Evolution and Optimum Seeking

350 Appendix A
Constraints:
Gj(x) =xj 0 for j = 1(1)3
G 4(x) =;x 1 ; 2 x 2 ; 2 x 3 +72 0
The underlying question here was: What dimension should a parcel of maximum volume
have, if the sum of its length and transverse circumference is bounded?
Minimum:
Start:
x =(24 12 12) F (x )=;3456 G 4 active
x (0) =(0 0 0) F (x (0) )=0
All variants of the evolution strategy converged only to within the neighborhood of the
minimum sought, because in the end only a fraction of all trials were feasible.
Problem 2.36
This is derived from Problem 2.35 by treating the constraint G 4,which is active at the
minimum, as an equation, and thereby eliminating one of the free variables. With
we obtain
x 0
1 +2x 0
2 +2x 0
3 =72
F 0 (x) =;(72 ; 2 x 0
2 ; 2 x 0
3) x 2 x 3
or by renumbering of the variables a new objective function:
F (x) =;x 1 x 2 (72 ; 2 x 1 ; 2 x 2)
Figure A.22: Graphical representation of Problem 2.36
F (x) == ; 3400 ;3000 ;2000 ;1000 ;300 300 1000=