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For the purposes of this section, assume that the fields in every
profile are identically ordered. The exact order is not important, as
long as it is the same in all profiles. So, for example, in every
profile, the newsgroup field is the first, the keyword field second,
and so on.
Let 
and 
be the parent profiles:
The crossover operator takes two parents and produces two offsprings.
Each offspring inherits some attributes from one parent and the rest
from the other. A two-point crossover is used by the crossover
operator. Two points are randomly selected in the list of fields. All
the fields lying between the two points are exchanged between the two
parents to create two new offsprings. Since the fields in both the
parents are in the same order, each offspring will have one field of
each kind. The fitness of the offsprings is set to a default initial
value. Formally:
Equation 
defines the crossover operation, where parents
and produce offsprings
and 
.
The two crossover points are generated as shown in equation ,
where the random number function gives an integer in range specified by the
two parameters inclusive (the index of the first field is 0). If the offspring
profiles are as defined in equation ,
each field is derived as shown in equations
and .
The fitness of the offspring profile is set to its default value, as in equation
.
