Evolutionary Computation - Computational Intelligence in Time Series Forecasting - page 211

operator procedure and eventually by applying the elitist strategy , which could
amend the selection of parents for the next generation.

5.5.1 Evolutionary Programming Mechanism

In evolutionary programming, each offspring is generated from its parent by
changing one or more alleles in the chromosome. In biological terms, this
represents a mutation. Now, because the selection of a new parent is based on the
fitness of the organism, the Darwinian procedure of “ survival of the fittest ” is
applied. Therefore, the procedure listed above can be described as a living
organism that produces one or more offspring through mutation. A survival-of-the-
fittest procedure helps in selecting the best parents for the next generation, so that
the organism evolves by trying to maximize its fitness ( i.e . trying to solve the given
problem as best as possible).

5.6 Differential Evolution

Differential evolution is a population-based search strategy and an evolutionary
algorithm that has recently proven to be a valuable method for optimizing real-
valued multi-modal objective functions (Storn and Price 1995, 1996). It is a
parallel direct search method having good convergence properties and simplicity in
implementation. The method utilizes N pop parameter vectors as a population X

iG

for each generation G , where " . The number of parameter vectors,

i.e. N pop , does not change during the optimization (minimization) process and the
initial population is chosen randomly, unless a preliminary solution is available.
Where a preliminary solution is available, then the remaining population of the
starting generation is often generated by adding normally distributed random
deviations to the nominal solution.
The crucial idea behind the differential evolution is a new scheme for
generating trial parameter vectors by adding the weighted difference vector
between two population members to a third member. If the newly generated vector
results in a lower objective function value (higher fitness) than the predetermined
population member, then the resulting vector replaces the vector with which it was
compared. The comparison vector can, but need not essentially, be part of the
above generation process. In addition, the best parameter vector is evaluated for
every generation G in order to keep track of the progress that is made during the
minimization process. Extracting both distance and direction information from the
population to generate random deviations results in an adaptive scheme that has
excellent convergence properties (Storn and Price, 1995).
There are several variants of differential evolution, with the two most
promising variants being

i 0, 1, 2, , N

pop 1

x DE1, the first variant of differential evolution
x DE2, the second variant of differential evolution.