I have a model that is solved, returns a single output value and plots it. From those values, I plot a surface using x-values varying from 1-35 and y-values varying from 1-39, and have the returned values as values on the z-axis. See below.
This figure does not behave according to a defined function, it is simply a plot of output values.
I've been trying to use a random optimization algorithm that I created in an attempt to find the global maximum, but it takes a very long time and isn't always correct (when compared to a grid-search algorithm that I use as a comparison). The surface that is created has subtle changes in it, enough to create multiple troublesome local minima and maxima. I'm looking for a way to find the global maximum of this non-convex surface in a relatively quick fashion.
EDIT:
35-by-39 is the search area and that's as big as it gets. The values of the x and y axes are the input values of the model (probably shouldve mentioned that), so each of the z-values are associated with an x and y input coordinate. And my initial guess is usually smack dab in the middle of the search area.
The creation of this figure took about 50 minutes, because each of the 1365 z-values takes about 3 seconds to compute. I'd like to do this without having to use exhaustive enumeration (evaluating every point for a z-value). I'd like this to take around 5 minutes instead of 50.
EDIT(2):
Sorry for the confusion. The figure below is a 35-by-39 grid of z-values and is used purely for reference. In the actual executing of the program, all I have is the x- and y-coordinates, and I am trying to find the global maximum z-value in the fewest function evaluations possible in order to save time. So horchler, in reference to your comment, the latter.
EDIT(3):
The thing with this figure is its only a single example. There are multiple different figures that are formed when I use data from a separate source (i.e. the left side might be uninteresting in this example, but for a separate set of data, it may or may not contain the global max). And this adds to the complexity. It is impossible to tell from the data where the location of the global max will be. Some surfaces are incredibly smooth, others have large and frequent peaks throughout.