Evolution and Optimum Seeking

A Multimembered Evolution Strategy 147
Parents of
generation g
Descendants
x x x . . .
x
1 2 3 n
Discrete global recombination
Figure 5.15: Scheme of global uniform recombination
Recombination
by choosing
components
columnwise
and at random
This is, however, the only way to arrive atquantitative statements, free from confusing
side e ects.
It is thus hard to explain the origin of the accelerating e ect of recombination. It
may, for example, lie in the fact that instead of di erent starting points, the bisexual
scheme o ers
2 + (
n;2 X
; 1) 2i possible combinations in the case of n variables. With multirecombination, as chosen
here, there are as many as n ,which is far more than could be put into e ect. A more
detailed investigation may be found in Back (1994a).
So far we have only considered recombination of the object variables, but the strategy
variables, the step lengths, can be recombined in just the same way. Even if all the parents
start with equal i = for all i = 1(1)n, and if all the step length components are varied
by a common random factor in the production of descendants, the variances i of all the
individuals for each i = 1(1)n di er from each other in the subsequent generations.
Thus by recombination is it possible for the step lengths to adapt individually in
this way to circumstances. A better combination a ords a higher chance of survival to
its bearer. It can therefore be expected that in the course of the optimum search, the
currently best combination of the f i i= 1(1)ng prevails{the one that is associated with
the fastest rate of progress. In attempting to verify this in a practical test, an unpleasant
phenomenon occurs. It can happen that one of the standard deviations i is suddenly
i=1