T Cell–Inspired Algorithms - Immunological Computation: Theory and Applications - page 88

NS Algorithm 6: NS-fuzzy-detector-rules ( Self )

Input: Self ' : set of self samples; Fuzzy Membership function

Output: A Fuzzy Rule set as Negative Detectors

1 initialize population with random individuals
2 for j

=

1 to num_gen
3 for k

=

1 to pop_size/2

4 select two individuals, ( parent 1, parent 2), with uniform

probability and without replacement

5 apply crossover to generate an off spring ( child )

6 mutate child

<

7 if dist ( child, parent 1) dist ( child, parent 2)

>

^ fi t n e s s ( child )

fi t n e s s ( parent 1)

←

8 then parent 1 child

≥

9 elseIf dist ( child, parent 1) dist ( child, parent 2)

>

10

^ fi t n e s s ( child )

fi t n e s s ( parent 2)

11 then parent 2 ← child

12 endIf
13 endFor
14 endFor
15 Take the better individuals from the population and add them to
the detector set

4.6.3 Randomized Approaches in Generating
(Fixed Size) Spherical Detectors

Gonzalez et al. (2003b) proposed a randomized approach based on “Monte Carlo
integration” (Monte, 1995; Liu, 2001) to generate negative detectors. h is approach
assumed that all detectors had the same shape and size; particularly, hyperspheres
of a fi xed radius in an n -dimensional space were considered. Particularly, (1) Monte
Carlo integration was used to estimate the volume of the self and nonself space,
and it is also used to compute a rough estimate of the number of detectors needed
to cover the nonself space; then (2) “simulated annealing” was used to optimize the
detector distribution in the nonself space. Because the detectors are hyperspheres,
the volume of the eff ective coverage of a detector was approximated as the volume
of the inscribed hypercube:

n

2 r

n

V

d