Numerical Results

A numerical simulation of constructional selection in the NK model was performed using the genome growth algorithm illustrated in Figure 1:

1.

  Add a new gene to the genome:

(a)

create a new pleiotropy vector $\mbox{\boldmath\(p\)\unboldmath }_{n+1}$, choosing uniformly (from $\{1, \ldots, 31\}$) the number, k_n+1, of fitness components to be affected by the new gene, and then selecting randomly which fitness components these are, from a set of f=31 possible;

(b)

pick the allelic value, x_n+1, of the new gene with probability 1/2 being either 0 or 1.

2.

  If the new gene decreases fitness, reject it and repeat step 1. Otherwise, keep it.

3.

Adapt $\mbox{\boldmath\(x\)\unboldmath }$ to the new (local) optimum $\hat{\mbox{\boldmath\(x\)\unboldmath }}$ by allelic substitution through a ``greedy'' 1-mutant adaptive walk.

4.

Repeat step 1 until the genome has 31 genes.

The pleiotropy vectors, $\mbox{\boldmath\(p\)\unboldmath }_{n+1}$, are chosen from the same uniform distribution throughout the run. As a basis for comparison, the genome growth algorithm is also run without step 2, giving the result of choosing representations a priori.