The initial population for a GA search is usually selected randomly, although there may be occasions when heuristic selection is appropriate (Grefenstette ). 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.