Evolution and Optimum Seeking

Chapter 5
Evolution Strategies for Numerical
Optimization
The task of mimicking biological structures and processes with the object of solving
technical problems is as old as engineering itself. Mimicry itself, as a natural \strategy",
is even older than mankind. The legend of Daedalus and Icarus bears early witness
to such human endeavor. A sign of its scienti c coming of age is the formation of the
distinct branch of science known as bionics (e.g., Hertel, 1963 Gerardin, 1968 Beier
and Gla , 1968 Nachtigall, 1971 Heynert, 1972 Zerbst, 1987), which is concerned with
the recognition of existing biological solutions to problems that also happen to arise
in engineering, and with the adequate emulation of these examples. It is always thereby
supposed that evolution has found particularly good, perhaps even optimal solutions. This
assumption has often proved to be correct, or at any rate useful. Only a few attempts to
imitate the actual methods of natural development are known (Ashby, 1960 Bremermann,
1962{1973 Rechenberg, 1964, 1973 Fogel, Owens, and Walsh, 1965, 1966a,b Holland,
1975 see also Chap. 4) since they are curiously regarded a priori as being especially bad,
meaning costly.
Rechenberg proposed the hypothesis \that the method of organic evolution represents
an optimal strategy for the adaptation of living things to their environment," and he
concludes \it should therefore be worthwhile to take over the principles of biological
evolution for the optimization of technical systems."
5.1 The Two Membered Evolution Strategy
Rechenberg's two membered evolution scheme, suggested in similar form by other authors
as a random strategy (see Chap. 4) will be expressed in this chapter as an algorithm for
solving non-discrete, non-stochastic, parameter optimization problems. As in Chapter 3,
the problem is
F (x) ! min
where x 2 IR n . In the constrained case x has to be in an allowed region G IR n , where
G = fx 2 IR n j Gj(x) 0 j = 1(1)nGj restriction functionsg
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