Information Technology Reference
In-Depth Information
3.1.1 Creation of the Initial Population
The chromosomes of the individuals of the initial population are randomly
generated using the symbols representing the functions and terminals thought
appropriate to solve the problem at hand. These initial individuals are the
first set of candidate solutions to the problem at hand. Because they are to-
tally random and not yet toughened up by the environment, these founder
individuals are almost always not very good solutions. Notwithstanding, they
are everything that is necessary to get things started, as evolution takes care
of the rest and, soon enough, very good solutions will start to appear in the
population. Let us illustrate this with a concrete example.
Suppose, for instance, that we wanted to know how to express the Boolean
Majority(
a
,
b
,
c
) function in terms of ANDs, ORs, and NOTs. In this case, the
choice of the function set is not problematic and consists of F = {A, O, N},
representing, respectively, the Boolean functions AND, OR, and NOT. The
choice of the terminal set is also simple and consists of T = {a, b, c},
representing the three arguments to the majority function. Therefore, for this
problem, the heads of the genes will be randomly generated using six differ-
ent symbols {A, O, N, a, b, c}, whereas the tails will be randomly generated
using a smaller alphabet of just three symbols {a, b, c}.
The truth table for the majority function is shown in Table 3.1. For this
problem, the complete set of transition states is used as the selection envi-
ronment. So, the fitness of each candidate solution will be evaluated against
this set of fitness cases (also called training set, as it is used to evaluate the
performance during the adaptive process). A good fitness function for this
simple problem is also not very difficult to design and will correspond to the
number of fitness cases correctly evaluated by a particular individual.
Table 3.1
Majority function.
abc
y
000 0
001 0
010 0
011 1
100 0
101 1
110 1
111 1
