Evolution and Optimum Seeking

238 Summary and Outlook
methods for many variables, for example those that employ costly orthogonalization processes.
The external control of step lengths sometimes, however, worsens the reliabilityof
the strategy. In \pathological" cases it leads to premature termination of the search and
reduces besides the chance of global convergence.
Now instead of concluding like Bremermann that organic evolution has only reached
stagnation points and not optima, for example, in ecological niches, one should rather
ask whether the imitation of the natural process is su ciently perfect. One can scarcely
doubt the capability ofevolution to create optimal adaptations and ever higher levels
of development the already familiar examples of the achievements of biological systems
are too numerous. Failures with simulated evolution should not be imputed to nature
but to the simulation model. The two membered scheme incorporates only the principles
of mutation and selection and can only be regarded as a very simple basis for a true
evolution strategy. On the other hand one must proceed with care in copying nature, as
demonstrated by Lilienthal's abortive attempt, which is ridiculed nowadays, to build a
ying machine by imitating the birds. The objective, to produce high lift with low drag,
is certainly the same in both cases, but the boundary conditions (the ow regime, as
expressed by the Reynolds number) are not. Bionics, the science of evaluating nature's
patents, teaches us nowadays to beware of imitating in the sense of slavishly copying all the
details but rather to pay attention to the principle. Thus Bremermann's concept of varying
the variables individually instead of all together must also be regarded as an inappropriate
way to go about an optimization with continuously variable quantities. In spite of the
many, often very detailed investigations made into the phenomenon of evolution, biology
has o ered no clues as to how an improved imitation should look, perhaps because it has
hitherto been a largely descriptive rather than analytic science. The di culties of the two
membered evolution with step length adaptation teach us to look here to the biological
example. It also alters the standard deviations through the generations, as proved by
the existence of mutator genes and repair enzymes. Whilst nature cannot in uence the
mutation-provoking conditions of the environment, it can reduce their e ects to whatever
level is suitable. The step lengths are genetically determined they can be thought ofas
strategy parameters of nature that are subject to the mutation-selection process just like
the object parameters.
To carry through this principle as the algorithm of an improved evolution strategy
one has to go over from the two membered toamultimembered scheme. The ( , )
strategy does so by employing the population principle and allowing parents in each
generation to produce descendants, of which the best are selected as parents of the
following generation. In this way the sequential as well as the simultaneous character
of organic evolution is imitated the two membered concept only achieves this insofar
as a single parent produces descendents until it is surpassed by one of them in vitality,
the biological criterion of goodness. According to Rechenberg's hypothesis that the forms
and intricacies of the evolutionary process that weobservetoday are themselves the result
of development towards an optimal optimization strategy, our measures should lead to
improved results. The test results show that the reliability of the (10 , 100) strategy,
taken as an example, is indeed better than that of the (1+1) evolution strategy. In
particular, the chances of locating global optima in multimodal problems have become