<s>
In	O
computer	B-General_Concept
programming	I-General_Concept
,	O
gene	B-Algorithm
expression	I-Algorithm
programming	I-Algorithm
(	O
GEP	O
)	O
is	O
an	O
evolutionary	B-Algorithm
algorithm	I-Algorithm
that	O
creates	O
computer	O
programs	O
or	O
models	O
.	O
</s>
<s>
These	O
computer	O
programs	O
are	O
complex	O
tree	B-Data_Structure
structures	I-Data_Structure
that	O
learn	O
and	O
adapt	O
by	O
changing	O
their	O
sizes	O
,	O
shapes	O
,	O
and	O
composition	O
,	O
much	O
like	O
a	O
living	O
organism	O
.	O
</s>
<s>
Evolutionary	B-Algorithm
algorithms	I-Algorithm
use	O
populations	O
of	O
individuals	O
,	O
select	O
individuals	O
according	O
to	O
fitness	O
,	O
and	O
introduce	O
genetic	O
variation	O
using	O
one	O
or	O
more	O
genetic	O
operators	O
.	O
</s>
<s>
But	O
it	O
was	O
with	O
the	O
introduction	O
of	O
evolution	B-Algorithm
strategies	I-Algorithm
by	O
Rechenberg	O
in	O
1965	O
that	O
evolutionary	B-Algorithm
algorithms	I-Algorithm
gained	O
popularity	O
.	O
</s>
<s>
A	O
good	O
overview	O
text	O
on	O
evolutionary	B-Algorithm
algorithms	I-Algorithm
is	O
the	O
book	O
"	O
An	O
Introduction	O
to	O
Genetic	B-Algorithm
Algorithms	I-Algorithm
"	O
by	O
Mitchell	O
(	O
1996	O
)	O
.	O
</s>
<s>
Gene	B-Algorithm
expression	I-Algorithm
programming	I-Algorithm
belongs	O
to	O
the	O
family	O
of	O
evolutionary	B-Algorithm
algorithms	I-Algorithm
and	O
is	O
closely	O
related	O
to	O
genetic	B-Algorithm
algorithms	I-Algorithm
and	O
genetic	B-Algorithm
programming	I-Algorithm
.	O
</s>
<s>
From	O
genetic	B-Algorithm
algorithms	I-Algorithm
it	O
inherited	O
the	O
linear	O
chromosomes	O
of	O
fixed	O
length	O
;	O
and	O
from	O
genetic	B-Algorithm
programming	I-Algorithm
it	O
inherited	O
the	O
expressive	O
parse	O
trees	O
of	O
varied	O
sizes	O
and	O
shapes	O
.	O
</s>
<s>
In	O
gene	B-Algorithm
expression	I-Algorithm
programming	I-Algorithm
the	O
linear	O
chromosomes	O
work	O
as	O
the	O
genotype	O
and	O
the	O
parse	O
trees	O
as	O
the	O
phenotype	O
,	O
creating	O
a	O
genotype/phenotype	O
system	O
.	O
</s>
<s>
Because	O
these	O
parse	O
trees	O
are	O
the	O
result	O
of	O
gene	O
expression	O
,	O
in	O
GEP	O
they	O
are	O
called	O
expression	B-Algorithm
trees	I-Algorithm
.	O
</s>
<s>
The	O
genome	O
of	O
gene	B-Algorithm
expression	I-Algorithm
programming	I-Algorithm
consists	O
of	O
a	O
linear	O
,	O
symbolic	O
string	O
or	O
chromosome	O
of	O
fixed	O
length	O
composed	O
of	O
one	O
or	O
more	O
genes	O
of	O
equal	O
size	O
.	O
</s>
<s>
These	O
genes	O
,	O
despite	O
their	O
fixed	O
length	O
,	O
code	O
for	O
expression	B-Algorithm
trees	I-Algorithm
of	O
different	O
sizes	O
and	O
shapes	O
.	O
</s>
<s>
where	O
“	O
L	O
”	O
represents	O
the	O
natural	O
logarithm	O
function	O
and	O
“	O
a	O
”	O
,	O
“	O
b	O
”	O
,	O
“	O
c	B-Language
”	O
,	O
and	O
“	O
d	O
”	O
represent	O
the	O
variables	O
and	O
constants	O
used	O
in	O
a	O
problem	O
.	O
</s>
<s>
As	O
shown	O
above	O
,	O
the	O
genes	O
of	O
gene	B-Algorithm
expression	I-Algorithm
programming	I-Algorithm
have	O
all	O
the	O
same	O
size	O
.	O
</s>
<s>
However	O
,	O
these	O
fixed	O
length	O
strings	O
code	O
for	O
expression	B-Algorithm
trees	I-Algorithm
of	O
different	O
sizes	O
.	O
</s>
<s>
can	O
also	O
be	O
represented	O
as	O
an	O
expression	B-Algorithm
tree	I-Algorithm
:	O
</s>
<s>
This	O
kind	O
of	O
expression	B-Algorithm
tree	I-Algorithm
consists	O
of	O
the	O
phenotypic	O
expression	O
of	O
GEP	O
genes	O
,	O
whereas	O
the	O
genes	O
are	O
linear	O
strings	O
encoding	O
these	O
complex	O
structures	O
.	O
</s>
<s>
which	O
is	O
the	O
straightforward	O
reading	O
of	O
the	O
expression	B-Algorithm
tree	I-Algorithm
from	O
top	O
to	O
bottom	O
and	O
from	O
left	O
to	O
right	O
.	O
</s>
<s>
Going	O
from	O
k-expressions	O
to	O
expression	B-Algorithm
trees	I-Algorithm
is	O
also	O
very	O
simple	O
.	O
</s>
<s>
The	O
k-expressions	O
of	O
gene	B-Algorithm
expression	I-Algorithm
programming	I-Algorithm
correspond	O
to	O
the	O
region	O
of	O
genes	O
that	O
gets	O
expressed	O
.	O
</s>
<s>
The	O
genes	O
of	O
gene	B-Algorithm
expression	I-Algorithm
programming	I-Algorithm
are	O
therefore	O
composed	O
of	O
two	O
different	O
domains	O
–	O
a	O
head	O
and	O
a	O
tail	O
–	O
each	O
with	O
different	O
properties	O
and	O
functions	O
.	O
</s>
<s>
It	O
encodes	O
the	O
expression	B-Algorithm
tree	I-Algorithm
:	O
</s>
<s>
It	O
's	O
not	O
hard	O
to	O
see	O
that	O
,	O
despite	O
their	O
fixed	O
length	O
,	O
each	O
gene	O
has	O
the	O
potential	O
to	O
code	O
for	O
expression	B-Algorithm
trees	I-Algorithm
of	O
different	O
sizes	O
and	O
shapes	O
,	O
with	O
the	O
simplest	O
composed	O
of	O
only	O
one	O
node	O
(	O
when	O
the	O
first	O
element	O
of	O
a	O
gene	O
is	O
a	O
terminal	O
)	O
and	O
the	O
largest	O
composed	O
of	O
as	O
many	O
nodes	O
as	O
there	O
are	O
elements	O
in	O
the	O
gene	O
(	O
when	O
all	O
the	O
elements	O
in	O
the	O
head	O
are	O
functions	O
with	O
maximum	O
arity	O
)	O
.	O
</s>
<s>
The	O
chromosomes	O
of	O
gene	B-Algorithm
expression	I-Algorithm
programming	I-Algorithm
are	O
usually	O
composed	O
of	O
more	O
than	O
one	O
gene	O
of	O
equal	O
length	O
.	O
</s>
<s>
Some	O
examples	O
of	O
more	O
complex	O
linkers	O
include	O
taking	O
the	O
average	O
,	O
the	O
median	O
,	O
the	O
midrange	O
,	O
thresholding	O
their	O
sum	O
to	O
make	O
a	O
binomial	O
classification	B-General_Concept
,	O
applying	O
the	O
sigmoid	O
function	O
to	O
compute	O
a	O
probability	O
,	O
and	O
so	O
on	O
.	O
</s>
<s>
These	O
linking	O
functions	O
are	O
usually	O
chosen	O
a	O
priori	O
for	O
each	O
problem	O
,	O
but	O
they	O
can	O
also	O
be	O
evolved	O
elegantly	O
and	O
efficiently	O
by	O
the	O
cellular	O
system	O
of	O
gene	B-Algorithm
expression	I-Algorithm
programming	I-Algorithm
.	O
</s>
<s>
In	O
gene	B-Algorithm
expression	I-Algorithm
programming	I-Algorithm
,	O
homeotic	O
genes	O
control	O
the	O
interactions	O
of	O
the	O
different	O
sub-ETs	O
or	O
modules	O
of	O
the	O
main	O
program	O
.	O
</s>
<s>
However	O
,	O
gene	B-Algorithm
expression	I-Algorithm
programming	I-Algorithm
also	O
explores	O
other	O
chromosomal	O
organizations	O
that	O
are	O
more	O
complex	O
than	O
the	O
head/tail	O
structure	O
.	O
</s>
<s>
For	O
instance	O
,	O
these	O
numerical	O
constants	O
may	O
be	O
the	O
weights	O
or	O
factors	O
in	O
a	O
function	O
approximation	O
problem	O
(	O
see	O
the	O
GEP-RNC	O
algorithm	O
below	O
)	O
;	O
they	O
may	O
be	O
the	O
weights	O
and	O
thresholds	O
of	O
a	O
neural	B-Architecture
network	I-Architecture
(	O
see	O
the	O
GEP-NN	O
algorithm	O
below	O
)	O
;	O
the	O
numerical	O
constants	O
needed	O
for	O
the	O
design	O
of	O
decision	B-Algorithm
trees	I-Algorithm
(	O
see	O
the	O
GEP-DT	O
algorithm	O
below	O
)	O
;	O
the	O
weights	O
needed	O
for	O
polynomial	O
induction	O
;	O
or	O
the	O
random	O
numerical	O
constants	O
used	O
to	O
discover	O
the	O
parameter	O
values	O
in	O
a	O
parameter	O
optimization	O
task	O
.	O
</s>
<s>
Like	O
all	O
evolutionary	B-Algorithm
algorithms	I-Algorithm
,	O
gene	B-Algorithm
expression	I-Algorithm
programming	I-Algorithm
works	O
with	O
populations	O
of	O
individuals	O
,	O
which	O
in	O
this	O
case	O
are	O
computer	O
programs	O
.	O
</s>
<s>
In	O
the	O
genotype/phenotype	O
system	O
of	O
gene	B-Algorithm
expression	I-Algorithm
programming	I-Algorithm
,	O
it	O
is	O
only	O
necessary	O
to	O
create	O
the	O
simple	O
linear	O
chromosomes	O
of	O
the	O
individuals	O
without	O
worrying	O
about	O
the	O
structural	O
soundness	O
of	O
the	O
programs	O
they	O
code	O
for	O
,	O
as	O
their	O
expression	O
always	O
results	O
in	O
syntactically	O
correct	O
programs	O
.	O
</s>
<s>
The	O
first	O
type	O
of	O
problem	O
goes	O
by	O
the	O
name	O
of	O
regression	O
;	O
the	O
second	O
is	O
known	O
as	O
classification	B-General_Concept
,	O
with	O
logistic	O
regression	O
as	O
a	O
special	O
case	O
where	O
,	O
besides	O
the	O
crisp	O
classifications	O
like	O
"	O
Yes	O
"	O
or	O
"	O
No	O
"	O
,	O
a	O
probability	O
is	O
also	O
attached	O
to	O
each	O
outcome	O
;	O
and	O
the	O
last	O
one	O
is	O
related	O
to	O
Boolean	O
algebra	O
and	O
logic	O
synthesis	O
.	O
</s>
<s>
Such	O
functions	O
include	O
the	O
mean	B-Algorithm
squared	I-Algorithm
error	I-Algorithm
,	O
root	B-General_Concept
mean	I-General_Concept
squared	I-General_Concept
error	I-General_Concept
,	O
mean	B-General_Concept
absolute	I-General_Concept
error	I-General_Concept
,	O
relative	O
squared	O
error	O
,	O
root	O
relative	O
squared	O
error	O
,	O
relative	O
absolute	O
error	O
,	O
and	O
others	O
.	O
</s>
<s>
The	O
design	O
of	O
fitness	O
functions	O
for	O
classification	B-General_Concept
and	O
logistic	O
regression	O
takes	O
advantage	O
of	O
three	O
different	O
characteristics	O
of	O
classification	B-General_Concept
models	O
.	O
</s>
<s>
In	O
a	O
binary	O
classification	B-General_Concept
task	O
,	O
correct	O
classifications	O
can	O
be	O
00	O
or	O
11	O
.	O
</s>
<s>
The	O
counts	O
of	O
TP	O
,	O
TN	O
,	O
FP	O
,	O
and	O
FN	O
are	O
usually	O
kept	O
on	O
a	O
table	O
known	O
as	O
the	O
confusion	B-General_Concept
matrix	I-General_Concept
.	O
</s>
<s>
+	O
Confusion	B-General_Concept
matrix	I-General_Concept
for	O
a	O
binomial	O
classification	B-General_Concept
task	O
.	O
</s>
<s>
Some	O
popular	O
fitness	O
functions	O
based	O
on	O
the	O
confusion	B-General_Concept
matrix	I-General_Concept
include	O
sensitivity/specificity	O
,	O
recall/precision	O
,	O
F-measure	B-General_Concept
,	O
Jaccard	O
similarity	O
,	O
Matthews	B-General_Concept
correlation	I-General_Concept
coefficient	I-General_Concept
,	O
and	O
cost/gain	O
matrix	O
which	O
combines	O
the	O
costs	O
and	O
gains	O
assigned	O
to	O
the	O
4	O
different	O
types	O
of	O
classifications	O
.	O
</s>
<s>
These	O
functions	O
based	O
on	O
the	O
confusion	B-General_Concept
matrix	I-General_Concept
are	O
quite	O
sophisticated	O
and	O
are	O
adequate	O
to	O
solve	O
most	O
problems	O
efficiently	O
.	O
</s>
<s>
But	O
there	O
is	O
another	O
dimension	O
to	O
classification	B-General_Concept
models	O
which	O
is	O
key	O
to	O
exploring	O
more	O
efficiently	O
the	O
solution	O
space	O
and	O
therefore	O
results	O
in	O
the	O
discovery	O
of	O
better	O
classifiers	B-General_Concept
.	O
</s>
<s>
This	O
new	O
dimension	O
involves	O
exploring	O
the	O
structure	O
of	O
the	O
model	O
itself	O
,	O
which	O
includes	O
not	O
only	O
the	O
domain	O
and	O
range	O
,	O
but	O
also	O
the	O
distribution	O
of	O
the	O
model	O
output	O
and	O
the	O
classifier	B-General_Concept
margin	O
.	O
</s>
<s>
By	O
exploring	O
this	O
other	O
dimension	O
of	O
classification	B-General_Concept
models	O
and	O
then	O
combining	O
the	O
information	O
about	O
the	O
model	O
with	O
the	O
confusion	B-General_Concept
matrix	I-General_Concept
,	O
it	O
is	O
possible	O
to	O
design	O
very	O
sophisticated	O
fitness	O
functions	O
that	O
allow	O
the	O
smooth	O
exploration	O
of	O
the	O
solution	O
space	O
.	O
</s>
<s>
For	O
instance	O
,	O
one	O
can	O
combine	O
some	O
measure	O
based	O
on	O
the	O
confusion	B-General_Concept
matrix	I-General_Concept
with	O
the	O
mean	B-Algorithm
squared	I-Algorithm
error	I-Algorithm
evaluated	O
between	O
the	O
raw	O
model	O
outputs	O
and	O
the	O
actual	O
values	O
.	O
</s>
<s>
Or	O
combine	O
the	O
F-measure	B-General_Concept
with	O
the	O
R-square	O
evaluated	O
for	O
the	O
raw	O
model	O
output	O
and	O
the	O
target	O
;	O
or	O
the	O
cost/gain	O
matrix	O
with	O
the	O
correlation	O
coefficient	O
,	O
and	O
so	O
on	O
.	O
</s>
<s>
More	O
exotic	O
fitness	O
functions	O
that	O
explore	O
model	O
granularity	O
include	O
the	O
area	O
under	O
the	O
ROC	B-Algorithm
curve	I-Algorithm
and	O
rank	O
measure	O
.	O
</s>
<s>
Also	O
related	O
to	O
this	O
new	O
dimension	O
of	O
classification	B-General_Concept
models	O
,	O
is	O
the	O
idea	O
of	O
assigning	O
probabilities	O
to	O
the	O
model	O
output	O
,	O
which	O
is	O
what	O
is	O
done	O
in	O
logistic	O
regression	O
.	O
</s>
<s>
Then	O
it	O
is	O
also	O
possible	O
to	O
use	O
these	O
probabilities	O
and	O
evaluate	O
the	O
mean	B-Algorithm
squared	I-Algorithm
error	I-Algorithm
(	O
or	O
some	O
other	O
similar	O
measure	O
)	O
between	O
the	O
probabilities	O
and	O
the	O
actual	O
values	O
,	O
then	O
combine	O
this	O
with	O
the	O
confusion	B-General_Concept
matrix	I-General_Concept
to	O
create	O
very	O
efficient	O
fitness	O
functions	O
for	O
logistic	O
regression	O
.	O
</s>
<s>
Popular	O
examples	O
of	O
fitness	O
functions	O
based	O
on	O
the	O
probabilities	O
include	O
maximum	O
likelihood	O
estimation	O
and	O
hinge	B-Algorithm
loss	I-Algorithm
.	O
</s>
<s>
In	O
logic	O
there	O
is	O
no	O
model	O
structure	O
(	O
as	O
defined	O
above	O
for	O
classification	B-General_Concept
and	O
logistic	O
regression	O
)	O
to	O
explore	O
:	O
the	O
domain	O
and	O
range	O
of	O
logical	O
functions	O
comprises	O
only	O
0	O
's	O
and	O
1	O
's	O
or	O
false	O
and	O
true	O
.	O
</s>
<s>
So	O
,	O
the	O
fitness	O
functions	O
available	O
for	O
Boolean	O
algebra	O
can	O
only	O
be	O
based	O
on	O
the	O
hits	O
or	O
on	O
the	O
confusion	B-General_Concept
matrix	I-General_Concept
as	O
explained	O
in	O
the	O
section	O
above	O
.	O
</s>
<s>
In	O
gene	B-Algorithm
expression	I-Algorithm
programming	I-Algorithm
mutation	O
is	O
the	O
most	O
important	O
genetic	O
operator	O
.	O
</s>
<s>
In	O
gene	B-Algorithm
expression	I-Algorithm
programming	I-Algorithm
mutation	O
is	O
totally	O
unconstrained	O
,	O
which	O
means	O
that	O
in	O
each	O
gene	O
domain	O
any	O
domain	O
symbol	O
can	O
be	O
replaced	O
by	O
another	O
.	O
</s>
<s>
In	O
gene	B-Algorithm
expression	I-Algorithm
programming	I-Algorithm
insertion	O
sequences	O
might	O
appear	O
anywhere	O
in	O
the	O
chromosome	O
,	O
but	O
they	O
are	O
only	O
inserted	O
in	O
the	O
heads	O
of	O
genes	O
.	O
</s>
<s>
So	O
,	O
in	O
gene	B-Algorithm
expression	I-Algorithm
programming	I-Algorithm
transposition	O
can	O
be	O
implemented	O
using	O
two	O
different	O
methods	O
:	O
the	O
first	O
creates	O
a	O
shift	O
at	O
the	O
insertion	O
site	O
,	O
followed	O
by	O
a	O
deletion	O
at	O
the	O
end	O
of	O
the	O
head	O
;	O
the	O
second	O
overwrites	O
the	O
local	O
sequence	O
at	O
the	O
target	O
site	O
and	O
therefore	O
is	O
easier	O
to	O
implement	O
.	O
</s>
<s>
In	O
gene	B-Algorithm
expression	I-Algorithm
programming	I-Algorithm
it	O
can	O
be	O
easily	O
implemented	O
in	O
all	O
gene	O
domains	O
and	O
,	O
in	O
all	O
cases	O
,	O
the	O
offspring	O
produced	O
is	O
always	O
syntactically	O
correct	O
.	O
</s>
<s>
Several	O
other	O
genetic	O
operators	O
exist	O
and	O
in	O
gene	B-Algorithm
expression	I-Algorithm
programming	I-Algorithm
,	O
with	O
its	O
different	O
genes	O
and	O
gene	O
domains	O
,	O
the	O
possibilities	O
are	O
endless	O
.	O
</s>
<s>
Numerical	O
constants	O
are	O
essential	O
elements	O
of	O
mathematical	O
and	O
statistical	O
models	O
and	O
therefore	O
it	O
is	O
important	O
to	O
allow	O
their	O
integration	O
in	O
the	O
models	O
designed	O
by	O
evolutionary	B-Algorithm
algorithms	I-Algorithm
.	O
</s>
<s>
Gene	B-Algorithm
expression	I-Algorithm
programming	I-Algorithm
solves	O
this	O
problem	O
very	O
elegantly	O
through	O
the	O
use	O
of	O
an	O
extra	O
gene	O
domain	O
–	O
the	O
Dc	O
–	O
for	O
handling	O
random	O
numerical	O
constants	O
(	O
RNC	O
)	O
.	O
</s>
<s>
'	O
s	O
in	O
the	O
expression	B-Algorithm
tree	I-Algorithm
are	O
replaced	O
from	O
left	O
to	O
right	O
and	O
from	O
top	O
to	O
bottom	O
by	O
the	O
symbols	O
(	O
for	O
simplicity	O
represented	O
by	O
numerals	O
)	O
in	O
the	O
Dc	O
,	O
giving	O
:	O
</s>
<s>
the	O
expression	B-Algorithm
tree	I-Algorithm
above	O
gives	O
:	O
</s>
<s>
This	O
elegant	O
structure	O
for	O
handling	O
random	O
numerical	O
constants	O
is	O
at	O
the	O
heart	O
of	O
different	O
GEP	O
systems	O
,	O
such	O
as	O
GEP	O
neural	B-Architecture
networks	I-Architecture
and	O
GEP	O
decision	B-Algorithm
trees	I-Algorithm
.	O
</s>
<s>
An	O
artificial	B-Architecture
neural	I-Architecture
network	I-Architecture
(	O
ANN	O
or	O
NN	O
)	O
is	O
a	O
computational	O
device	O
that	O
consists	O
of	O
many	O
simple	O
connected	O
units	O
or	O
neurons	O
.	O
</s>
<s>
These	O
weights	O
are	O
the	O
primary	O
means	O
of	O
learning	O
in	O
neural	B-Architecture
networks	I-Architecture
and	O
a	O
learning	O
algorithm	O
is	O
usually	O
used	O
to	O
adjust	O
them	O
.	O
</s>
<s>
Structurally	O
,	O
a	O
neural	B-Architecture
network	I-Architecture
has	O
three	O
different	O
classes	O
of	O
units	O
:	O
input	O
units	O
,	O
hidden	O
units	O
,	O
and	O
output	O
units	O
.	O
</s>
<s>
In	O
summary	O
,	O
the	O
basic	O
components	O
of	O
a	O
neural	B-Architecture
network	I-Architecture
are	O
the	O
units	O
,	O
the	O
connections	O
between	O
the	O
units	O
,	O
the	O
weights	O
,	O
and	O
the	O
thresholds	O
.	O
</s>
<s>
So	O
,	O
in	O
order	O
to	O
fully	O
simulate	O
an	O
artificial	B-Architecture
neural	I-Architecture
network	I-Architecture
one	O
must	O
somehow	O
encode	O
these	O
components	O
in	O
a	O
linear	O
chromosome	O
and	O
then	O
be	O
able	O
to	O
express	O
them	O
in	O
a	O
meaningful	O
way	O
.	O
</s>
<s>
In	O
GEP	O
neural	B-Architecture
networks	I-Architecture
(	O
GEP-NN	O
or	O
GEP	O
nets	O
)	O
,	O
the	O
network	O
architecture	O
is	O
encoded	O
in	O
the	O
usual	O
structure	O
of	O
a	O
head/tail	O
domain	O
.	O
</s>
<s>
Besides	O
the	O
head	O
and	O
the	O
tail	O
,	O
these	O
neural	B-Architecture
network	I-Architecture
genes	O
contain	O
two	O
additional	O
domains	O
,	O
Dw	O
and	O
Dt	O
,	O
for	O
encoding	O
the	O
weights	O
and	O
thresholds	O
of	O
the	O
neural	B-Architecture
network	I-Architecture
.	O
</s>
<s>
The	O
Dt	O
comes	O
after	O
Dw	O
and	O
has	O
a	O
length	O
dt	O
equal	O
to	O
t	O
.	O
Both	O
domains	O
are	O
composed	O
of	O
symbols	O
representing	O
the	O
weights	O
and	O
thresholds	O
of	O
the	O
neural	B-Architecture
network	I-Architecture
.	O
</s>
<s>
For	O
example	O
,	O
below	O
is	O
shown	O
a	O
neural	B-Architecture
network	I-Architecture
with	O
two	O
input	O
units	O
(	O
i1	O
and	O
i2	O
)	O
,	O
two	O
hidden	O
units	O
(	O
h1	O
and	O
h2	O
)	O
,	O
and	O
one	O
output	O
unit	O
(	O
o1	O
)	O
.	O
</s>
<s>
This	O
representation	O
is	O
the	O
canonical	O
neural	B-Architecture
network	I-Architecture
representation	O
,	O
but	O
neural	B-Architecture
networks	I-Architecture
can	O
also	O
be	O
represented	O
by	O
a	O
tree	O
,	O
which	O
,	O
in	O
this	O
case	O
,	O
corresponds	O
to	O
:	O
</s>
<s>
As	O
a	O
more	O
concrete	O
example	O
,	O
below	O
is	O
shown	O
a	O
neural	B-Architecture
net	I-Architecture
gene	O
for	O
the	O
exclusive-or	O
problem	O
.	O
</s>
<s>
Its	O
expression	O
results	O
in	O
the	O
following	O
neural	B-Architecture
network	I-Architecture
:	O
</s>
<s>
So	O
,	O
GEP-nets	O
can	O
be	O
used	O
not	O
only	O
in	O
Boolean	O
problems	O
but	O
also	O
in	O
logistic	O
regression	O
,	O
classification	B-General_Concept
,	O
and	O
regression	O
.	O
</s>
<s>
Furthermore	O
,	O
multinomial	O
classification	B-General_Concept
problems	O
can	O
also	O
be	O
tackled	O
in	O
one	O
go	O
by	O
GEP-nets	O
both	O
with	O
multigenic	O
systems	O
and	O
multicellular	O
systems	O
.	O
</s>
<s>
Decision	B-Algorithm
trees	I-Algorithm
(	O
DT	O
)	O
are	O
classification	B-General_Concept
models	O
where	O
a	O
series	O
of	O
questions	O
and	O
answers	O
are	O
mapped	O
using	O
nodes	O
and	O
directed	O
edges	O
.	O
</s>
<s>
Decision	B-Algorithm
trees	I-Algorithm
have	O
three	O
types	O
of	O
nodes	O
:	O
a	O
root	O
node	O
,	O
internal	O
nodes	O
,	O
and	O
leaf	O
or	O
terminal	O
nodes	O
.	O
</s>
<s>
Most	O
decision	B-Algorithm
tree	I-Algorithm
induction	O
algorithms	O
involve	O
selecting	O
an	O
attribute	O
for	O
the	O
root	O
node	O
and	O
then	O
make	O
the	O
same	O
kind	O
of	O
informed	O
decision	O
about	O
all	O
the	O
nodes	O
in	O
a	O
tree	O
.	O
</s>
<s>
Decision	B-Algorithm
trees	I-Algorithm
can	O
also	O
be	O
created	O
by	O
gene	B-Algorithm
expression	I-Algorithm
programming	I-Algorithm
,	O
with	O
the	O
advantage	O
that	O
all	O
the	O
decisions	O
concerning	O
the	O
growth	O
of	O
the	O
tree	O
are	O
made	O
by	O
the	O
algorithm	O
itself	O
without	O
any	O
kind	O
of	O
human	O
input	O
.	O
</s>
<s>
There	O
are	O
basically	O
two	O
different	O
types	O
of	O
DT	O
algorithms	O
:	O
one	O
for	O
inducing	O
decision	B-Algorithm
trees	I-Algorithm
with	O
only	O
nominal	O
attributes	O
and	O
another	O
for	O
inducing	O
decision	B-Algorithm
trees	I-Algorithm
with	O
both	O
numeric	O
and	O
nominal	O
attributes	O
.	O
</s>
<s>
This	O
aspect	O
of	O
decision	B-Algorithm
tree	I-Algorithm
induction	O
also	O
carries	O
to	O
gene	B-Algorithm
expression	I-Algorithm
programming	I-Algorithm
and	O
there	O
are	O
two	O
GEP	O
algorithms	O
for	O
decision	B-Algorithm
tree	I-Algorithm
induction	O
:	O
the	O
evolvable	O
decision	B-Algorithm
trees	I-Algorithm
(	O
EDT	O
)	O
algorithm	O
for	O
dealing	O
exclusively	O
with	O
nominal	O
attributes	O
and	O
the	O
EDT-RNC	O
(	O
EDT	O
with	O
random	O
numerical	O
constants	O
)	O
for	O
handling	O
both	O
nominal	O
and	O
numeric	O
attributes	O
.	O
</s>
<s>
In	O
the	O
decision	B-Algorithm
trees	I-Algorithm
induced	O
by	O
gene	B-Algorithm
expression	I-Algorithm
programming	I-Algorithm
,	O
the	O
attributes	O
behave	O
as	O
function	O
nodes	O
in	O
the	O
basic	O
gene	O
expression	O
algorithm	O
,	O
whereas	O
the	O
class	O
labels	O
behave	O
as	O
terminals	O
.	O
</s>
<s>
Class	O
labels	O
behave	O
like	O
terminals	O
,	O
which	O
means	O
that	O
for	O
a	O
k-class	O
classification	B-General_Concept
task	O
,	O
a	O
terminal	O
set	O
with	O
k	O
terminals	O
is	O
used	O
,	O
representing	O
the	O
k	O
different	O
classes	O
.	O
</s>
<s>
The	O
rules	O
for	O
encoding	O
a	O
decision	B-Algorithm
tree	I-Algorithm
in	O
a	O
linear	O
genome	O
are	O
very	O
similar	O
to	O
the	O
rules	O
used	O
to	O
encode	O
mathematical	O
expressions	O
(	O
see	O
above	O
)	O
.	O
</s>
<s>
So	O
,	O
for	O
decision	B-Algorithm
tree	I-Algorithm
induction	O
the	O
genes	O
also	O
have	O
a	O
head	O
and	O
a	O
tail	O
,	O
with	O
the	O
head	O
containing	O
attributes	O
and	O
terminals	O
and	O
the	O
tail	O
containing	O
only	O
terminals	O
.	O
</s>
<s>
This	O
again	O
ensures	O
that	O
all	O
decision	B-Algorithm
trees	I-Algorithm
designed	O
by	O
GEP	O
are	O
always	O
valid	O
programs	O
.	O
</s>
<s>
For	O
example	O
,	O
consider	O
the	O
decision	B-Algorithm
tree	I-Algorithm
below	O
to	O
decide	O
whether	O
to	O
play	O
outside	O
:	O
</s>
<s>
The	O
process	O
of	O
decision	B-Algorithm
tree	I-Algorithm
induction	O
with	O
gene	B-Algorithm
expression	I-Algorithm
programming	I-Algorithm
starts	O
,	O
as	O
usual	O
,	O
with	O
an	O
initial	O
population	O
of	O
randomly	O
created	O
chromosomes	O
.	O
</s>
<s>
Then	O
the	O
chromosomes	O
are	O
expressed	O
as	O
decision	B-Algorithm
trees	I-Algorithm
and	O
their	O
fitness	O
evaluated	O
against	O
a	O
training	O
dataset	O
.	O
</s>
<s>
Decision	B-Algorithm
trees	I-Algorithm
with	O
both	O
nominal	O
and	O
numeric	O
attributes	O
are	O
also	O
easily	O
induced	O
with	O
gene	B-Algorithm
expression	I-Algorithm
programming	I-Algorithm
using	O
the	O
framework	O
described	O
above	O
for	O
dealing	O
with	O
random	O
numerical	O
constants	O
.	O
</s>
<s>
encodes	O
the	O
decision	B-Algorithm
tree	I-Algorithm
shown	O
below	O
:	O
</s>
<s>
These	O
random	O
numerical	O
constants	O
are	O
encoded	O
in	O
the	O
Dc	O
domain	O
and	O
their	O
expression	O
follows	O
a	O
very	O
simple	O
scheme	O
:	O
from	O
top	O
to	O
bottom	O
and	O
from	O
left	O
to	O
right	O
,	O
the	O
elements	O
in	O
Dc	O
are	O
assigned	O
one-by-one	O
to	O
the	O
elements	O
in	O
the	O
decision	B-Algorithm
tree	I-Algorithm
.	O
</s>
<s>
the	O
decision	B-Algorithm
tree	I-Algorithm
above	O
results	O
in	O
:	O
</s>
<s>
which	O
can	O
also	O
be	O
represented	O
more	O
colorfully	O
as	O
a	O
conventional	O
decision	B-Algorithm
tree	I-Algorithm
:	O
</s>
<s>
GEP	O
has	O
been	O
criticized	O
for	O
not	O
being	O
a	O
major	O
improvement	O
over	O
other	O
genetic	B-Algorithm
programming	I-Algorithm
techniques	O
.	O
</s>
<s>
GeneXproTools	O
GeneXproTools	O
is	O
a	O
predictive	B-General_Concept
analytics	I-General_Concept
suite	O
developed	O
by	O
Gepsoft	O
.	O
</s>
<s>
GeneXproTools	O
modeling	O
frameworks	O
include	O
logistic	O
regression	O
,	O
classification	B-General_Concept
,	O
regression	O
,	O
time	O
series	O
prediction	O
,	O
and	O
logic	O
synthesis	O
.	O
</s>
<s>
GEP4J	O
–	O
GEP	O
for	O
Java	B-Language
Project	O
Created	O
by	O
Jason	O
Thomas	O
,	O
GEP4J	O
is	O
an	O
open-source	O
implementation	O
of	O
gene	B-Algorithm
expression	I-Algorithm
programming	I-Algorithm
in	O
Java	B-Language
.	O
</s>
<s>
It	O
implements	O
different	O
GEP	O
algorithms	O
,	O
including	O
evolving	O
decision	B-Algorithm
trees	I-Algorithm
(	O
with	O
nominal	O
,	O
numeric	O
,	O
or	O
mixed	O
attributes	O
)	O
and	O
automatically	O
defined	O
functions	O
.	O
</s>
<s>
GEP4J	O
is	O
hosted	O
at	O
Google	B-Protocol
Code	I-Protocol
.	O
</s>
<s>
PyGEP	O
–	O
Gene	B-Algorithm
Expression	I-Algorithm
Programming	I-Algorithm
for	O
Python	B-Language
Created	O
by	O
Ryan	O
O'Neil	O
with	O
the	O
goal	O
to	O
create	O
a	O
simple	O
library	O
suitable	O
for	O
the	O
academic	O
study	O
of	O
gene	B-Algorithm
expression	I-Algorithm
programming	I-Algorithm
in	O
Python	B-Language
,	O
aiming	O
for	O
ease	O
of	O
use	O
and	O
rapid	O
implementation	O
.	O
</s>
<s>
PyGEP	O
is	O
hosted	O
at	O
Google	B-Protocol
Code	I-Protocol
.	O
</s>
<s>
jGEP	O
–	O
Java	B-Language
GEP	O
toolkit	O
Created	O
by	O
Matthew	O
Sottile	O
to	O
rapidly	O
build	O
Java	B-Language
prototype	O
codes	O
that	O
use	O
GEP	O
,	O
which	O
can	O
then	O
be	O
written	O
in	O
a	O
language	O
such	O
as	O
C	B-Language
or	O
Fortran	B-Application
for	O
real	O
speed	O
.	O
</s>
<s>
jGEP	O
is	O
hosted	O
at	O
SourceForge	B-Application
.	O
</s>
