Self-Adaptive Crossover - Self-Adaptive Heuristics for Evolutionary Computation - page 95

self-adaptive 1-point crossover selects the crossover point Λ ζ of one of the two
parents according to the proposed selection schemes and creates the two children

o 1 =( p 1 ,...,p Λ ζ ,p Λ ζ +1 ,...,p l ,Λ ζ ) (6.7)

and

o 2 =( p 1 ,...,p Λ ζ ,p Λ ζ +1 ,...,p l ,Λ ζ ) . (6.8)

The crossover point Λ k at locus k is the position between element k and k +1.
We proposed three schemes for the decision, which crossover point to take in
section 6.1.3. The strategy part Λ ζ may be encoded as an integer or in binary
representation as well. In order to enable self-adaptation the crossover point Λ ζ
has to be mutated. For this purpose meta-EP or log-normal mutation and the
usage of rounding procedures is proposed, see section 6.1.3.

Experimental settings
Population model generational, μ = 150

Mutation type bit flipping, p m =0 . 001 (onemax, sphere),

p m =0 . 005 (ackley, 3-SAT)

Strategy mutation meta-EP

1-point, SA-1-point, p c =1 . 0

Crossover type

Selection type generational model

Initialization random bits

Termination optimum found

Runs 50

The bigger mutation strength of p m =0 . 005 on the problems ackley and 3-
SAT showed better results than p m =0 . 001, which was better on onemax and
sphere. We used gray coding for the numerical functions. Table 6.1 shows the

Table 6.1. Experimental comparison of 1-point and SA-1-point crossover on onemax,
sphere, ackley and 3-SAT. The figures show the number of generations until the op-
timum is found. No significant superiority of any of the two 1-point variants can be
detected.

best worst mean dev

onemax
1-point 16 93 28.88 2.23

SA-1-point 13 71 27.68 1.97

sphere
1-point

11 102 42.25 4.99

SA-1-point 16 89 40.33 4.10

ackley
1-point 13 438 63.50 86.83

SA-1-point 15 455 57.01 58.95

3-SAT
1-point 15 491 63.68 291

SA-1-point 7 498 62.72 264