Abstract: In this paper the design of maximally flat linear phase
finite impulse response (FIR) filters is considered. The problem is
handled with totally two different approaches. The first one is
completely deterministic numerical approach where the problem is
formulated as a Linear Complementarity Problem (LCP). The other
one is based on a combination of Markov Random Fields (MRF's)
approach with messy genetic algorithm (MGA). Markov Random
Fields (MRFs) are a class of probabilistic models that have been
applied for many years to the analysis of visual patterns or textures.
Our objective is to establish MRFs as an interesting approach to
modeling messy genetic algorithms. We establish a theoretical result
that every genetic algorithm problem can be characterized in terms of
a MRF model. This allows us to construct an explicit probabilistic
model of the MGA fitness function and introduce the Ising MGA.
Experimentations done with Ising MGA are less costly than those
done with standard MGA since much less computations are involved.
The least computations of all is for the LCP. Results of the LCP,
random search, random seeded search, MGA, and Ising MGA are
discussed.