The initial population for a GA search is usually selected randomly,
although there may be occasions when heuristic selection is
appropriate (Grefenstette [34]). Within the algorithm, population
selection is based on the principle of `survival of the fittest.'
The standard procedure is to define the probability of a particular
solution **i**'s survival to be:

if the objective function is to
be maximized, where is
the * fitness* (objective value) of solution **i**, and

is the total fitness of the population (of size **N**), or

if **f** is to be minimized. The new population is then selected by
simulating the spinning of a suitably weighted roulette wheels **N**
times.