IEEE Computational Intelligence Magazine - February 2023 - 58

FIGURE 4 An illustration of the representation in a social
network with nine nodes, where k ¼ 3.
FIGURE 6 An illustration of the mutation operator on
individual p.
degree heuristic-based warm starting method is described as
follows:
1) Each individual is initialized by selecting k seeds with the
highest degree in the social network G;
2) Each node contained in each individual is replaced with a
certain probability of0.5 by its neighbor nodes in the social
network except the nodes are contained in the current
individual.
After performing the above initialization, a population
with degree-based knowledge and diversity can be obtained.
C. Genetic Operators
After the population is initialized, genetic operators including
crossover and mutation are performed on the initial population
to generate a better seed set.
For every two individuals in the population, the seed information
is shared to obtain a higher potential seed set in the crossover
operator with the probability pc. In this article, the twopoint
crossover [51] is employed due to its high efficiency and
low complexity. An illustration of the two-point crossover on
individuals p1 and p2 is shown in Fig. 5. Given two parent individuals
p1 and p2 from the parent population, two crossover
positions x1 and x2 are generated first, where {x1, x2 j 1 x1, x2
k, x1< x2}. Then, two new candidates, p1
, andp2
, and p2
,, are generated
by swapping the seed between positions x1 and x2 ofp1 and
p2. Next, the validity ofp1
, should be guaranteed, that is,
there is no identical seed in an individual. Specifically, new seeds
are randomly generated to replace repetitive seeds in candidates.
For each individual p in the population, the following
mutation operator [52] is conducted to help escape from local
optima after crossover. An illustration ofthe mutation operator
on individual p is given in Fig. 6. Each seed in the individual is
replaced with other nodes in the network with a certain probability
pm and ensure the feasibility ofthe individual.
D. Estimating the Inter-Transformation Relationship
The inter-transformation relationship is employed to guide
the knowledge transfer across different transformations.
During the evolution, each transformation is assigned a
selected most relevant auxiliary transformation. Knowledge
transfer takes place between them with the individual as a
carrier. Generally, the more similar the two transformations
are, the more common knowledge they may contain. This
is because similar transformations contain more common
knowledge for searching, for example, similar fitness landscapes
(see Fig. 1). Because landscape analysis is computationally
expensive, populations are used to implicitly
estimate the inter-transformation relationship in the multitransformation
environment.
The degree of overlap between two seed sets can
directly reflect their correlation. Therefore, the degree of
overlap between individuals in the two populations corresponding
to two transformations is estimated to obtain the
FIGURE 5 An illustration of the two-point crossover on individual p1 and p2.
58 IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | FEBRUARY 2023
IEEE Computational Intelligence Magazine - February 2023

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