Evolutionary Computation - Computational Intelligence in Time Series Forecasting - page 212

5.6.1 First Variant of Differential Evolution (DE1)

The first variant of differential evolution works as follows: for each vector in
generation G , i.e.

iG X i

,( 0,1,2, , " N ) , a trial vector X is generated as

, pop 1 vG

XX KX X

vG , a G , a G , a G ,

1 3 2

with

¼ . The integers a 1 , a 2 and a 3 are mutually different from

aa a , , ¬ ª , N º

1 2 3 pop 1

each other, and K > 0.

K .( X a3,G - X a2,G )

global minimum

X 2

o

o

o

o o

o o o

o

X a1,G

X a2,G

o

o

X a3,G

o N

X i,G

o

X v,G+1 o

N Newly generated vector

o

o Vector from generation G

X 1

Figure 5.6. First variant of differential evolution (DE1)

Furthermore, the integers a 1 , a 2 and a 3 are chosen randomly from the interval
[0, N pop-1 ] such that they are different from the running index i . The real constant
factor K controls the amplification of the differential variation X X .

Figure 5.6 shows a two-dimensional example that illustrates the different vectors
and generation of a trial vector which play an important role in DE1.
In order to increase the potential diversity of the perturbed parameter vectors,
crossover is introduced. The crossover operation generates the perturbed vector as
follows:

aG , aG ,

3 2

X X , X , " , X

uG , 1 u G , 1 u G , 1 u , G 1

0 1 ( D 1)

with,

- X for j n , n 1 , " , n L 1 .

°
®

vG , 1

D D D

j

X

uG , 1

> @

j

X for all other j 0, D 1 .

° ¯ ji G ,