Computational Intelligence and Neuroscience
other related substances construct a network. CAS combing
with immune network theory is more suitable for handling
multimodal function optimization.
e opt-AINet algorithm is an earlier version of CSA
with articial immune networks, which is proposed to
solve multimodal continuous function optimization [].
Uniform cloning operator, anity-based Gaussian mutation,
and similarity-based suppressor are proposed. To enhance
the parameter adaptation, an improved adaptive Articial
Immune Network called IA-AIS is proposed, where anity-
based cloning operator, controlled anity-based Gaussian
mutation, and dynamic suppressor are introduced []. By
imitating the social behaviors of animals, social leaning
mechanism is introduced to the immune network; an algo-
rithm called AINet-SL is proposed. e population is sepa-
rated into elitist swarm (ES) and the common swarm (CS).
Nonlinear anity-based cloning, self-learning mutation, and
social learning mutation are employed []. Based on the
anity measure, the candidate solution space is divided into
the elitist space, the common space, and the poor space, and
dierent hypermutation strategies are applied, respectively,
in MPAINet []. Concentration-Based Articial Immune
Network, where the concentration of antibody is introduced
to stimulate and maintain the diversity of the population,
is applied to continuous optimization [], combinatorial
optimization [], and multiobjective optimization [].
2.2.3. Hybrid CSA. CSAisalsohybridwithPSO,DE,and
other evolutionary strategies. Hill-climbing local search oper-
ator is combined with immune algorithm in []. Dierential
immune clonal selection algorithm (DICSA) is put forward
by Gong et al. [], where the dierential mutation and
dierential crossover operators are introduced. Orthogonal
initialization and neighborhood orthogonal cloning operator
areproposedinanorthogonalimmunealgorithm(OIA)[].
CSA with nondominated neighborhood selection strategy
(NNIA) [] was proposed for multiobjective optimization.
Shang et al. [] proposed an immune clonal algorithm
(NICA) for multiobjective optimization problems, which
makes improvements on four aspects in comparison with the
traditional clonal selection computing model.
Baldwin eect is introduced into CSA and formulated
the Baldwinian clonal selection algorithm (BCSA), which
guides the evolution of each antibody by the dierential
information of other antibodies in the population []. Gong
et al. [] substitute the mutation in CSA with the local
search technique in Lamarckian Clonal Selection Algorithm
(LCSA) and adopt recombination operator and tournament
selection operator for numerical optimization. An enhanced
CSA, hybrid learning CSA (HLCSA) [], is proposed by
introducing two learning mechanisms: Baldwinian learning
and orthogonal learning.
Although many improvements on immune inspired algo-
rithm have been realized, the abovementioned shortcoming
of articial immune algorithm, such as premature conver-
gence, high computational cost, and unsatised accuracy that
can negatively aect the application of immune algorithm,
remains a problem. e search ability of immune algorithm
is limited when dealing with high-dimensional complex
optimization with dierent characteristics. In this paper, we
propose an improved CSA, by introducing a recombination
operator and modifying the hypermutation operator to cope
with the complex optimization problems with the character-
istic high-dimensional, nonconvex, rotated, and composed
optimization problems.
3. CSA with Combinatorial Recombination
and Modified Hypermutation
3.1. Combinatorial Recombination. In immunology, the pres-
ence of both recombination and somatic mutation takes the
responsibility for the diversication of antibody genes. e
recombination of the immunoglobulin gene segments is the
rst step when the cells are rst exposed to antigen. In the past
few decades, recombination is mentioned more as crossover
in GA. However, as depicted in [], the recombination of
immunoglobulin genes involved in the production of anti-
bodies diers from the recombination (crossover) of parental
genes in sexual reproduction. In the former, nucleotides can
be inserted and deleted randomly from the recombined gene
segments, while in the latter the genetic mixture is generated
from parental chromosomes.
e basic unit of antibody molecule has a Y-shape
structure, which contains two identical light chains and
two identical heavy chains as shown in Figure (a). Variable
regions located at the tips of the Y are primarily responsible
for antigen recognition. Within these variable regions, some
polypeptide segments show exceptional variability. e anti-
body molecules can be synthesized by an individual lying
in the way of encoding the amino acid sequences of the
variable domains into DNA chains as well as the random
selection and recombination of gene segments as shown
in Figure (b). During the development of B cell, the gene
segments in the libraries are combined and rearranged at the
level of the DNA. With the recombination of gene segments,
recombination creates a population of cells that vary widely in
their specicity. In this way, few immune cells are compatible
with various antigens. Aer altering the base of antibody, the
mutations ne-tune the lymphocyte receptor to better match
the antigen [, ].
In the perspective of optimization, recombination func-
tions as the coarse-grained exploration while hypermutation
works the same way as ne-grained exploitation. Inspired by
this, a combinatorial recombination operator is proposed as
follows.
To avoid the truncation error and the complexity of
thecoding,ouralgorithmiscodedinrealnumberand
each dimension of a solution is viewed as a gene segment.
e whole population forms the gene fragments library.
According to the recombination in immunology, any orderly
rearrangement of gene segments would generate a new B
cell. As presented in Figure , the recombination could be (a)
between two individuals as crossover or (b) among several
individuals as the combination of randomly selected gene
segments. With the help of normalization, the combination
of gene segments could be in the specic order, such as
in Figure (a) or can be randomly arranged as shown in
Figure (b) in the computational respective.