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The evolutionary process of GA begins with initialization of the population.
Then GA embarks on reproduction to generate new candidate solutions: First,
the selection operator picks two chromosomes from the population to serve as
parents. The two parents carry out the crossover operator to produce their off-
spring, where the crossover rate defines the probability to perform crossover.
Afterward, mutation is performed with a probability, i.e., mutation rate, on the
offspring to slightly change some genes. The above reproduction process repeats
until the set of offspring is filled. Following “Survival of the Fittest,” the survivor
operator picks the fittest chromosomes out of the offspring population with (or
without) the primitive population to survive and constitute the population for
the next generation.
Design of GA for a given problem concerns representation, fitness function,
selection, crossover, and mutation operators. The following describes our design
of GA for generation of paintings.
3.1 Representation
A chromosome in the GA represents multiple agents to generate images. For-
mally, a chromosome
I
is represented by
I
=(
k,
(
ind
H
,ind
S
,ind
B
)
,a
1
,...,a
k
)
,
where
k
is the number of agents, (
ind
H
,ind
S
,ind
B
) indicates the
background color, and
a
1
,...,a
k
are painters.
The agents paint by assigning colors at some pixels. An agent can be defined
∈{
2
,...,
6
}
by
a
=(
sD,delay,
(
a
H
,a
S
,a
B
)
,a
dir
,life
)
,
where
sD
[0
,
0
.
5] determines
whether the agent paints this pixel or not, and
life
is the agent's moving time.
The terms (
a
H
,a
S
,a
B
)and
a
dir
is generated by a GP-tree, which indicates the
color to paint at the current pixel and the direction for the subsequent move.
In the beginning, each agent randomly generates a GP-tree. Then, agents
conduct the following actions at every time step:
∈{
0
,...,
8
}
denotes the starting direction,
delay
∈
1. Collect data from its local neighborhood as input.
An agent will collect data from its Moore neighborhood (see Fig 2). These
data, including eight directions and eight colors, are used to calculate the
following input variables:
-
(
H
c
,S
c
,B
c
): The hue (
H
), saturation (
S
), and brightness (
B
)valuesof
the pixel at the agent's current location
-
(
H
p
,S
p
,B
p
): The hue, saturation, and brightness values of the pixel at
the agent's previous location
-
(
H
mean
,S
mean
,B
mean
): The mean hue, saturation, and brightness values
of the agent's neighborhood
-
(
ind
H
,ind
S
,ind
B
): The chromosome's initial background color
-
d
p
: The agent's previous direction
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