Evolution and Optimum Seeking

Genetic Algorithms 159
Average
Number of
Offspring
5
4
3
2
1
0
1 5 10
Average
Number of
Offspring
5
4
3
2
1
0
Fitness 1 5 10
Figure 5.17: Comparison of selection consequences in EAs
left: ES right: GA
Fitness
de nes the initial distance from the optimum and thus determines largely the number of
iterations needed to approximate the solution at the prede ned accuracy, but also because
it may provide more or less topological di culties in its vicinity. GAs, however, should
be started at random in the whole hypercube de ned by the lower and upper bounds
of the variables, in order to give themachance of approaching the global or, at least,
avery good local optimum. Reliability tests (see Appendix A, Sect. A.2), especially
in cases of multimodal functions would thus be biased against all other methods, if one
allows the GA to start from many points at the same time and if one gives the GA the
needed extra information about the relevant search region that is not available for the
other methods. One might provide special test conditions to compare di erent EAs with
each other without giving one of them an advantage from the very beginning, but no large
e ort of this kind has been made so far.
Even in cases of special constraints or side conditions one may formulate appropriate
instantiations of suitable GA versions. This has been done, for example, for the
combinatorial optimization task of solving the travelling salesperson problem (TSP) by
Gorges-Schleuter (1991a,b) repair mechanisms were used in cases where unfeasible tours
were caused by recombination. Beyer (1992) has investigated ESs for solving TSP-likeoptimization
problems. It is much better to look for data structures tted to the special task
and to rede ne the genetic operators to keep to the feasible solution set (see Michalewicz,
1992, 1994). The time for developing such special EAs must be added to the run time
on the computer, and one argument infavor of EAs is lost, i.e., their simplicity of use or
generality of application.
As the short analysis of GA mutation and recombination operators above has clearly