Evolutionary Computation - Computational Intelligence in Time Series Forecasting - page 195

5.2.1.1 Selection
Individuals or chromosomes are selected from the mating pool , based on a roulette
wheel ( RW ) selection procedure . This selection emulates the survival-of-the-fittest
mechanism in nature. It is expected that a fitter chromosome will give rise to a
higher number of offspring and thus will have a higher chance of surviving in the
subsequent generation. There are many ways to achieve effective selection,
including ranking, tournament, and proportionate schemes (Tang et al ., 1996), but
the key assumption is to give preference to fitter individuals. The RW selection
procedure commonly used to implement the proportionate scheme can be described
as follows.

x Sum the fitness of all population members, termed total fitness F s .
x Generate a random number r between 0 and 1 and multiply this by the total
fitness, i.e.

0 < r <1 and 0 < rF s < F s (5.1a)

x Pick up the i th population member whose fitness added to the sum of the
fitness of the preceding population members is greater than or equal to rF s,
as expressed by

i 1

r d ¦ f f , i d (5.1b)

F N

s pop

i j

j 1

5.2.1.2 Reproduction
In the reproduction process, once an individual is selected, this is simply
reproduced (copied) into the next generation's population if a certain test condition
is satisfied. For example, the individual j selected from the mating pool is simply
copied into the next generation if a random number generated is greater than the
probability of reproduction (a small number less than 1). If a new individual is
generated through reproduction then the population counter is incremented by 1
starting with a 0 value. Using the reproduction operator, only 20% of the total
population is created for the next generation.

5.2.1.3 Mutation
Mutation is an operator that introduces variations into the chromosomes. The
variation can be global or local. The operation occurs occasionally (usually with
small probability P ( M )) but randomly alters the value of the string position. In the
mutation process, any particular bit location of an individual is changed to 1 if it
was 0, or vice versa . Once an individual is selected, then the particular bit of the
same chromosome is simply mutated if a certain condition is satisfied, i.e . if it
passes the probability test condition. For example, the bit location 1 of an
individual j will undergo mutation if a random number generated is greater than
probability of mutation (a very small number less than 1). Otherwise, that
particular bit remains unaffected. The same process is continued from bit location