Fig.1. RGA-algorithm in action: global optimization
via regularized approximation of an unknown objective function
(: again -
no smoothness/continuity is assumed a priori, the OF
acts
as a black box, we should evaluate the
OF at points
"enforced" by RGA only. NB! RGA
does not use any regular grid.).
a) the true function on a regular grid 201x201 with minimum
-0.9953 at the point (0.555, 0.665),
b) movie composed with 7 sequential 'tries' for
reconstructing the OF (and finding the global minimum).
While the first try the RGA evaluates
the OF at 11 (initial, random) points,
and constructs
the differential (regularized)
approximationf
of the OF in the entire area of search (global),
defines extreme points of the f
,
selects
them and enforces to evaluate the OF
at a subset of the extra points :
these extreme points and
relevant OF-values plus
those induced by the initial set of the previous,
first
try
yield data for the second try, and so forth.
The last, seventh try occurred when
200 points/ OF-calls were utilized in total.
The global minimum is detected at the point (0.5588, 0.6641)
with the value -0.9942.
a)
b)
 .
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