Evolution and Optimum Seeking

100 Random Strategies
surpass the capabilities of highly developed technical systems. Recognition of this has for
years led many authors to suspect that nature is in possession of optimal solutions to her
problems. In some cases the optimality of biological subsystems can even be demonstrated
mathematically, for example for the ratios of diameters in branching arteries (Cohn, 1954),
for the hematocrit value (the volume fraction of solid particles in the blood Lew, 1972),
and the position of branch points in a level system of blood vessels (Kamiya andTogawa,
1972 see also Grassmann, 1967, 1968 Rosen, 1967 Rein and Schneider, 1971).
According to the theory of the descent of the species, all organisms that exist today
are the (intermediate) result of a long process of development: evolution. Based on the
multitude of nds of transitional species that have since become extinct, paleontology is
providing a gradually more complete picture of this development. Leaving aside supernatural
explanations, one must assume that the development of optimal or at least very
good structures is a property ofevolution, i.e., evolution is, or possesses, an optimization
(or better, meliorization) strategy.
In evolution, the mechanism of variation is the occurrence of random exchanges, even
\errors," in the transfer of genetic information from one generation to the next. The selection
criterion favors the better suited individuals in the so-called struggle for existence.
The similarityofvariation and selection to the iteration rules of direct optimization methods
is, in fact, striking. This analogy is most often drawn for random strategies, since
mutations can best be interpreted as random changes. Thus Ashby (1960) regards as
mutations the stochastic parameter variations in his blind homeostatic process. For many
variables, however, the pure or blind random search requires so many trials that it offers
no acceptable explanation of the capabilities of natural structures, processes, and
systems. With the highest possible physical rate of transfer of information, as given by
Bremermann (1962 see also Ashby, 1965, 1968) of 10 47 bits per second and gram of computer
mass, the mass of the earth and the extent of its lifetime up to now would not
be su cient to solve even simple combinatorial problems by complete enumeration or a
blind random search, never mind to determine the optimal con guration of the 10 4 to 10 5
genes with their information content of around 10 10 bits (Bremermann, 1963). Evolution
must rather be considered as a sequential process that exploits the information from preceding
successes and failures in order to follow a trajectory, although not a completely
deterministic one, in the n-dimensional parameter space. Brooks (1958) and Favreau and
Franks (1958) are therefore right to compare their creeping random search with biological
evolution. Yet it is also certainly a very much simpli ed imitation of the natural process
of development. In the 1960s, two proposals that consciously think of higher evolution
principles as optimization rules to be simulated are due to Rechenberg (1964, 1973) and
Bremermann (1962, 1963, 1967, 1968a,b,c, 1970, 1971, 1973a,b see also Bremermann,
Rogson, and Sala , 1965, 1966 Bremermann and Lam, 1970). Bremermann reasons from
the (nowadays!) low mutation rates observed in nature that only one component of the
variable vector should be varied at a time. He then encounters with this scheme the
same di culties as arise in the coordinate method. On the basis of his failure with the
mutation-selection scheme, for example on linear programming problems, he comes to the
conclusion that ecological niches are actually only stagnation points in development, and
they do not represent optimal states of adaptation. None of his many attempts to invoke