which the asterisks indicate "don't care" bits. The bit locations at which the schema is
specified are the defining locations of the schema. The order of the schema, designated
by o(H), is the number of its defining locations and can range from 0 to L. In this exam-
ple, o(H) = 2. The defining length of the schema, designated 8(H), is the number of bit
positions subtended by its outermost defining bit locations minus 1. In this example,
6(H)= 5 -2 = 3.
For a bit-string space of length L, there are exactly 3L distinct schemata. This can be
readily determined by noting that the distinct schemata are selected from {0, 1,*}L. A
given string selected from the space represents exactly 2L distinct schemata. This results
from the fact that the string is defined at all L bit positions, and hence is selected from
{0, 1} The schemata of an optimization problem's search space are the building blocks
from which good solutions are to be constructed.
3.3.2 Schema Processing and the Fundamental Theorem
Let the constant population size of a simple genetic algorithm be designated M.
Then, each generation produced by the algorithm represents some number, N, of distinct
schemata that is bounded as follows
2L< N