B Cell–Inspired Algorithms - Immunological Computation: Theory and Applications - page 137

f ( x )

P 1/2 ( x 1/2 ,f ( x 1/2 ))

P 2 ( x 2 ,f ( x 2 ))

P ′

. P 1 ( x 1 ,f ( x 1 ))

x

Figure 5.9 B cell suppression. Here P ′ is used to determine the suppression

distance between the two points.

Also, a modifi cation to the cell-suppression mechanism used in opt-aiNet is
introduced. h e new mechanism, termed “cell-line suppression,” is proposed to
reduce the probability of having more than one cell located at each peak of the
fi tness landscape. h is suppression mechanism not only uses information of the
domain space but also information of the fi tness function as follows. When a B cell
suppresses another B cell, instead of considering the distance between the points
x 1 and x 2 that represent the two B cells, points of the form ( x , f ( x )) are used, which
is described as follows. Let P 1

=

( x 1 , f ( x 1 )), P 2

=

( x 2 , f ( x 2 )), and P

′ =

projection of

= +

P 1/2 onto P 2 , where P 1/2 P 2 )/2 (Figure 5.9). h e suppression between the

B cells with values x 1 and x 2 is computed based on the distance between P 1/2 and a
point P , which is computed as

( P 1

⋅

vw
v

P v

if P falls inside segment P P

1

112

P

P if P falls outside segment P P and is closer to P

( 5.18 )

12 1

1

P if P falls outside segment P P and is closer to

12

P

2 2

= − = − ′

where v ) is below a thresh-

old value σ s , then the B cell with the worst fi tness between the two is removed.
To limit the growth of the population, a maximum number of cells is prespeci-
fi ed in such a way that when the B cell population reaches this value, B cells with
the worst fi tness are deleted from the population.
h e dopt-aiNet algorithm is summarized in Figure 5.10.
Varga s et a l. (2003) proposed the CL A R INET model, which combines learning
classifi er systems, evolutionary algorithms, and AIN where classifi er systems are

P 2 P 1 and w P 1/2 P 1 . Accordingly, if dist ( P 1/2 , P