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Title |
New Function Approximation Algorithms for Optimization of Nonconvex Complex Models
With Application to Costly Functions Involving Partial Differential Equations
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| Speaker |
Christine A. Shoemaker
Joseph P. Ripley Professor of Engineering
Department of Civil and Environmental Engineering
Cornell University
cas12@cornell.edu |
| Date |
Wednesday, March 24, 2004 |
| Time |
10-11am (PT)
11-12am (MT)
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| Location |
Bldg. 921, Room 137 (Sandia - CA)
Bldg. 980, Room 95 (Sandia - NM)
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| Abstract |
We present a strategy for the constrained global optimization of
expensive black box functions using response surface models. A
response surface model is simply a multivariate approximation of a
continuous black box function which is used as a surrogate model for
optimization in situations where function evaluations are
computationally expensive.
Prior global optimization methods that utilize response surface
models were limited to box-constrained problems, but one of our new
methods (Regis and Shoemaker, Jn. Of Global Optimization, in press)
can easily incorporate general nonlinear constraints. With this
method, which we refer to as the CORS (Constrained Optimization
using Response Surfaces) Method, the next point for costly function
evaluation is chosen to be the one that minimizes the current
response surface model subject to the given constraints and to
additional constraints that the point be of some distance from
previously evaluated points. The distance requirement is allowed to
cycle, starting from a high value (global search) and ending with a
low value (local search). The purpose of the constraint is to drive
the method towards unexplored regions of the domain and to prevent
the premature convergence of the method to some point that may not
even be a local minimizer of the black box function. The new method
can be shown to converge to the global minimizer of any continuous
function on a compact set regardless of the response surface model
that is used.
Numerical results will be shown for our two response surface
algorithms on a range of problems including test functions for
global optimization and some complex real environmental problems
based on field data that require as long as 3 hours per simulation.
The response surface method performs very well in comparison to
other optimization methods.
I will also discuss the development of a new parallel algorithm MAPO
that utilizes function approximation methods. Numerical results
will be presented that demonstrates that MAPO is more robust and
faster than other alternatives.
Joint work with Prof. Shoemaker's Ph.D. student Rommel Regis,
Operations Research and Industrial Engineering
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About the Speaker |
Christine Shoemaker is the Joseph P. Ripley Professor of Engineering
at Cornell University, a position to which she was elected in 2002.
Her long history of research in environmental management,
particularly ground and surface water supply quality, is
distinguished by numerous awards she has received throughout her
career.
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| Host |
Patty Hough, pdhough@ca.sandia.gov, 294-1518
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This seminar series is hosted by the Computational Sciences and
Mathematics Research Department at Sandia National Labs in
Livermore, CA.
This seminar is funded by the Computer Science Research
Institute (CSRI).
To schedule a time to meet with the speaker before or after the talk,
please make arrangements with the host listed above.
Visitors from outside Sandia require at least 3 days notice in order
to attend. For more information, see http://csmr.ca.sandia.gov/csri/visitor.html.
The exception is any U.S. Citizens with a valid DOE badge. In this
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access by going to the badge office in buidling 911 (this access is
valid for a period of one year). Click here
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