Adaptive Genetic Algorithms - Computational Intelligence in Time Series Forecasting - page 317

p rk () (9.5)

2rep

where selre f represents the fitness value of the chromosome (individual) selected
by the roulette wheel selection mechanism for further genetic (reproduction)
operation. The values of other constant terms in the right-hand side expression, e.g.

k have been selected in the adaptive GA
experiment (Palit and Popovic, 2000). Note that, in (9.4), when the best individual
with highest fitness

k 0.9, k and 0, 0.1,

1rep 2rep 1repbias

, the
probability of reproduction p ( r ) = 1 and that for an average individual

f is selected by the roulette wheel, i.e. f f

max selrep max

avg f is
only 0.1 (set by the bias term in (9.4)). On the other hand, the sub-average
individual cannot be reproduced at all, as per (9.5), since p ( r ) = 0.
Similarly, for the adaptive probability of mutation, i.e. for p ( m ), the following
mathematical expressions were used. If

f t f

selmu avg

then

§ ·

f f

pm () k

max selmu

k . (9.6)

¨ ¸

¨ ¸

1mu 1mubias

f f

© ¹

max avg

Otherwise, when

f f

selmu avg

then,

§ f f ·

avg selmu

pm () k k , (9.7)

¨ ¸

¨ ¸

2mu 2mubias

f f

© ¹

avg min

where the following values for the constant terms have been selected: k 0.01 ,

1mu

k Here, as per (9.6), the best
individual will undergo the lowest mutation (since p ( m ) = 0.005), whereas the
average individual will undergo a moderate level of mutation (since p ( m ) = 0.015).
On the other hand, the worst chromosome, as per (9.7), will have the highest
possibility of mutation (since p ( m ) = 0.095).
Furthermore, for the crossover probability p ( c ) the following relations hold. If

k 0.09, k 0.005, and 0.005.

2mu 1mubias 2mubias

f t f

selcross2 avg