g$01$

$$

$$

Minimize The following function using harmony search

$f(vec(x))=5{\displaystyle \underset{i=1}{\overset{4}{}}}{x}_i-5{\displaystyle \underset{i=1}{\overset{4}{}}}{x}_i^2-{\displaystyle \underset{i=5}{\overset{13}{}}}{x}_i$

Subject to:

$g_1(vec(x))=2x_1+2x_2+x_{10}+x_{11}-100$

$g_2(vec(x))=2x_1+2x_3+x_{10}+x_{12}-100$

$g_3(vec(x))=2x_2+2x_3+x_{11}+x_{12}-100$

$g_4(vec(x))=-8x_1+x_{10}0$

$g_5(vec(x))=-8x_2+x_{11}0$

$g_6(vec(x))=-8x_3+x_{12}0$

$g_7(vec(x))=-2x_4-x_5+x_{10}0$

$g_8(vec(x))=-2x_6-x_7+x_{11}0$

$g_9(vec(x))=-2x_8-x_9+x_{12}0$

where $)=(1,$dots,$9(i=10,11,12)$ y $0x_{13}1.$ The feasible global optimum is located at $x^{**}=(1,1,1,1,1,1,1,1,1,3,3,3,1)$ where $f(x^{**})=-15$ and $g_1,g_2,g_3,g_7,g_8,g_9$ are active constraints.