Evolution and Optimum Seeking

102 Random Strategies
(1972), and Papentin (1972) are so di erent in emphasis that they are not applicable to
the kind of problems considered here. The ways in which a process of mathematization
can be implemented in theoretical biology are documented in for example the books by
Waddington (1968) and Locker (1973), whichcontain a number of contributions of interest
from the optimization point of view, as well as many articles in the journal Mathematical
Biosciences, which has been published by R. W. Bellman since 1967, and some papers
from two Berkeley symposia (LeCam and Neyman, 1967 LeCam, Neyman, and Scott,
1972). Whereas many modern books on biology, such as Riedl (1976) and Roughgarden
(1979), still give mainlyverbal explanations of organic evolution, in general, this is no
longer the case. Physicists like Ebeling and Feistel (see Feistel and Ebeling, 1989) and
biologists like Maynard Smith (1982, 1989) meanwhile have contributed mathematical
models. The following two paragraphs thus no longer represent the actual situation, but
before we add some new aspects they will be presented, nevertheless, to characterize the
situation as perceived by the author in the early 1970s (Schwefel, 1975a):
Relationships have been seen between random strategies and biological evolution
on the one hand and the psychology of recognition processes on the other,
for example, by Campbell (1960) and Khovanov (1967). The imitation of such
processes{the catch phrase is arti cial intelligence{always leads to the problem
of choosing or designing a suitable search algorithm, which should rather
be heuristic than strictly deterministic. Their simplicity, reliability (even in
extreme, unfamiliar situations), and exibility give the random strategies a
special r^ole in this eld. The topic will not be discussed more fully here, except
to mention some publications that explicitly deal with the relationship
to optimization strategies: Friedberg (1958), Friedberg, Dunham, and North
(1959), Minsky (1961), Samuel (1963), J. L. Barnes (1965), Vagin and Rudelson
(1968), Thom (1969), Minot (1969), Ivakhnenko (1970), Michie (1971),
and Slagle (1972). A particularly impressive example is given by the work of
Fogel, Owens, and Walsh (1965, 1966a,b), in which imitation of the biological
evolutionary principles of mutation and selection gives a (mathematical)
automaton the ability to recognize prescribed sequences of numbers.
It may be that in order to match the capabilities of the human brain{and
to understand them{there must be a move away from the digital methods of
present serial computers to quite di erent kinds of switching elements and
coupling principles. Such concepts, as pursued in neurocybernetics and neurobionics,
are described, for example, by Brajnes and Svecinskij (1971). The
developmentoftheperceptron by Rosenblatt (1958) can be seen as a rst step
in this direction.
Two research teams that have emphasized the adaptive capacity ofevolutionary procedures
and who have shown interesting computer simulations are Allen and McGlade
(1986), and Galar, Kwasnicka, and Kwasnicki (see Galar, Kwasnicka, and Kwasnicki,
1980 Galar, 1994). In terms of the optimization tasks looked at throughout this book,
one might call their point of view dynamic or on-line optimization, including optimum
holding against environmental changes. As Schwefel and Kursawe (1992)have pointed