Self-Adaptive Crossover - Self-Adaptive Heuristics for Evolutionary Computation - page 97

Table 6.2. Experimental comparison of 5-point and SA-5-point crossover on onemax,
sphere, ackley and 3-SAT. The figures show the number of generations to reach the
optimum. Again, no consistent picture can be drawn concerning the superiority of any
variant.

best worst mean dev

onemax
5-point 12 32 17.25 0.12

SA-5-point 12 44 18.07 0.22

sphere
5-point

11 83 26.03 2.39

SA-5-point 10 83 27.23 2.73

ackley
5-point 14 412 50.44 58.96

SA-5-point 16 494 52.7 95.11

3-SAT
5-point 11 467 46.57 166

SA-5-point 14 499 42.96 152

experimental analysis. Again, given two parents p 1 and p 2 , the genes are taken
from one of the two parents randomly, in most cases with probability p =0 . 5.
This becomes

o i = p i , j ∈ random { 1,2 } . (6.11)

To equip uniform crossover with self-adaptation (SA uniform), we introduce a
strategy set Σ =( Λ 1 ,...,Λ l )with Λ i ∈{ 0 , 1 } determining from which parents

to take the genes

o i = p Λ i
i

(6.12)

It is equivalent to dSAR, presented in section 6.4.3. We point out the opinion
that self-adaptive uniform crossover could make sense, in particular when the
involved parents come from different mating pools, from different subpopulations
or exhibit maximal Euclidean distance.
In nature, genetic material is exclusively exchanged between two parents.
But the artificial modeling allows to acquit from this restriction. Thus, MPGAs
allow more than two parents to participate in crossover simultaneously. An anal-
ysis of MPGAs can be found in the paper of Ting [153]. The idea of diagonal
crossover is, similarly to N-point crossover, the division of the parental genomes
into N+1 parts and the alternate assembly of the offspring. Self-adaptive di-
agonal crossover (SA-diagonal) works as follows: given ρ , typically ρ = n +1,
parents p 1 ,..., p ρ

and n crossover points Λ 1 ,...,Λ n− 1 ∈{ 1 ,...,l − 1 } with