Mitchell, T. J. (2010) An exploration of evolutionary computation ...

t = 0;
initialise P(t);
evaluate P(t);
loop begin
loop end;
P'(t) = select(P(t));
P(t+1) = recombine(P'(t));
P(t+1) = mutate(P(t+1));
evaluate(P(t+1));
t = t + 1;
Figure 2.2: Canonical GA pseudocode
Where P and P' denote the population and mating pool respectively at time t. Subsequent
to initialisation (usually random), each individual of the population is decoded and applied
to the objective function to retrieve a value of fitness. In the canonical GA, selection is
facilitated probabilistically using the so-called roulette wheel selection mechanism. Each
individual is represented by a sector of a notional wheel, sized in proportion to its fitness.
A spin of the wheel yields a mating candidate, which is copied into a temporary mating
pool (P') in preparation for variation by recombination and mutation.
The recombination operator is termed crossover, and provides the primary source of
variation within a GA. The most basic GA recombination technique is known as single-
point crossover, which operates by simply concatenating the first part of one parent string
with the second part of another; where both the crossover point and the participating parent
strings are chosen at random. Crossover is responsible for combining useful segments from
the gene pool to form fitter solutions. This concept is otherwise known as the building
block hypothesis, which states that short combinations of highly fit genes (building blocks)
evolve simultaneously throughout the population (implicit parallelism). Well-adapted
building blocks are assembled by recombination to create highly fit descendants
(Goldberg, 1989). This also relates to Holland‘s schema theory, which states that an
exponentially increasing number of trials are allocated to useful building blocks (or
schemata) from one generation to the next (Holland, 1975).
In the theory that relates to the canonical GA, it is considered that the genes of the optimal
individual are distributed throughout the population from the outset. Optimisation is then
the process of correctly assembling those genes, which is achieved principally by the
recombination operator. The mutation operator is widely considered to be the background
source of variation (Goldberg, 1989, pp14), as it has the potential to destroy building
blocks through random change. However, it is possible that a 0 or 1 positioned at a certain
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