CRPC-TR95550: Managing Approximation Models in Optimization

J. E. Dennis, Virginia Torczon

July, 1995

It is standard engineering practice to use approximation models in place 
of expensive simulations to drive an optimal design process based on 
nonlinear programming algorithms.  This paper uses well-established 
notions from the literature on trust-region methods and a powerful 
global convergence theory for pattern search methods to manage the 
interplay between optimization and the fidelity of the approximation 
models to insure that the process converges to a reasonable solution of 
the original design problem.  We present a specific example from the 
class of algorithms outlined here, but many other interesting options 
exist that we will explore in later work.

The algorithm we present as an example of the management strategies we 
propose is based on a family of pattern search algorithms developed by 
the authors.  Pattern search methods can be successfully applied when 
only ranking (ordinal) information is available and when derivatives are 
either unavailable or unreliable.  Since we are interested here in using 
approximations to provide arguments for the objective function, our 
choice seems relevant.

This work is in support of the Rice effort in a collaboration with 
Boeing and IBM to look at the problem of designing helicopter rotor 
blades.