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the latter relies heavily on the experiences of the particular user and the obtainable
higher-level problem information. The higher-level information is used to choose a
preference vector so that multiple objectives can be aggregated into a single objective.
In doing so, MOP is actually transformed into SOP. However, because of its high
dependence on preference information this approach is sometimes subjective and im-
practical. Facing the possibility of lacking the problem information, the ideal multi-
objective optimization procedure has been given more attention. Through this
method, a set of trade-off solutions is found. By finding the set of solutions humans
can understand the problem in greater depth, and finally a single optimal solution to a
specific scenario is finally decided.
The prevalence of the ideal method calls for a new philosophy to deal with the
problem since one wants to find a set of uniform-distributed optimal solutions simul-
taneously through a single run, rather than several runs. For this reason, population-
based
Genetic algorithm
(GA) steps in sight. GA was originally developed to solve
SOP. In this case, all solutions in the population will finally converge to a single op-
timum. To make traditional GA suitable to maintain a solution set, the sharing method
is used [17]. In this way and alike, different species can format and co-exist in the fi-
nal population. Despite its great ability in maintaining trade-off solutions and dealing
with non-convex problems, population-based GA suffers from two main problems:
1.
It is sensitive to the setting of the sharing parameters.
2.
It depends highly on the population size to preserve its search capability.
Solving the above problems is our initial intention to develop a population adaptive
based immune algorithm (PAIA), which is further discussed in Section 3.
2.2 The Immune System
The vertebrate immune system is highly complex and possesses multi layers. Here,
what one is interested in is the third layer, namely, the adaptive immune system,
which can learn and adapt to most previously unseen antigens, and can respond to
such patterns quickly in the next sample. Among many immunological models, the
Clonal Selection and the Immune Network theories are the two branches which were
emulated in this work. Another immune metaphor which was exploited is the way that
the immune system controls its Abs' concentration.
Clonal Selection Principle.
The Clonal Selection Principle describes the basic fea-
tures of an immune response to an antigenic stimulus, and establishes the idea that
only those cells that recognize the antigen are selected to proliferate. The key proce-
dures are: 1)
Selection
: the B-cell with a higher affinity than a threshold is selected to
clone itself; 2)
Proliferation
: the selected B-cells produce many offspring with the
same structure as themselves; the clone size is proportional to the individual's affin-
ity; 3)
Affinity Maturation
: this procedure consists of
Hypermutation
and
Receptor
Editing
[18]; in the former case, clones are subjected to a high-rate mutation in order
to differentiate them from their parents; the higher the affinity, the lower the mutation
rate; in the latter case, cells with a low affinity, or self-reactive cells, can delete their
self-reactive receptors or develop entirely new receptors; 4)
Reselection
: after
affinity
