Evolution and Optimum Seeking

106 Evolution Strategies for Numerical Optimization
In this, as in all direct search methods, it is not possible to deal with constraints in the
form of equalities.
5.1.1 The Basic Algorithm
The two membered scheme is the minimal concept for an imitation of organic evolution.
The two principles of mutation and selection, which Darwin (1859) recognized to be most
important, are taken as rules for variation of the parameters and for ltering during the
iteration sequence respectively.
In the language of biology, the rules are as follows:
Step 0: (Initialization)
A given population consists of two individuals, one parent and one descendant.
They are each identi ed by their genotype according to a set of n genes. Only
the parental genotype has to be speci ed as starting point.
Step 1: (Mutation)
The parent E (g) of the generation g produces a descendant N (g) , whose genotype
is slightly di erent from that of the parent. The deviations refer to the
individual genes and are random and independent of each other.
Step 2: (Selection)
Because of their di erent genotypes, the two individuals have a di erent capacity
for survival (in the same environment). Only one of them can produce
further descendants in the next generation, namely the one which represents
the higher survival value. It becomes the parent E (g+1) of the generation g +1.
Thus the simplest possible assumptions are made:
The population size remains constant
An individual has in principle an in nitely long life span and capacity for producing
descendants (asexually)
No di erence exists between genotype (encoding) and phenotype (appearance), or
that one is unambiguously and reproducibly associated with the other
Only point mutations occur, independently of each other at all single parameter
locations
The environment andthus the criterion of survival is constant over time
This minimal concept takes no accountoftheevolutionary factors familiar to the modern
synthetic evolution theory (e.g., Stebbins, 1968 Cizek and Hodanova, 1971 Osche,
1972), such aschromosome mutations, bisexuality, recombination, diploidy, dominance
and recessiveness, population size, niching, isolation, migration, etc. Even the concepts
of mutation and selection are not applied here with their full biological meaning. Natural
selection does not simply mean the struggle between just two individuals in which the