Evolution and Optimum Seeking

152 Evolution Strategies for Numerical Optimization
book of Holland (1975) and the dissertation of De Jong (1975) were published. Thus this
work was unknown in Europe at the time when Rechenberg's and the author's dissertations
were completed and, later on, published as books. Only 10 years later, however, in
1985, a series of biennial conferences (ICGA, International Conferences on Genetic Algorithms)
has been started (Grefenstette, 1985, 1987 Scha er, 1989 Belew and Booker,
1991 Forrest, 1993) to bring together those who are interested in the theory or application
of GAs. On the Eastern side of the Atlantic, a similar revival of the eld began in
1990 with the rst conference on parallel problem solving from nature (PPSN) (Schwefel
and Manner, 1991 Manner and Manderick, 1992 Davidor, Schwefel, and Manner, 1994).
During the PPSN 90 and the ICGA 91 events, proponents of GAs and ESs agreed upon
the common denominators evolutionary algorithms (EAs) for both approaches as well as
evolutionary computation (EC) for a new international journal (see De Jong, 1993). The
latter term has been adopted among others by the Institute of Electrical and Electronics
Engineers (IEEE) for an international conference during the 1994 World congress on computational
intelligence (WCCI). Surveys of the history have been attempted by De Jong
and Spears (1993) and Spears et al. (1993). As forerunners of the genetic simulation,
Fraser (1957), Friedberg (1958), and Hollstien (1971) should at least be mentioned here.
5.3.1 The Canonical Genetic Algorithm for Parameter
Optimization
Even if the originators of the GA approach emphasized that GAs were designed for general
adaptation processes, most applications reported up to now concern numerical optimization
by means of digital computers, including discrete as well as combinatorial optimization.
Books by Ackley (1987), Goldberg (1989), Davis (1987, 1991), Davidor (1990),
Rawlins (1991), Michalewicz (1992, 1994), Stender (1993), and Whitley (1993) may serve
as sources for more details in this eld. As for so-called classi er systems (CS see Holland
et al., 1986) and genetic programming (GP see Koza, 1992), two very interesting special
areas of evolutionary computation{in which GAsplay an important r^ole in searching
for production rules in so-called knowledge-based systems and for correct expressions in
computer programs, respectively{the reader must be referred to the relevant andvast
literature (Alander, 1994 he compiled more than 3,000 references).
The GA for parameter optimization usually has been presented in the following general
form:
Step 0: (Initialization)
Agiven population consists of individuals. Each ischaracterized by its
genotype consisting of n genes, which determine the vitality, or tnessfor
survival. Each individual's genotype is represented by a (binary) bit string,
representing the object parameter values either directly or by means of an
encoding scheme.
Step 1: (Selection)
Two parents are chosen with probabilities proportional to their relative position
in the current population, either measured by their contribution to the