6. CONCLUSION
The multiset representation of populations in MuGA allows the
development of specific genetic operators useful for typically difficult
problems. In this paper we explored an adaptation of the mutation
operator and an adaptation of the replacement operator. Both use the
number of copies in a multi-individual (MI) enabling MuGA to obtain
interesting results in deceptive problems.
The multiset wave mutation operator (MWM) uses the multiple
copies of a multi-individual (MI) to modulate the probability of
mutation of an individual. The proposed modulating function is
shaped as a wave, which combines well a conservative approach for
MI with a small number of copies with a exploratory approach, with
high mutation rates for most of the copies of MI that have them in
large quantities.
The multiset decimation replacement operator (MDR) integrates MI
from parents’ and offspring populations, so that the winners of
successive tournaments among randomly selected MI in this multiset
will completely replace the parents’ population. This will usually
produce new populations with most of the high fitness MI, which
typically have a large number of copies that can be used in the next
generation by the MWM operator.
Results obtained with benchmark deceptive problems show that
together the two adapted operators, MWM-MDR, produced a robust
version of MuGA. They are not the best in all the problems but had
good performance in most of them. Tests performed with nondeceptive
functions showed that the new operators did no
compromise performance, as it should be expected by their design. It
is important to highlight this integrated functioning of operators, since
this is one of the most important features for an evolutionary
algorithm (EA). A single operator of an EA is seldom a solution. It
needs an adequate pairing with the other operators. Obtained results
seem to confirm this.
In this research we also had difficulty in establishing clear
comparisons with other algorithms due to the way results are often
presented. We showed that the success rate is much more informative
measure of performance than the average fitness, in particular for
deceptive problems, where we are mostly interested in finding the
optimum, or optima.
From this first set of functions we may infer that in problems where
building blocks are possible in the chromosome, MuGA with Multiset
Wave Mutation and Multiset Decimation Replacement is very robust.
For future work we will explore more complex problems, especially
larger versions of functions with intermingled parts. The results
obtained in some of these functions already tested showed
limitations on the configuration used for MWM-MDR. However we