Self-Adaptive Crossover - Self-Adaptive Heuristics for Evolutionary Computation - page 100

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cp right

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generations generations

Fig. 6.1. Comparison of both randomized crossover points of PMX (left) and both
self-adaptive crossover points of SA-PMX (right) on problem bier127 during 3000 gen-
erations. Each figure shows the two average crossover points of each generation. Left:
The crossover points of PMX are stable, oscillating around the same values during the
whole optimization. Right: The crossover points of SA-PMX are less oscillating, but
drifting into changing directions for many generations.

same values during the whole optimization. The crossover points of SA-PMX are
less oscillating, but drifting into changing directions for many generations. The
question stays open, whether we can derive from these observations that a mean-
ingful adaptation of crossover points occurs and building blocks are identified. In
particular, we see the challenge to tighten the link between strategy parameter
adaptation and fitness. We we hold an undersized link responsible for the short-
comings in comparison to self-adaptation of step sizes. But as already pointed
out in chapter 3, a the convergence of strategy parameters is not a necessary
condition for self-adaptation.

6.4 Self-Adaptive Recombination for Evolution Strategies

(SAR)

We let the concept of self-adaptation discover the beneficial settings for the var-
ious types of crossover parameters of the different operator types. Concerning
its benefits we can argue from different directions. From the point of view of
the BBH this approach is supposed to identify the useful building blocks. From
the point of view of the GR hypothesis self-adaptive crossover can automatically
increase the probability of common successful parental genes. In the following we
will recapitulate the two main crossover operators for ES, intermediate and dom-
inant crossover. Afterwards we introduce a more general operator, self-adaptive
recombination (SAR).