Evolution and Optimum Seeking

Test Problems for the Second Part of the Strategy Comparison 333
Start:
Figure A.7: Graphical representation of Problem 2.7 on the planes
left: x3 = 0, right: x3 = ;1,
F (x) ==0:03 0:3 1' 3:064 10 30=
x (0) =(0 20 20) F (x (0) ) ' 1022
Many strategies only roughly located the rst of the strong minima de ned above. The
evolution strategies tended to converge to the weak minimum, since the minima are at
equal values of the objective function. The second strong minimum, which is never referred
to in the relevant literature, was sometimes found by the multimembered evolution
strategy.
Problem 2.8
As Problem 2.7, but with
Start:
Problem 2.9
Objective function:
Minimum:
Start:
x (0) =(0 10 20) F (x (0) ) ' 1031
F (x) =
nX
i=1
(
iX
j=1
xj) 2 for n =5
x i =0 for i = 1(1)n F (x )=0
x (0)
i =10 for i = 1(1)n F (x (0) ) = 5500