B Cell–Inspired Algorithms - Immunological Computation: Theory and Applications - page 135

with ε (a Gaussian random variable with zero mean and standard deviation) equal
to 1 (i.e., ε (1 /ε ) e - f is a factor that decays exponentially with the

value of the B cell fi tness f, which has been normalized to [0,1] and β is a parameter
that controls the decay of the exponential function. In addition, a mutation can
only be accepted if c

∼ N (0,1)) and α =

′

falls in the feasible space.
h e opt-aiNet termination criterion is based on the size of the memory-cell
population after network suppression. If the number of memory cells does not vary
between subsequent network suppressions, then it is assumed that the network has
reached stability and, therefore, the current population of memory cells gives a set
of solutions of the problem at hand.
A feature of opt-aiNet is that it considers the interaction of the network cells with
the environment (fi tness) and with one another (a nity), allowing dynamical control
of the size of the population. In opt-aiNet, new cells are allowed to enter the popula-
tion only after the current cell population cannot signifi cantly improve its average
fi tness. Opt-aiNet uses a Gaussian mutation that is inversely proportional to the
normalized fi tness of each parent cell. It also presents some general features similar
to evolutionary strategies (ES). Selection mechanism is similar to a ( µ

+

λ )

−

ES,
in which a population of size µ parents generate λ off spring; the population formed
by parents and off spring undergoes a selection process to reduce it to µ individuals
again. Parents survive, unless they are suppressed by one of the off spring. In opt-
aiNet, parameters µ and λ become N and N c , the number of clones of each indi-
vidual and size of the population, respectively.
Both opt-aiNet and ES use Gaussian mutation; however, opt-aiNet uses an a n-
ity proportional to Gaussian mutation, whereas mutation used in ES is not based
on fi tness. Another important diff erence is that opt-aiNet allows variable population
size, and the size of the population is dynamically adjusted through the introduc-
tion of diversity (network metadynamics) and discarding the least-fi t B cells through
network suppression. In contrast, the size of the population in ES is fi xed.
Another model (IPD aiNet) was proposed by Alonso et al. (2004), which is a
modifi cation of aiNet model representing antigens and B cells as iterated prisoner's
dilemma (IPD) strategies. h e main modifi cation is that if a B cell is added to
memory, it will never be removed. h e immune agent perceives the opponent's
strategy and tries to fi nd a strategy (most stimulated B cell), in the immune mem-
ory, which provides it the highest payoff to confront the playing opponent.

5.2.3.2 Dynamic Optimization AiNet

Olivetti et al. (2005) proposed a modifi cation of opt-aiNet to deal with dynamic
environment. Particularly, the following modifi cations are proposed:

h e use of a separate memory subpopulation
A procedure to adjust the parameter that controls the decay of the inverse
exponential function, denoted by β