Evolution and Optimum Seeking

358 Appendix A
Figure A.29: Graphical representation of Problem 2.46
F (x) ==0:04 0:36 1:00 1:96 3:24 4:84 6:76=
Problem 2.47 after Ueing (1971)
Objective function:
Constraints:
Minimum:
F (x) =;x 2
1 ; x 2
2
Gj(x) = xj 0 for j =1 2
G 3(x) = x 2
1 + x 2
2 ; 17 x 1 ; 5 x 2 +66 0
G 4(x) = x 2
1
+ x2
2 ; 10 x 1 ; 10 x 2 +41 0
G 5(x) = x 2
1 + x 2
2 ; 4 x 1 ; 14 x 2 +45 0
G 6(x) = ;x 1 +7 0
G 7(x) = ;x 2 +7 0
x =(6 0) F (x )=;36 G 2 and G 3 active
Besides the global minimum x there are three other local minima:
Start:
x 0 ' (2:116 4:174) F (x 0 ) ';21:90
x 00 =(0 5) F (x 00 )=;25
x 000 =(5 2) , F (x 000 )=;29
x (0) =(0 0) F (x (0) )=0