B Cell–Inspired Algorithms - Immunological Computation: Theory and Applications - page 140

where X denotes an input antigen set, which generally consists of foreign antigens
and other ARBs. h erefore, antigens closer to the center of the ARB will stimulate
it more. In this fuzzy AIS (Figure 5.11), the value of the radius of infl uence of each
ARB is also adapted at each iteration to maximize the ARB stimulation level and,
hence, the ARB probability of survival. h is is done by merging neighboring ARBs,
when they are ver y close to other A R Bs infl uence regions, which also help in limiting
the growth of the population. Besides, some suppression eff ect among neighboring
A R Bs is introduced in the model. In this case, the infl uence of an ARB is adjusted by
subtracting a suppression factor, due to neighboring antibodies, from the stimulation
caused by the antigen set; and then this value is scaled accordingly. h ereby,

∑ ∑

2 2

fxd xc () ( , ) () t f yd yc ( ) ( , )

i i i i

∈ ∈

xX yA

i

2

(5.21)

∑ ∑

fx () () t f ()

i i

xX ∈ yA ∈

where A is the set of all the ARBs in the IN.
It is important to note that in the cloning process, the value of σ is inherited
from the corresponding parent ARB. As mentioned earlier, the ARBs compete for
a fi nite number of resources (B cells) and that the resources allocated depend on
the fuzzy ARB stimulation levels. h erefore, to avoid this in the resource alloca-
tion process, the best ARBs overtake the whole population; the algorithm limits
the infl uence of the best ARBs; and thus, the number of allocated resources r is
computed in proportion to the total stimulation level sl as

=

r k · sl (5.22)

where k is a constant.
In addition, to limit the growth of the population, if two fuzzy ARBs represent
identical data (i.e., have identical centers) after cloning and mutation, then, they
are merged into a single ARB. Accordingly, in fuzzy AINE, a postprocessing stage
takes place to consolidate the fi nal population of fuzzy ARBs as outlined in the
pseudocode shown in Figure 5.12.
In this postprocessing process, crossover operation can be easily designed by
randomly exchanging information of the centers of the two ARBs selected to be
merged, or by computing the center of the new fuzzy ARB as a convex combination of
the centers of the original fuzzy ARBs, if a real-vector representation is being used.
In experiments reported by Nasraoui et al. (2002), note that at the beginning
of the evolution process, denser cluster dominate; but as the process goes on, those
ARBs around less populated clusters start to increase their stimulation levels, until
reaching the same stimulation levels as other ARB clusters. h is is due to the way
stimulated levels are computed today. Specifi cally, the penalization of neighbor
fuzzy ARBs due to suppression, combined with the cloning mechanism that
promotes the proliferation of highly stimulated fuzzy ARBs, prevents very good