 st division 
 2nd division .
(a) (b)
Figure 83. 1 st iteration of DIRECT windowing for 2 dimensional example, Goldstein
Price (GP) function (Finkel, 2003), and (b) further iterations on GP function
with potentially optimal boxes shaded and subsequently divided along longest
dimensionss.
The design space is divided into thirds along the dimension with the minimum wi.
The center box is then divided again into thirds along the dimension with the next
smallest wi, and so on. Thus, the minimum function value for the iteration is in the largest
subdivision of the original box in the iteration (Figure 83 (a)). DIRECT then determines
potentially optimal boxes, using both the function value at the center of the box and the
size of the box. DIRECT divides potential optimum boxes along their longest
dimensionss, using the same procedure at the initial division. Thus, if, as in the initial
division, the box is a hypercube in n = N dimensions with the side length of the cube
greater than the other side lengths, it is divided along those n dimensions. Multiple
67207
3542.4 6 00.4 200.6

107
we =min f c + ) /( e , er fri=(1 ,..N (6)
w, = 200.6 "" "
alaa 5 b b b
l ~ ~ ll1