Machine learning in engineering : techniques to speed up numerical optimization Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/jw827h26w

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  • 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.
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  • Figures in original document are black and white photocopies. Best scan available.
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