Evolution and Optimum Seeking

Test Problems for the Second Part of the Strategy Comparison 347
Problem 2.30
As Problem 2.3, but with the constraints
G 1(x) =;x +300 0 G 2(x) =x +300 0
The introduction of constraints gives rise to two equivalent, global minima at the edge of
the feasible region:
Minima:
x = 300 F (x ) ';299:7 G 1 or G 2 active
In addition there are ve local minima within the feasible region. Here too, the absolute
minima were only located by the multimembered evolution strategy.
Problem 2.31
As Problem 2.4, but with constraints:
Minimum:
Start:
Gj(x) =xj ; 1 0 for j =1(1)n n =5
x i =1 for i = 1(1)n F (x )=0 all Gj active
x (0)
i = ;10 for i = 1(1)n F (x (0) ) = 61105
The starting point is located outside of the feasible region.
Figure A.20: Diagram F (x) for Problem 2.30