Self-Adaptive Crossover - Self-Adaptive Heuristics for Evolutionary Computation - page 101

6.4.1 Intermediate and Dominant Recombination

Two main variants of recombination for ES exist. Intermediate crossover pro-
duces new offspring solutions o =( o 1 ,...,o N ) by calculating the arithmetic
median of ρ randomly selected parents p k with 1

ρ and p k =( p 1 ,...,p N ):

≤ k ≤

ρ

1
ρ

p i o i := (6.15)

k =1

The equation yields the centroid of the selected parents. For discrete represen-
tations rounding procedures have to be used. Dominant crossover chooses each
component from one of the ρ parents randomly with uniform distribution:

o i := p i

with k := Random { 1 ,...,ρ } (6.16)

Dominant crossover became famous as uniform crossover in the field of GAs. In
the case of ρ = μ it is also called global discrete recombination.

6.4.2 Self-Adaptive Recombination

The idea of our SAR is to morph between intermediate and dominant recom-
bination for two parents ( ρ = 2) self-adaptively. We introduce a recombination
coecient vector Ξ , which determines the amount of information inherited by
each parent:

Ξ = ν i with ν i ∈ [0 , 1] and 1 ≤ i ≤ N (6.17)

Hence, each individual a now consists of a vector

a =( x 1 ,...,x N ,σ 1 ,...,σ N ,ν 1 ,...ν N ) (6.18)

During recombination each component o i of the objective part of the offspring
o =( o 1 ,...,o N ) is produced in the following way given the two randomly se-
lected parents p 1 and p 2 :

o i = ν i ν i )

p i +(1 p i

· − · (6.19)

with the strategy variables from parent ζ . In order to enable self-adaptation,
the recombination coecients have to be mutated. We propose to mutate the
recombination coecients with Gaussian meta-EP mutation

ν = ν + γ

·N

(0 , 1) (6.20)

with γ 0 . 1, similar to the mutation of angles [132] and bias coecients, see

section 4. We use the best scheme proposed in section 6.1.3 to determine the
parent ζ .

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