness of 
.
Since the members added by mutation and crossover search for newer
kinds of information, the serendipity in the system is
proportional to the new members added every generation i.e.
proportional to 
. The stability of the system is
proportional to , which indicates the proportion of the population
that is stable across generations. These values can be appropriately
modified to better suit user preferences.