7 SUMMARY
AND CONCLUSIONS
This paper has introduced the Chemnitz Hybrid
Evolutionary Optimization System to the scientific
community. Being a non

standard genetic algorithm
framework, CHEOPS allows simple as well as ad
vanced modes of operation.
In the present paper we have restricted ourselves
to single

objective optimization, because CHEOPS
is still under construction. It will be enhanced to
solve multi

objective problems as well. Thus, an
other paper might take up the comparison in the near
future. Surprisingly, steady state genetic algorithms
like CHEOPS are rather unusual in multi

objective
optimization practice

without any justification and
perhaps unaware of their main advantage. The
proposed enhancement to solve multi

objective
problems simply by appropriate selection methods
and elite population archiving strategies is indeed
quite straightforward. Furthermore, CHEOPS does
not need any other modifications such as variable
space and objective space crowding, or niche and
speciation methods.
In their pioneering papers, Deb and Tiwari
(2005, 2008) have argued that multi

objective,
multi

optima optimization problems are the most
generic ones. They have concluded that, if designed
carefully, an algorithm capable of solving such
problems should also solve single

objective and
/
or
uni

optimal problems in a straightforward, so

called
“degenerated” manner. However, due to the
disappointment of their (extended) Omni Optimizer
with regard to its single

objective optimization
results as assessed in the present paper, a high

performance genetic algorithm well

suited for solv
ing both single

and multi

objective optimization
problems is still a matter of serious research. It
might be acknowledged by the scientific community
in the near future and should find increasing use in
real

world optimization practice, too.
Let us finally think about that reasoning of Deb
and Tiwari
in more detail. In multi

objective
optimization, the optimization tool should output
lots of such candidate solutions that cannot be
dominated by any other(s), thus spanning the trade

off surface for the current optimization problem in
the objective space. That is known as Pareto

optimality, but being a pareto

optimal candidate
solution does not require getting close to extreme in
one or more objective function(s). Unlike, getting
close to extreme is what single

objective
optimization is all about! In multi

objective
optimization, there are usually infinitely many
pareto

optimal candidate solutions

in single

objective optimization, the optimization tool has to
push the objective function to its very extreme to
find the true, one and only global optimum. Thus, it
is the author’s opinion, that single

and multi

objective optimization are two different jobs, and
you cannot perform well in one job just by “de
generation” of the skills you have trained for and
practiced in another job.
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