Evolution and Optimum Seeking

136 Evolution Strategies for Numerical Optimization
Making use of the relation (see Ryshik and Gradstein, 1963)
one nally obtains
Zp
y=0
erf( y) dy = p erf( p)+ exp(; 2 p2 ) ; 1
p
~p(jx`ij b) = erf
p !
2 b
+ 1 p
2 b
In the following we refer to this expression as item v.
v =~p(jx`ij b)
"
exp
; 2 b2
2
!
#
; 1
(5.24)
With the above de nition of v, the total probability that a descendant N` is feasible, i.e.,
that it satis es all the constraints, is
pf eas =
and the probability that N` is lethal is
nY
i=2
= v n;1
~p(jx`ij b)
pleth =1; pf eas =1; v n;1
Only non-lethal mutants come into consideration as parents of the next generation. Hence,
instead of w(s` = s0 )wemust insert into Equation (5.15) the expression
w(s` = s 0 ) pf eas = 1
p 2
and instead of p(s`