Evolution and Optimum Seeking

Test Problems for the Second Part of the Strategy Comparison 343
Start:
x (0)
i =10 for i = 1(1)n F (x (0) )=5 10 10
Only the two strategies that have a quadratic internal model of the objective function,
namely the variable metric and conjugate directions methods, failed to converge, because
the function F (x) isofmuch higher (10th) order.
Problem 2.24 after Rosenbrock (1960)
Objective function:
Minimum:
Start:
Problem 2.25
Objective function:
Minimum:
F (x) =
F (x) = 100 (x 2 ; x 2
1) 2 +(x 1 ; 1) 2
x =(1 1) F (x )=0
x (0) =(;1:2 1) F (x (0) )=24:2
nX
i=2
x 1 ; x 2
i
2
+(xi ; 1) 2 for n =5
x i =1 for i = 1(1)n F (x )=0
Figure A.17: Graphical representation of Problem 2.24
F (x) ==0:5 4 20 100 250 500 1000 2000 5000=