Applications of the SDL Global Optimization Method in DNA Microarray Data Analysis - DNA Microarray Technology and Data Analysis in Cancer Research - page 77

Fig. 5.10. Local optimization methods locate the minimum closest to the starting
point. Global optimization techniques may find other local minima, but cannot ensure that
the absolute lowest has been found. The region investigated by SDL sampling is progres-
sively narrowed (designated as 1 to 6) to ascertain a true global minimum.
to a two-gene problem. Let the values along the x -axis represent gene
IDs of the first gene variable; and values along the y -axis, gene IDs of
the second gene variable. The objective function value is plotted in the
z -direction.
The task of the process then is to find the x and y values that generate
the highest value of the objective function. In this description, one shall
invert the objective function back since a peak is easier to see than a val-
ley. One form of objective function can be transformed into the other by
taking a reciprocal of it. Therefore, one chooses the form of objective func-
tion whose value increases as the design performance improves, i.e. we
want to maximize the objective function. The game is to change each gene
variable in order to maximize the objective function. To help understand
the optimization process, consider the analogy of a man wandering in a
cratered terrain with a global positioning satellite (GPS) receiver, which
displays his absolute x- , y- , and z -coordinates. Height ( z ) is the objective
function, and x , y represent the gene IDs of each gene variable in a
two-gene problem. His task is to find the highest point (largest objective