Adaptive Genetic Algorithms - Computational Intelligence in Time Series Forecasting - page 318

then,

§ f f ·

selcross2 avg

pc () k k (9.8)

¨ ¸

¨ ¸

1cross 1crossbias

f f

© ¹

max avg

elseif,

f f

selcross2 avg

It is

§ ·

f f

selcross min

pc () k ¨ ¸ k (9.9)

¨ ¸

2cross crossbias

f f

© ¹

avg min

with f

corresponds to the fitness of parent 2 and the same is only selected through roulette
wheel, since parent 1 is always the best individual selected of all generations for
the crossover operation. This is because, when the crossover is performed between
the best individual of all generations and worst individual of current generation, the
possibility of generating better individuals is generally low, hence, as per (9.9), the
probability of crossover for such a case is low (set by

k 0.5, k 0.2, k 0.5, and k 0.3. Here,

1cross 2cross 1crossbias 2crossbias selcross2

k 0.3 ).

2crossbias

9.4 Adaptation of Population Size

Genetic algorithm starts with an initial population that is randomly generated so
that it - as far as possible - uniformly represents the entire search space. This
assumes that the knowledge about the search space and the problem to be solved is
a priori available. This also helps - using an efficient heuristics - drive the initial
population in the direction of the most promising problem solution.
The initial population size potentially defines the size of the search space to be
considered and it directly influences the convergence speed and the achievable
solution accuracy. This is closely related to the problem of premature convergence
of the search process and to the problem of search crashes. Therefore, it is
advisable to adapt the population size steadily while executing the search process.
Baker (1985) was the first to show how this could be done. He noticed that the
chromosomes that produce a large number of offspring during the process of
crossover and mutation contribute considerably to the acceleration of convergence
speed. Owing to the limited population size, this forces the rest of the population to
produce a reduced number of offspring, even it prevents some chromosomes from
contributing any offspring at all. This causes a rapid decrease in the population
diversity, which leads to premature convergence of the search process. In order to
monitor this phenomenon, Baker introduced the percent involvement as a measure