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Finance Notes_Part_41 - Interpolate or smooth to f,C on...

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A strawman surrogate approach Given surrogates s f and S Ω of both the objective function and the constraints. Minimize s f ( x ) for S Ω ( x ) 0 to obtain x s . Every user has their favorite approach for this part Compute f ( x s ) , C ( x s ) to determine if improvement has been made over the best x found to date. But, what if no improvement was found? Audet and Vicente (SIOPT 2008) Surrogates, global DFO, software, and references 95/109
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A strawman surrogate approach Given surrogates s f and S Ω of both the objective function and the constraints. Minimize s f ( x ) for S Ω ( x ) 0 to obtain x s . Every user has their favorite approach for this part Compute f ( x s ) , C ( x s ) to determine if improvement has been made over the best x found to date. But, what if no improvement was found? Audet and Vicente (SIOPT 2008) Surrogates, global DFO, software, and references 95/109
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Response surface global models Choose a space filling set of points. – say by Latin hypercube or orthogonal array sampling. Run the expensive simulations at these sites.
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Unformatted text preview: Interpolate or smooth to f,C on this data. May be able to interpolate to gradients as well – Alexandrov Audet and Vicente (SIOPT 2008) Surrogates, global DFO, software, and references 96/109 Form of the DACE interpolants Polynomials introduce extraneous extremes that trap strawman Spline-like DACE interpolants can be written ˆ s ( x ) = d X i =1 w i ( x ) f ( x i ) . DACE predictions at any x are weighted averages of f at the data sites. Weight depends on how far site is from x . Correlation parameters for each site are estimated. Audet and Vicente (SIOPT 2008) Surrogates, global DFO, software, and references 97/109 Surrogate Management Framework-6 ± ± ± ± ± ± ±² f x 1 x 2 * * * is the incumbent solution Audet and Vicente (SIOPT 2008) Surrogates, global DFO, software, and references 98/109...
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