On Tue, Oct 19, 2010 at 1:02 AM, Steven G. Johnson <[email protected]>wrote:
> On Oct 18, 2010, at 7:41 PM, Gregory Maxwell wrote: > >> Perhaps your problem is agreeable to this kind of subdivision. >> Otherwise you can probably only hope to search a regular grid of the >> possible integer space and the do only local optimization. The 3^140 >> operations to search the unit-hypercube around even a single integer >> grid point is too computationally expensive to do even with a very >> fast objective function. >> > > Another possibility to consider is a continuous relaxation of your problem. > Can you replace the integer variables approximately by continuous real > variables and optimize that problem? > > (For example, something like this is common in topology optimization where > in principle you are optimizing 0/1 integer variables, and you relax it to > [0,1] continuous variables which are much easier to optimize. Then, if > necessary, you add some penalty function; e.g. a common penalty function in > topology optimization is called "SIMP" for "Solid Isotropic Microstructures > with Penalization".) > > Steven > > Thanks, Each function evaluation is a run over some historical physical daily measurements . With the dimensions I gave above, we would have 40 historical physical measurements. So far there are 3 different kinds of runs. Most of the time, the same kind of run (same computer code) is executed over the 40 historicals. This run uses 5 parameters ( 2 reals between 1 between [0,0.3] and the other between [0.0,1.0] although I can take out this 2nd one from the param space because the function is always decreasing with this param over the 40 historicals) The remaining 3 parameters are number of days in the historical measurements (they can be bound by 500 days) Also 40 is quite an extreme upper bound to the number of historical measurements. The most frequent case is under 15. Can this then be subdivided as in G. Maxwell's email? Should the optimization be over [1.0, 500.0] in continuous? Thank you,
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