6.2 Random Search Methods 311
Figure 6.3 (continued).
6.2.1 Random Jumping Method
Although the problem is an unconstrained one, we establish the boundslianduifor
each design variablexi, i = 1 , 2 ,... , n, for generating the random values ofxi:
li≤xi≤ui, i= 1 , 2 ,... , n (6.16)
In the random jumping method, we generate sets ofnrandom numbers,(r 1 , r 2 ,... , rn),
that are uniformly distributed between 0 and 1. Each set of these numbers is used to
find a point,X, inside the hypercube defined by Eqs. (6.16) as
X=
x 1
x 2
..
.
xn
=
l 1 +r 1 (u 1 −l 1 )
l 2 +r 2 (u 2 −l 2 )
..
.
ln+rn(un−ln)
(6.17)
and the value of the function is evaluated at this pointX. By generating a large number
of random pointsXand evaluating the value of the objective function at each of these
points, we can take the smallest value off (X)as the desired minimum point.
