If you have no clue about your objective? Then you should spend some time in learning about it, thinking about it, plot it, etc. If you know absolutely nothing about what you are trying to solve, are unwilling to do the necessary work in advance, then you are probably the wrong person to be doing this optimization.
You should never just throw a function at some optimizer and expect something meaningful to come out, with no thought invested. Well, if you do, expect less than useful results. So plot your function. Does it appear to have simple behavior? Is it continuous? Differentiable? Smoothly so? Are there bumps in the function, multiple dips? Should there be? Verify that your plots make sense in context of what you know or expect. Do there appear to be local minima on the boundary?
Yes, if your function is highly multi-dimensional, then all of this gets harder. Things can get nasty in high dimensions.
In general, an objective can be arbitrarily complex. There is no simple scheme that will always work to come up with a good set of starting values. If there were, then optimization tools would use it!
In the case of your plotted function, it appears to live on a triangular domain. (If not, then why is that what you have shown us?) So I assume the region arises from your constraints. The function appears to be relatively well posed, with a probable minimum somewhere in the interior.
If the function has some global minimum that lies outside of your constraint boundary, that is irrelevant. All you care about are minima that lie inside, and it appears to be quite a simple shape. So what is the problem?
If you are worried and still have no clue, then pick multiple points inside the boundary. Use the best of the lot as your start point.