IEEE Computational Intelligence Magazine - May 2023 - 85

The three-stage EA can effectively balance exploration
and exploitation by the environmental selection
process criteria based on the NTK and individual
lifespans.
Criterion ¼
KN
if 0 < G G1 or G2 < G Max gen
Lifespan if G1 < G G2
KN result. In addition, performing multiple
calculations ensures that the network
receives most input data rather
than a small part of the data, which
improves the generalization of the network
to the input data. In [37], KN
was combined with another indicator
calculated by normalization. In this
paper, only KN is applied to rank the
overall network architectures, as this
approach is simpler and thus accelerates
the search process.
D. Three-Stage EA Based on MultipleCriteria
Environmental Selection
To balance exploration and exploitation,
a three-stage EA is proposed based on a
multiple-criteria environmental selection
strategy, which differs from other threestage
EA methods [53], [54] with multiple
mutation strategies. The two criteria
are KN and the Lifespan [7], which indicates
the number ofevolution rounds an
individual has experienced.
1) Process ofthe Three-Stage EA
The environmental selection criteria are
determined as follows:
where G1 and G2 are the round numbers
used to divide the evolution process,
G represents the current round,
and Max gen is the maximum number
(3)
of evolution rounds. Fig. 5 shows the
whole evolution process of the threestage
EA.
In the first stage (0 < G G1)
and third stage (G2 < G Max gen),
KN is applied as the environmental selection
criterion. In the second stage
(G1 < G G2), the individual'slifespan
Lifespan is used as the environmental selection
criterion. The evolution starts after
the population is initialized with n individuals.
First, k individuals are randomly
selected. From these k individuals, t individuals
with the best fitness are sampled as
the parents. t offspring individuals are constructed
from the parents according to the
set ofmutation operators described in Section
III-E. Once the offspring individuals
are constructed, they are evaluated and
added to the existing population, resulting
in t þ n individuals. Then, according to
the stage of the current evolutionary
round, the corresponding criterion is used
for environmental selection, eliminating
the t worst individuals. The remaining n
individuals form a new population that
enters the next evolution round.
2)Advantages ofthe Three-StageEA
The search process of traditional EA
approaches is easily trapped in local
optima since most offspring inherit only
some of the good parents during evolution
process [7]. In aging evolution [7],
individuals are discarded according to
their lifespans. During evolution, older
individuals with good fitness continue
to be discarded. These individuals are
removed as potential optimal solutions
from the search space, which slows the
population's convergence, causing convergence
instability.
Comprehensively considering the
traditional EA and aging evolution process,
a three-stage EA is proposed in this
paper. In the first and third stages ofevolution,
individuals with smallerKN values
are retained during the selection process.
In the second stage, younger individuals
in the population are saved. During the
first stage, outstanding individuals are
selected to enter the later evolutionary
process to ensure that offspring can
inherit from these individuals, improving
the overall performance of the population
and ensuring that sufficient potential
optimal solutions are contained in the
population. Then, in the second stage,
the population is frequently renewed,
enabling more exploration of the search
space and increasing the diversity ofindividuals.
Moreover, a limited number of
rounds are performed to ensure that not
all good individuals are discarded. Finally,
in the third stage, outstanding individuals
are retained during the environmental
selection process, leading the population
to converge to the optimal solution,
which helps ensure exploitation. The
experiments conducted in Section IV
study the effectiveness of the multiplecriteria
environmental selection strategy.
FIGURE 5. The whole evolution process of the three-stage EA according to the different
environmental selection criteria.
E. Mutation Operators for the BlockBased
Network Architecture
The offspring individuals in the population
are generated from mutation operations.
In this paper, mutation operators
are performed only in the Reg Unit,
while the Conv Unit is not involved due
to its specific function. For the mutation
operators, a mutation position posij,
which represents the position of the jth
Reg Block in the ith Reg Unit, is randomly
selected according to the length of
the parent individuals. TheReg Unit and
Reg Block positions determine the
MAY 2023 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE 85
IEEE Computational Intelligence Magazine - May 2023

Table of Contents for the Digital Edition of IEEE Computational Intelligence Magazine - May 2023
