IEEE Computational Intelligence Magazine - February 2020 - 82

The research community regularly opens monolingual
and multilingual competitions with topics going from
opinion mining to detect humor, emotion, or hatespeech in micro-blogging platforms, in monolingual and
multilingual datasets.
function, f, is randomly selected from F,
f \s arguments are randomly taken from
L without replacement. This process
continues until either all the elements of
L have been selected, or the population
size has been reached. In the former case,
the process is to add one element at a
time to P 0, choosing f ! F with the
difference that f \s arguments are randomly taken from P 0; this mechanism
continues until the population size is
reached. For example, let F = {+ , sin}
and L = {x 1, x 2, x 3} then P 0 s t a r t s
with {i 1 x 1, i 2 x 2}, this is followed by
selecting a function, assume + is selected,
P 0 is {i 1 x 1, i 2 x 2, i 3 x 1 + i 4 x 2}, assume
the next function selected is sin, consequently, P 0 = {i 1 x 1, i 2 x 2, i 3 x 1 + i 4 x 3,
i 5 sin (x 2)}. At this point all the inputs
have been selected so the process
continues by selecting the arguments
from P 0, suppose sin is selected and
i 3 x 1 + i 4 x 3 is its argument, this makes
P 0 = {i 1 x 1, i 2 x 2, i 3 x 1 + i 4 x 3, i 5 sin (x 2),
i 6 sin (i 3 x 1 + i 4 x 3)}. This process is
repeated until ; P 0 ; reaches the population size.
Once the initial population is created, P 0, the evolution starts. EvoDAG
uses a steady-state evolution, and, thus, it

In more detail, EvoDAG's search
space is as follows: let Fc 3 F be the
functions with cardinality c in the function set, and X i be the elements created at iteration i, starting from i = 0.
Using this notation, the first elements,
i.e., i = 0, are X 0 = {ix j ; x j ! L} ,
' c { f (x 1, f, x c ; i) ; x j ! L, f ! Fc }.
The rest of the elements are composed
recursively using X i = ' c { f (x 1, f,
x c ; i) ; x j ! X i - 1, f ! Fc}; consequently,
the search space is defined as X = ' i X i.
Using this notation, it is difficult to indicate
that in the case of a commutative operator it
is only included one of them, e.g., x i + x j is
included in the search space and x j + x i it is
not. The second restriction is that some
functions require unique arguments. A
function is decided to require unique arguments when f (a, b, b, d ) = if (a, b, d ) such
as: min, max, and addition, among others.
EvoDAG searches X using a similar
procedure than the one used to describe
it. It is not possible to test all the elements
at X i; instead, X i is sampled, storing the
elements in population P. The initial
population, P 0, contains {ix ; x ! L}, a
set of functions such as Nearest Centroid
Classifier, and other elements that are
selected using the following procedure. A

is not necessary to keep track of the
population through the generations,
therefore P = P 0. The procedure used
in the first generation is to create an element by selecting a function from F,
and its arguments are randomly selected
from P. The element created replaces
an element of P which is selected using
a negative tournament selection. From
the second generation to the end of the
run an element is created by first selecting f and its argument are selected using
tournament selection on P, the element created replaces an element selected, from P, with a negative tournament.
Traditionally in GP, the evolution stops
when the maximum number of generations is reached, or the fitness reaches a
particular value; however, EvoDAG uses
an early stopping approach. That is, the
training set is split into a smaller training
set, used to identify i and the fitness of
the individuals, and a validation set. Then,
the best element is the one with the best
performance on the validation set. The
evolution stops when the best individual
has not been updated in some evaluations,
4000 is the default.
EvoDAG function set is F = {R 60,
atan, NC 2, ; $ ;, hypot, max 5, min 5, P 20,
NB 5, MN 5, sin, , tan, tanh}. Let us
start by describing the addition which is
defined as f (x 1, f, x 60) = R i i i x i where
coefficients i are identified with ordinary least squares (OLS) using the training set. Functions such as min and
trigonometric functions are defined as
if (x i, f) where i is identified using
OLS. For classification problems, the

Max

Sin

Tanh

NaiveBayesMN

Fabs

Add

NaiveBayes

NaiveBayes

NaiveBayesMN

Hypot

Centroid

x1

FIGURE 3 An example of an evolved model by EvoDAG for the Arabic sentiment analysis task.

82

IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | FEBRUARY 2020

x2

Tanh

x0

Centroid
IEEE Computational Intelligence Magazine - February 2020

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