Many important application problems in engineering can be formalized as nonlinear
optimization tasks. However, numerical methods for solving such problems
are brittle and do not scale well. For example, these methods depend critically
on choosing a good starting point from which to perform the optimization search.
In high-dimensional spaces, numerical methods have difficulty finding solutions
that are even locally optimal. The objective of this thesis is to demonstrate how
machine learning techniques can improve the performance of numerical optimizers
and facilitate optimization in engineering design.
The machine learning methods have been tested in the domain of 2-dimensional
structural design, where the goal is to find a truss of minimum weight that bears a
set of fixed loads. Trusses are constructed from pure tension and pure compression
members. The difference in the load-bearing properties of tension and compression
members causes the gradient of the objective function to be discontinuous, and this
prevents the application of powerful gradient-based optimization algorithms in this
domain.
In this thesis, the approach to numerical optimization is to find ways of transforming
the initial problem into a selected set of subproblems where efficient,
gradient-based algorithms can be applied. This is achieved by a three-step "compilation"
process.
The first step is to apply speedup learning techniques to partition the overall
optimization task into sub-problems for which the gradient is continuous. Then,
the second step is to further simplify each sub-problem by using inductive learning
techniques to identify regularities and exploit them to reduce the number of
independent variables.
Unfortunately, these first two steps have the potential to produce an exponential
number of sub-problems. Hence, in the third step, selection rules are derived
to identify those sub-problems that are most likely to contain the global optimum.
The numerical optimization procedures are only applied to these selected
sub-problems.
To identify good sub-problems, a novel ID3-like inductive learning algorithm
called UTILITYID3 is applied to a collection of training examples to discover
selection rules. These rules analyze the problem statement and identify a small
number of sub-problems (typically 3) that are likely to contain the global optimum.
In the domain of 2-dimensional structural design, the combination of these
three steps yields a 6-fold speedup in the time required to find an optimal solution.
Furthermore, it turns out that this method is less reliant on a good starting point
for optimization.
The methods developed in this problem show promise of being applied to a
wide range of numerical optimization problems in engineering design. / Graduation date: 1992
| Identifer | oai:union.ndltd.org:ORGSU/oai:ir.library.oregonstate.edu:1957/36513 |
| Date | 13 April 1992 |
| Creators | Cerbone, G. (Giuseppe) |
| Contributors | Dietterich, Thomas G., Cull, Paul |
| Source Sets | Oregon State University |
| Language | en_US |
| Detected Language | English |
| Type | Thesis/Dissertation |
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