Multiple surrogates for prediction and optimization (my PhD dissertation)

[Felipe A. C. Viana]

Dear all:

I have the pleasure to tell you that I have successfully defended my
(second) PhD last May and now I have the final version of the
dissertation (after some minor corrections). If you are interested in
taking a look at it, it is available at:

https://sites.google.com/site/felipeacviana/publications
(scroll down, it is the first item after the journal publications)

This is a summary of the work:

The aim of surrogate modeling is to construct an approximation of a
response of interest based on a limited number of expensive
simulations. Nevertheless, after years of intensive research on the
field, surrogate-based analysis and optimization is still a struggle
to achieve maximum accuracy for a given number of simulations.

In this dissertation, we have taken advantage of multiple surrogates
to address the issues that we face when we
(i) want to build an accurate surrogate model under limited
computational budget,
(ii) use the surrogate for constrained optimization and the exact
analysis shows that the solution is infeasible, and
(iii) use the surrogate for global optimization and do not know where
to place a set of points in which we are most likely to have
improvement.

In terms of prediction accuracy, we have found that multiple
surrogates work as insurance against poorly fitted models.
Additionally, we propose the use of safety margins to conservatively
compensate for fitting errors associated with surrogates. We were able
to estimate the safety margin for a specific conservativeness level,
and we found that it is possible to select a surrogate with the best
compromise between conservativeness and loss of accuracy.

In terms of optimization, we proposed two strategies for enabling
surrogate-based global optimization with parallel function
evaluations. The first one is based on the simultaneous use of
multiple surrogates (a set of surrogates collaboratively provide
multiple points). The second strategy uses a single surrogate and one
cheap to evaluate criterion (probability of improvement) for multiple
point selection approximation. In both cases, we found that we could
successfully speed up the optimization convergence without clear
penalties as far as number of function evaluations.


Thank you very much,
Felipe A. C. Viana