Evolution and Optimum Seeking

A Multimembered Evolution Strategy 127
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Probability density
w(s’) for = 1
Parameter = number
of offspring
one obtains from the requirement
the relation
= 1
3
−4 −2 0 2 4
Useful distance s’
10
30
100
Figure 5.7: Probability distribution w(s 0 )
@
@
~'
= opt
opt =~' @
@ ~' = opt
!
=0
and, by substituting it back in Equation (5.17), the result
opt =1+
s
The value obtained iteratively is
5.2.2.2 The Sphere Model
2 opt
exp
1
2 opt
! 2
=
2
~' 2
0
41+ erf@
1
q
2 opt
opt ' 2:5 (as an integer: opt =2or3)
We willnowtry to calculate the rate of progress for the simple spherically symmetrical
model, which is of importance for considering the convergence rate properties of the
strategy. The contours of the objective function F (x) are concentric hypersphere surfaces,
given for example by
F (x) =
nX
i=1
x 2
i = const:
13
A5