Self-Adaptive Crossover - Self-Adaptive Heuristics for Evolutionary Computation - page 102

6.4.3 SAR Variants

We propose two obvious variants of the SAR operator. The variant individual
SAR ( iSAR ) makes use of only one self-adaptive parameter ν [0 , 1] on indi-

vidual and not component level. Hence, every individual a is now a vector

∈

a =( x 1 ,...,x N ,σ 1 ,...,σ N ,ν ) (6.21)

with only one recombination strategy variable. Similar to SAR, a new offspring
solution o is now produced with

p i +(1 p i

o i = ν · − ν ) · (6.22)

This variant reduces the self-adaptation effort, but does not allow a component
level adaptation.
The morphing between dominant and intermediate crossover is continuous for
the SAR operator. In order to switch discretely between both variants we intro-
duce the discrete SAR ( dSAR ), which uses an N-dimensional strategy vector of
bits.

Ξ = ν i with ν i ∈{ 0 , 1 } and 1 ≤ i ≤ N (6.23)

These bits determine, which recombinationtypetouse.Wedefine0forinter-
mediate and 1 for discrete recombination. Hence, o is produced by
o i := 2 p i + 2 p i

if ν i =0

(6.24)

p i with k := Random {

1 , 2

}

if ν i =1

From the EDA point of view, see section 3.7, SAR controls the distances of
particular distributions

M i with 1 ≤ i ≤ μ of the mixture distribution M .

6.4.4 Experimental Analysis

We tested the introduced variants on various typical test functions:

• sphere ( N = 10),

• rastrigin ( N = 10),

• rosenbrock with noise in fitness ( N = 10),

• sharp ridge ( N = 10),

• and the constrained problem 2.40 ( N =5).

Now we present a comparison of the proposed SAR variants with intermediate
(int) and dominant (dom) recombination. We use the following experimental
settings.