Evolution and Optimum Seeking

A Multimembered Evolution Strategy 141
7
6
5
4
3
2
1
0
1
Maximal universal rate
of progress
ϕ * ( σ * )
max opt
(1+1) - theory
Number of descendants
10 20 30 40 50 λ 60
Figure 5.14: Maximal rate of progress for the corridor model
+
=
opt
p
2
' + =
'max p
2 opt c
"
c = 1 ; 1 ; exp
; opt
p
2
Pairs of values found by iteration are shown in Figure 5.13. Figure 5.14 shows ' max
versus .To determine opt for the (1 , ) strategy, i.e., the value of for which ' max= is
a maximum, it is necessary to solve the system of three non-linear equations, comprising
Equation (5.29), Equation (5.30), and
The result is
opt = ' + np exp (' +2 )[ erf (' + ) + 2 exp ( + ) ; 1][1+2' +2 ]+2' + o
!#
( opt
c [1 ; exp (; + )] ln[1 ; exp(; + )]+ 1
opt ' 6:0 (as an integer: opt =6)
)
(5.31)