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considering the disruptive effects of operators. Analysis of the constructive ef-
fects of operators in creating new instances of schema H are harder, since these
effects depend heavily on the constitution of the current population.
Eiben about the results of the schema theorem [38], p. 192.
1. The answer whether an improvement of EAs with self-adaptive features of
crossover operators can be gathered, is negative. Our experiments show that
self-adaptive crossover achieves no significant improvements on combinato-
rial problems like the TSP, on continuous optimization problems, as well as
on bit-string problems. Although no significant results can be reported, no
deterioration has been observed. But the variants with changing , i.e. random
or self-adaptive, crossover points are better than the operators with constant
points.
2. The results of the crossover point optimization EA shows that on unimodal
and monotone functions, optimal crossover points can be found with an
optimization step .
3. We see two reasons for the failure of self-adaptive crossover:
a) The fitness gain achieved by optimal crossover settings is weak for many
problems, e.g. for multimodal continuous problems. Our experiments
could only discover valuable fitness gain on monotone functions like
sphere and ridge. In other words: it is easier to control the estimated
distribution functions of mutation than identifying the successive useful
crossover points or settings self-adaptively.
b) Even if the gain of a specific crossover strategy parameter set is advan-
tageous it may not be optimal in the following generation. The same
argument holds for the crossover points of PMX and N-point crossover
variants. Whenever a successful crossover step has been applied, there
seems to be a better crossover point set in the following generation.
Hence, a self-adaptive process can not be established.
4. For complex problems we see the challenge to tighten the link between strat-
egy parameter adaptation and fitness gain: choosing individuals from differ-
ent mating pools or subpopulations with different features may lead to im-
provements. If individuals are selected from these different sets, their combi-
nation at specific crossover points may make sense. But even though, the two
mentioned arguments might prevent the success of self-adaptive crossover.
 
 
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