IEEE Computational Intelligence Magazine - August 2021 - 73

unit number also needs to be modified. The pseudo-codes of
the crossover operator are described in Algorithm 4. A number
is randomly generated to determine whether to perform the
crossover operator or not. If it is determined to perform the
crossover operator, the binary competition strategy is used to
select parents firstly, then two crossover points are randomly
generated for the parents. Finally, the offspring are generated by
the crossover operator.
F. Self-Adaptive Mechanism Strategy Based on Blocks
The mutation operator usually explores the search space to
obtain individuals with promising performance. The proposed
algorithm uses three types of mutation methods, i.e.,
adding, removing, and replacing. Adding refers to adding a
unit at the selected location of the individual, removing
refers to removing the current unit at the designated location
of the individual, and replacing refers to randomly replacing
a new type of unit with a new one at the selected location of
the individual.
The self-adaptive mechanism has been widely used in the
evolutionary computation community [24], [34]. In this
paper, a self-adaptive mutation strategy pool with three candidate
offspring generation strategies (COGSs) is proposed. This
mechanism enables the algorithm to adaptively find mutation
operators that are more suitable for the current task. Thus it
can determine a more suitable generation strategy to match
the evolution process at different stages.
The self-adaptive mutation operator mechanism is described
as follows: First, each COGS has an initial probability /,N1 s
where Ns
represents the number of COGS in the strategy
pool. Let Pq represent the probability of the qth strategy being
selected (q = 1, 2,..., Ns). Next, the roulette strategy is used to
select a COGS. Through this strategy, a new individual is generated,
and it is compared with its parent. The result is recorded
in the initial zero matrix nsflag ,is
and nfflag ,is
and nfflag ,is
s = 1, 2,..., Ns) where N represents the number of individuals
in the population. After a generation, the sums of each column
of nsflag ,is
records the number of successes of the qth strategy in the kth
generation, and F records the number of failures of qth strategy
in the kth generation. After a generation, both nsflag
and nsflagNN, s are reset.
NN, s
After Ng generations, the total number of successes and failures
of all COGSs is calculated, and the probability of each
COGS is updated as follows:
Ng
SS,kq
k=1
1 /q =
S = ) 1
m ,
2
q
Sq
if S1
,
q = 0
otherwise
(1)
(2)
where q represents the strategy in the qth strategy pool, and m is
set to 0.0001 to prevent the probability of some strategies from
becoming 0. Next, the generation probability of a new COGS
is calculated using the following formulas:
SS SF,
Nq
PS S
=
q qq
q
=
where Sq
3
33
1
/
(4)
represents the new probability of the qth COGS
after the update. In addition, this probability needs to be normalized
by Equation (4). The above equations are used to
update the probability of each COGS according to the performance
of the offspring. Obviously, the better the performance
of a COGS, the higher the probability that it will be selected
during the entire evolutionary process.
In Algorithm 5, the implementation of the self-adaptive
mutation strategy is shown in details. First, three operations
are added to the strategy pool (line 1). Then, a random
number is generated to determine whether to perform
mutation operations. If a mutation occurs, a block operation
is selected to generate new offspring. The information
of generating offspring is used to update the probability
of the COGS. Finally, the mutated offspring population
is output.
(i= 1, 2,..., N,
are calculated, and they are
recorded in two new matrices S ,kq and F ,kq (k= 1,..., Ng,
q = 1,..., Ns, where Ng represents the updated period). S
Algorithm 4 Crossover operator of SaMuNet.
Input: Two parents p1, p2, the crossover probability m.
Output: Two offspring q1, q2.
1: Randomly generate a number v in range of [0,1];
2: if v < m then
3:
4:
5:
6:
G. Environmental Selection Based on Semi-Complete
Binary Competition
In the environmental selection stage, suitable individuals need to
be selected from the population to serve as the next generation
population. The simplest way to accomplish this is to select the
individual with the highest fitness value from the population
each time, but this will cause the population to lose diversity
and fall into a local optimum [48], [49].
For NAS applications, researchers have proposed many
selection strategies. Real et al. [50] used aging evolution to
32 2eo/
Ng
qq q=+ kq
k=1
(3)
Select two parents p1, p2 from Pt by binary tournament
selection;
Randomly generate two integer numbers to separate p1,
p2 into two parts, respectively;
Combine the first part of p1 and the second part of p2;
Combine the first part of p2 and the second part of p1;
7: else
8:
9:
q1 ! p1;
q2 ! p2;
10: end if
11: Output two offspring q1, q2;
AUGUST 2021 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE 73
IEEE Computational Intelligence Magazine - August 2021

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