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UTILIZING OBJECT-ORIENTED DESIGN TO BUILD ADVANCED
OPTIMIZATION STRATEGIES WITH GENERIC IMPLEMENTATION
M.S.
Eldred*, WE.
Had,
W.J.
Bohnhoff*,
V.J.
RorneroB, S.A. Hutchinsonq, and
AUG
1
fi
I996
Sandia National Laboratories**
Albuquerque,
NM
87
185
Abstract
The benefits of applying optimization to
computational models are well known, but their range of
widespread application to
date
has
been limited. This
effort attempts to extend the disciplinary
areas
to which
optimization algorithms may be readily applied through
the
development and application of advanced
optimization strategies capable of handling the
computational difficulties associated with complex
simulation codes. Towards
this
goal,
a
flexible software
framework is under continued development for the
application
of
optimization techniques
to
broad classes
of engineering applications, including those with high
computational expense and nonsmooth, nonconvex
design space features. Object-oriented software design
with C++ has been employed
as
a
tool in providing
a
flexible, extensible, and robust multidisciplinary toolkit
that establishes the protocol for interfacing optimization
with
computationally-intensive
simulations.
In
this
paper, demonstrations of advanced optimization
Strategies using the software are presented
in
the
hybridization and parallel processing research
areas.
Performance of the advanced strategies is compared
with
a
benchmark nonlinear programming optimization.
*Senior Member of Technical
Staff
(SMTS),
Structural Dynamics Dept.,
Mail
Stop
0439,
AIAA
member.
tSMTS,
Algorithms and Discrete Math DepL
Mail
h4TS,
Intelligent Systems Dept.,
Mail
Stop 1177.
§SMTS,
Thermal Sciences Dept.,
Mail
Stop 0835.
kvlTS,
Parallel Computational Sciences Dept.,
Mail
stop
1111.
'Research Fellow,
Parallel
Computational Sciences
Dept.,
Mail
Stop
1111.
P.O. Box 5800, Albuquerque,
NM
87185, USA.
This work performed at Sandia National Laboratories
supported by the U.S. Department
of
Energy under
contract DE-ACO4-94AL85000.
This
paper is declared
a
work of
the
U.S.
Government and is not subject to
stop 1110.
**
copyright protection in the United States.
n
Introduction
OSTI
Computational methods developed in fluid
mechanics, structural dynamics, heat transfer, nonlinear
large-deformation mechanics, manufacturing and
material processes, and many other fields of engineering
can
be an enormous aid to understanding the complex
physical systems they simulate. Often, it
is
desired to
utilize these simulations
as
virtual prototypes to improve
or optimize the design of
a
particular system. The
optimization effort at Sandia National Laboratories
seeks to enhance the utility of
this
broad class of
computational methods by enabling their use
as
design
tools,
so
that simulations may be used not just for
single-point predictions, but also for improving system
performance
in
an automated fashion. System
performance objectives can be formulated to minimize
weight or defects or to maximize performance,
reliabfity, throughput, reconfigurability, agility, or
design robustness (insensitivity to off-nominal
parameter values). A systematic, rapid method of
determining these optimal solutions
will
lead to better
designs and improved system performance and
will
reduce dependence on hardware and testing, which will
shorten the design cycle and reduce development costs.
Towards these ends,
this
optimization effort has
targeted the needs of
a
broad class of computational
methods in order to provide
a
general optimization
capability. Much work to date in the optimization
community has focused on applying either gradient-
based techniques
to
smooth, convex, potentially
expensive problems' or global techniques to nonconvex
but inexpensive problems2. When the difficulties
of
high
computational expense and nonsmooth, nonconvex
design spaces
are
coupled together, standard
techniques may
be
ineffective and advanced strategies
may
be
required. Moreover, since the challenges of each
application are frequently very different, generality and
flexibility of the advanced strategies
are
key concerns.
The coupling of optimization with complex
computational methods is difficult, and optimization
algorithms often fail to converge efficiently,
if
at
all.
The
difficulties arise from the following
traits,
shared by
many computational methods:
1.
The time required to complete
a
single function eval-
American Institute
of
Aeronautics and Astronautics
‘
uation with one parameter set
is
large. Hence,
mini-
mization of the number of function evaluations
is
vital.
2.
Analytic derivatives (with respect to the parameters)
of the objective and constraint functions are fre-
quently unavailable. Hence, sensitivity-based opti-
~--
I
,@tion methods depend upon numerically
gene&ted gradients which require additional func-
tion evaluations for each scalar parameter.
3.
The parameters may be either continuous or discrete,
or
a
combination of the two.
4.
The objective and constraint functions may not be
smooth or well-behaved; Le., the response surfaces
can be severely nonlinear, discontinuous, or even
undefined in some regions of the parameter space.
The existence of several local extrema (multi-modal-
ity)
is
common.
5.
Convergence tolerances
in
embedded iteration
schemes introduce nonsmoothness (noise)
in
the
function evaluation response surface, which can
result in inaccurate numerical gradients.
6.
Each function evaluation may require an “initial
guess.” Function evaluation dependence on the
ini-
tial guess can cause additional nonsmoothness in the
response surface. Moreover,
a
solution may not be
attainable for an inadequate
initial
guess, which can
restrict the size of the allowable parameter changes.
To
be effective
in
addressing these technical issues, one
must minimize the computational expense associated
with repeated function evaluations (efficiency) and
maximize the likelihood of successful navigation to the
desired optimum (robusmess). Imporrant research areas
for achieving these goals are fundamental algorithm
research, algorithm hybridization, function
approximation, parallel processing, and automatic
differentiation. Research activities
are
ongoing in each
of these
areas
at Sandia National Laboratories. The two
research areas of central interest
in
this paper are:
hybridization of optimization techniques exploits the
strengths of different approaches and avoids their
weaknesses.
In
a
nonconvex design space, for example,
one might initially employ
a
genetic algorithm to
identify regions of high potential, and then switch
to
nonlinear programming techniques to quickly converge
on the local extrema. Through hybridization, the
optimization strategy can be tailored to suit the specific
characteristics of
a
problem.
Parallelprocessing:
The iterative nature
of
optimization lends itself to parallel computing
environments. Since the simulation calls are
independent for methods such
as
genetic algorithms and
coordinate pattern search and for the finite difference
-
-_
Hybrid optimizulion techniques:
The
gradient calculations of
a
nonlinear programming
algorithm, parallelkation can
be
achieved for single
processor simulation codes by simultaneously executing
many simulations, one per processor. Alternatively,
parallel efficiencies can
be
gained through the
interfacing of sequential optimization with parallel (i.e.
multi-processor) simulations. More advanced strategies
involve multi-level parallelism, in which parallel
optimization strategies coordinate multiple
simultaneous simulations of multi-processor codes.
Software
Design
The DAKOTA @sign Analysis Kit for
OpTiition) toolkit utilizes object-oriented design
with C+k3
to
achieve
a
flexible, extensible interface
between analysis codes and system-level iteration
methods.
This
interface is intended to be very general,
encompassing broad classes of numerical methods
which have in common the need for repeated execution
of simulation codes. The scope of iteration methods
available in the DAKOTA system currently includes
a
variety of optimization, nondeterministic simulation,
and parameter study methods. The breadth of algorithms
reflects the belief that no one approach
is
a
“silver
bullet,” in that different problems can have vastly
different feature making some approaches more
amenable than others. Likewise, there
is
breadth
in
the
analysis codes which may be interfaced. Currently,
simulator programs in the disciplines of nonlinear solid
mechanics, structural dynamics, fluid mechanics, and
heat transfer have been
utilized.
The system,
as
will be
demonstrated
in
this
paper,
also
provides
a
platform for
research and development of advanced methodologies.
Accomplishing the interface between analysis
codes and iteration methods in
a
sufficiently general
manner poses
a
difficult software design problem. These
conceptual design
issues
are being resolved through the
use
of object-oriented programming techniques.
In
mating an iterator with an analysis code, generic
interfaces have been built such that the individual
specifics of each iterator and each analysis code
are
hidden. In
this
way, different iterator methods may be
easily interchanged and different simulator programs
may be quickly substituted without affecting the internal
operation
of
the software.
This
isolation of complexity
through the development of generic interfaces is
a
cornerstone of object-oriented design, and is required
for the desired generality and flexibility of advanced
strategies (e.g., hybrid algoriihms and sequential
approximate optimization).
The Application Interface (Figure
1)
isolates
application specifics from an iterator method by
providing
a
generic interface for the mapping of
a
set of
,
DISCLAIMER
Portions
of
this document may be illegible
in electronic image products. Images are
produced from the best available original
document.
,
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report
was
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States
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The views and opinions of authors expressed herein do not necessarily state or
reflect those
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States
Government or any agency thereof.
.