UCSC-SOE-10-10: Optimization Subject to Hidden Constraints via Statistical Emulation

Herbert Lee, Robert Gramacy, Crystal Linkletter, and Genetha Gray
04/04/2010 09:00 AM
Applied Mathematics & Statistics
We present new methodology for constrained optimization based on building a combination of models, one for the objective function and one for the constraint region. We use a treed Gaussian process as a statistical emulator for the complex objective function, and a random forest to model the probability of meeting the constraints. By combining these models, we can guide the optimization search to promising areas in terms of both the objective function and the constraint. This approach avoids the problem of becoming stuck in a local mode, as well as being able to deal with unconnected viable regions. We demonstrate our methodology on a simulated problem and an example from hydrology.