Genetic Algorithms and Multimodal Search - Advancing Artificial Intelligence Through Biological Process Applications - page 233

and they will be more adapted to the required
solution as generations pass.
Nevertheless, the traditional GAs find certain
restrictions when the search space where they work
has, either more than a global solution, or an unique
global solution and multiple local optima. When
faced with such scenarios, a classical GA tends
to focalise the search on the environment of the
global solution; however, it might be interesting to
know the higher possible number of solutions due
to different reasons: exact search space knowledge,
implementation ease of local solutions compared
with the global one, interpretation ease of some
solutions compared with other ones, etc. To get
this, an iterative process will be performed until
the desired goals might be achieved. The process
will start with the individuals grouping into spe-
cies that will search independently a solution into
their related environments. Following the later,
the crossover operation will involve individuals of
different species in order not to leave search space
areas unexplored. The process will be repeated ac-
cording to the achievement of the desired goals.

MULTIMODAL PRObLEMS

The multimodal problems can be defined as those
problems that have either multiple global optima
or multiple local optima (Harik, 1995).
For this type of problems, it is interesting to
obtain the greatest number of solutions due to
several reasons; on one hand, when there is not
a total knowledge of the problem, the solution
obtained might not be the best one, as it can not
be stated that no better solution could be found
at the search space not explored yet. On the other
hand, although being certain that the best solution
has been achieved, there might be other equally
fitted or slightly worse solutions that might be
preferred due to different factors (easier applica-
tion, simpler interpretation, etc.) and therefore
considered globally better.
One of the most characteristic multimodal
functions used in lab problems is the Rastrigin
function (see Figure 1) which offers an excellent
graphical point of view about what multimodal-
ity means.
Providing multiple optimal (and valid) solu-
tions, and not only a unique global solution, is
crucial in multiple environments. Usually, it is very

Figure 1. Rastrigin function: 3D and 2D representations