Evolution and Optimum Seeking

360 Appendix A
Start:
Figure A.31: Graphical representation of Problem 2.48
F (x) == ; 4 ;16 ;36 ;64 ;100 ;144 ;196 ;256=
x 00 ' (6:293 2:293) F (x 00 ) ';44:86
x (0) =(0 0) F (x (0) )=0
There are two feasible regions which are unconnected and closed. The starting point and
the global minimum are separated by a non-feasible region. Only the (10 , 100) evolution
strategy converged to the global minimum. It sometimes happened with this strategy that
one descendant of a generation would jump from one feasible region to the other however,
the group of remaining individuals would converge to one of the other local minima. All
other strategies did not converge to the global minimum.
Problem 2.49 after Wolfe (1966)
Objective function:
Constraints:
Minimum:
Start:
F (x) = 4
3 (x2
1 + x 2
2 ; x1 x2) 3
4 + x3 Gj(x) =xj 0 for j = 1(1)3
x =(0 0 0) F (x )=0 all Gj active
x (0) =(10 10 10) F (x (0) ) ' 52:16