Optimization

149Guided Random Search Methods

as Rastrigin and Schwefel’s function to demonstrate that GA can locate the

global minimum for these functions.

The two-variable Rastrigin’s function (see Figure 5.6) is given by

f x x x x

x

( ) cos( ) cos( )

.

x = + − + −

− ≤

20 10 2 10 2

5 12

1

2

1 2

2

2

1

π π

,, .x

2

5 12≤

The function has a number of local optima and the global minimum value

of the function is f(x*) = 0 and occurs at x* = (0, 0). The function can be plotted

in MATLAB using the following commands.

0 200 400 600 800 1000

1225

1225.05

1225.1

1225.15

1225.2

1225.25

1225.3

1225.35

1225.4

Generation number

U

FIGURE 5.5

Variation of objective function value with increase in nu