Evolutionary Computation - Computational Intelligence in Time Series Forecasting - page 214

5.6.2 Second Variant of Differential Evolution (DE2)

Basically the second variant of differential evolution also works in the same way as
the first variant DE1, but it generates a new trial vector X

according to vG , 1

X X K X X K X X ,

vG , 1 iG , bestG , iG , a G , a G , 3 2

because X X

K

X X , introducing an additional

vG 1, 1 iG , bestG , iG ,

control variable K.

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

global minimum

X 2

o

o

o

o

X v1,G

o o

o

o o

X best,G

o

o

X a2,G

o N

X i,G

o

o

X v,G+1

N Newly generated vector

o

o Vector from generation G

X a3,G

X 1

Figure 5.8. Second variant of differential evolution (DE2)

The idea behind K is to provide a means to enhance the greediness of the
scheme by incorporating the best vector from the current generation. In order to
reduce the differential evolution control parameters, K is usually set. This

feature can be useful for non-critical objective functions. Figure 5.8 illustrates the
trial vector generation process for the generation G +1, defined by the above
equation. The construction of perturbed vector

K

X

through a crossover uG , 1

operation from trial vector X and randomly selected i X vector, as well as

the decision process, are exactly same as the first variant of differential evolution.

vG , 1

References

[1] Fogel DB (1994) Evolutionary Programming: An introduction and some current

directions, Statistics and Computing, vol. 4: 113-129.

[2] Fogel LJ, Owens AJ, and Walsh MJ (1966) Artificial intelligence through Simulated

Evolution. Wiley, New York.

[3] Goldberg DE (1989) Genetic algorithms in search, optimization and machine

learning, Addison-Weseley publishing co. Inc., Reading, MA.