For the past some time I have been working on
multimodal GAs and wanted to discuss some doubts and observations about
The fundamental question, which arises in my mind
is which sets of points are actually desired at the end of the search,
are they solutions with a high fitness value or points located on peaks?
There is a large difference between the two. A peaks may have a low fitness
value, but will always follow the characterstic that points adjacent to it
will have lower fitness as compared to them. And my study of previous works on
multimodal GAs show that the functions on which experiments were
conducted, the desired idea was to find all the peaks rather than
points with high fitness value.
On the other hand, techniques generally being
designed for multimodal problems continue to concentrate on high
fitness value to choose individuals rather than having a look at the fitness of
indviduals around a point. This basic error is approach gives rise to
problems such as need for value of niche radius to run the
algorithm properly, algorithmic complexity, etc.
Considering the problem of maxima searching,
an approach to consider the value of the function for the points
around an individual to decide is fitness looks fundamentally more
impressive. The core idea is to shift the idea of fitness from absolute
function value to 'relative function value' (incremental function value
from neighbouring points). It could be like turning attention from the function
to its derivative!!!
I dont dare suggest a complete banishment
of idea of fitness value decided by function value, because
it may mean a complete change in the basic SGA and its effect, I can't
contemplate. But a decent change in the fitness function or employment of a
hybrid scheme on basis of this concept looks fundamentally more strong and may
render better results.
Any takers for this idea. Or am I making some
Eagerly waiting for your comments.