Evolutionary Computation - Computational Intelligence in Time Series Forecasting - page 199

a (5.7)

f f f

avg avg min

avg

b 1 a (5.8)

f

Once the values of a and b are calculated, the scaling is done as per Equation
(5.3). In order to avoid the division by zero situation, when the denominator of
(5.5) and (5.7) are close to zero during the matured run of the GA, a very small
constant ( k 1 ) of the order of k 1 = 0.0001 can be added to their denominators.

5.2.3 Real-coded Genetic Algorithms

Genetic algorithms, being gradient-free and parallel optimization algorithms, have
immense advantages over the conventional search methods.

01001000 01111000 11001100 011 010 01100101 Chromosome

Genes from chromosome

01001000 01111000

Gene elements

0 1 0 0 1

GA Binary Coding

2.5673 0.1492 1.4352 0.12 37 0.1191 Chromosome

Gene / elements

2.5673 0.1492

GA Real Coding

Figure 5.2. Coding in genetic algorithms

Genetic algorithms, like other parallel optimization algorithms, use a
performance criterion for evaluation and a population of possible solutions to
search for a global optimum (Michalewicz, 1994). In each search step, the
algorithms select the prosperous solutions and manipulate them using appropriate
genetic operators to achieve new, and possibly better solutions. The manipulations
are carried out on chromosomes in which the parameters of possible solutions are
encoded. In each generation of the GA, the new population replaces the solutions
in the population that are selected for deletion.
The chromosomes can be represented or encoded either by binary values
(Goldberg, 1989) or by real numbers (Michalewicz, 1994). The genetic algorithms
with binary coded chromosomes, when applied to multidimensional, high-precision
or continuous complex problems, are less efficient because, in such situations, the
bit-strings can become very long. Furthermore, CPU time is lost for the conversion
between the binary and real representation. Here, other alphabets, like real-coding,
can favourably be applied to parameters' or variables' presentation in the
continuous domain of values.