IEEE Computational Intelligence Magazine - August 2021 - 72

The method of population initialization is presented in
Algorithm 2. For each individual, we need to randomly generate
a positive integer k to determine the length of the individual
(i.e., the number of units that need to be initialized),
and then randomly generate a vector with length k. The vector
stores each unit that needs to be initialized. Then, the second
random number is used to determine whether to
generate RUs, DUs, or PUs. Note that, in line 7, the number
of PUs is limited. This is because the function of the pooling
layer is to halve the size of the input, and this operation is
widely used in many state-of-the-art CNNs [5], [10]-[12].
However, if an individual starts with the pooling layer, a lot of
information will be lost. In addition, if a 64 × 64 input image
passes through seven pooling layers continuously, the output
size will be 1 × 1; this operation will lead to logic errors and is
thus disallowed.
D. Evaluation of Individuals
The fitness value of each individual indicates the individual's
adaptivity to the environment. In the proposed algorithm, the
fitness value is the classification accuracy on the image datasets.
In EC, individuals with higher fitness values have a higher
probability of generating offspring with better performance
than themselves. In this paper, to obtain the fitness value, the
proposed algorithm decodes each individual into a CNN
architecture and trains it on the training set, then tests the
trained architecture on the validation set. In Algorithm 3, each
individual is decoded into a CNN architecture and its weights
are initialized, then the CNN will be trained until the iteration
reaches its maximum value. Finally, the trained CNN model
searched by the proposed algorithm is put on the validation
dataset to obtain the fitness value.
Algorithm 2 Initialize Population.
Input: The population size (N), the maximal PUs poolmax,
j = 0, i = 0.
Output: The initialized population P0.
1: P0 ! {};
2: while i < N do
3:
4:
5:
6:
7:
8:
9:
10:
11:
12:
13:
E. Crossover Operator
The offspring inherit the genes from the parents and are
expected to obtain a higher fitness than the parents. Therefore,
individuals with higher fitness values should be selected as parents.
In this paper, the binary competition strategy is used to
select parents [47]. This strategy first randomly selects two
individuals from the population, and then it chooses the fitter
of the two as a parent. The second parent is selected in the
same way.
After selecting the parents, the crossover operator which has
local ability is performed. To make each individual have better
flexibility, the fixed-length coding strategy is replaced by the
variable-length coding strategy. Because of the different lengths
of individuals, the traditional crossover operator is no longer
directly applicable. Yet, the crossover operator plays a key role in
the search process; a modified single point crossover operator is
used based on variable-length individuals. The specific operation
is shown in Figure 5.
It should be noted that the number of input channels at the
splicing place after the crossover needs to be adjusted, and the
Algorithm 3 Evaluation of the Individuals.
Input: The population Pt for fitness evaluation, training dataset
Dtrain, validation dataset Dvalid, i = 0.
Output: The fitness of the population.
1: for each individual in Pt do
2:
CNN;
3:
4:
5:
6:
7:
8:
Initialize the weights of CNN;
while i < epoch do
Train the CNN;
i ++ ;
end while
Evaluate the accuracy for the CNN on the Dvalid;
9: end for
10: Output the fitness values of the individuals in Pt;
Decode the encoded information to the architecture of
Randomly generate a positive number k to decide the
length of individual;
Initialize an array with the size of 1 k ;#
for j < k do
U ! Randomly choose one unit from {PU, RU, DU};
if The last unit of U is not PU and the number of PU
is less than poolmax then
U ! randomly choose one unit from {RU, DU};
end if
Put the information of U into the jth element of a;
end for
P0 ! P0 ∪ a;
ii ;1=+
14: end while
15: Output the initialized population P0;
72 IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | AUGUST 2021
Offspring 1:
Offspring 2:
RU DU PU RU RU DU PU RU
RU DU DU RU DU PU PU DU PU
FIGURE 5 The crossover operator based on variable-length encoding
strategy.
Parent 2:
RU DU DU PU RU DU PU RU
Parent 1:
RU DU PU RU DU PU PU DU PU
IEEE Computational Intelligence Magazine - August 2021

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