T Cell–Inspired Algorithms - Immunological Computation: Theory and Applications - page 100

A detector, D provides a better coverage if the volume of D is as large as possible,
while minimizing the overlap of D with S (the self-set) and the Detectors Set. h us,
the “fi tness function” is defi ned as

= − ×

fi t n e s s ( D ) eff ective-coverage(D) C(m) m

eff ective-coverage(D) = V ˆ ( D )

−

β

m
S

Cm () tan h

if m 0, and C m ( ) 0 if m 0

ln

where V ˆ ( D ) is an estimate of the volume of D , β an estimation of the net overlap
of D with the detector set, m the number of self-points that D matches, and C(m)
a “penalization factor” computed taking into account the number of self-points
that D matches. h e estimates of V ˆ ( D ) and β are obtained using a “Monte Carlo
technique.”
Balachandran et al. (2007) used tournament selection, two point crossover,
and bit fl ip mutation in st. GA implementation. h ese operators are applied to
each component of each gene of the chromosome. A specifi c mutation operator was
used on the hyperellipse orientation matrix V : column vectors S i and S j , 1

≤ ≤

n ,
are chosen at random, a real value θ is chosen from a “Gaussian distribution” with
µ

i , j

= =

π /2, and two components of vectors S i and S j to be mutated are
picked at random and calculated as

0 and σ

j j j

S ′

i

S

i i

cos S sin S ′ S

i i

sin S cos

i i i i

j j j

′

j i i

′

i

S S cos S s in S S sin S cos

j i j

Each run of the algorithm ends when certain coverage is reached, or when the
algorithm fails to increase the coverage above a certain threshold for a certain
number of iterations.
h is work (Balachandran et al., 2007) showed a way to develop a unifi ed frame-
work for generating multishaped detectors in RNS algorithm. Results showed that
multishaped detectors can provide better coverage compared to any single-shaped
detectors. h e uniform representation scheme and the evolutionary mechanism
used in this work also serve as a baseline to include other shapes for e cient cover-
age of nonself space.

4.7 Applicability Issues of Real-Valued
Negative Selection Algorithms

Real-valued representation seems appropriate if the underlying problem is continuous
and can capture some continuous properties in the problem space. h e paper by
Ji and Dasgupta (2006) tries to clarify some issues raised on the applicability and