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memory cells
guarantee a faster response to similar antigens that may invade the
organism in the future. After the cloning phase, the new generated cells suffer a
process of
hypermutation
with variation rates inversely proportional to each cell
anity to the antigen (the highest anity cells suffer the lowest variation and
vice-versa). The resulting cells with best anity are subsequently selected to
remain in the B cell population, while the cells with lower anity and cells that
have become harmful to the organism after the hypermutation are eliminated.
This cloning and hypermutation processes are essential parts of the
Clonal
Selection Principle
[2]. This principle is one of the main inspirations of the pro-
posed algorithm.
Another important immune concept is the
Immune Network Theory
proposed
by Jerne [11]. This theory states that antibodies are not only capable of rec-
ognizing antigens, but they are also capable of recognizing each other. When
an antibody is recognized by another one, it is suppressed. This mechanism al-
lows the immune system to remain in a dynamic equilibrium and to respond
accordingly to each external stimuli (antigen invasion).
Founded on the
Immune Network Theory
andonthe
Clonal Selection Princi-
ple
, the self-maintenance of diversity in the population and the simultaneous
search for multiple high-quality solutions are distinctive aspects of immune-
inspired algorithms devoted to the solution of optimization problems.
The omni-aiNet algorithm is proposed here as a new member of the aiNet fam-
ily of algorithms, which consists of four immune inspired algorithms. The first al-
gorithm, aiNet (Artificial Immune Network) was proposed by de Castro and Von
Zuben in [6] to perform data analysis and clustering tasks. In a subsequent work,
de Castro and Timmis developed a version of aiNet for multimodal optimiza-
tion problems, called opt-aiNet (Artificial Immune Network for Optimization)
[5]. The third algorithm, copt-aiNet was further proposed by Gomes
et al.
in [9]
as an extension of opt-aiNet for combinatorial optimization tasks. The fourth
algorithm, dopt-aiNet (Artificial Immune Network for Dynamic Optimization)
[7], is an improved and extended version of opt-aiNet for time-varying fitness
functions. In all works, the authors demonstrated empirically the suitability of
the cited algorithms for each kind of optimization problem, with competitive
results when compared to the literature. The essence of the proposal presented
in this work, omni-aiNet (Artificial Immune Network for Omni-optimization),
is mainly based on opt-aiNet, but incorporates some mechanisms introduced by
dopt-aiNet.
3
Basic Optimization Concepts
The main goal of this section is to formalize the kind of problems that will be
treated in this work and to give definitions of some concepts commonly adopted
in optimization (specially multi-objective optimization) that will be used in the
remaining parts of the paper.
In this work, all problems that will be treated by omni-aiNet will be considered
as a constrained
M
-objective (
M
≥
1) minimization problem as follows:
