Recent developments show that derivative free methods are highly demanded by researches for solving optimization problems in various practical contexts.
Although well-known optimization methods that employ derivative information can be very effcient, a derivative free method will be more effcient in cases
where the objective function is nondifferentiable, the derivative information is
not available or is not reliable. Derivative Free Optimization (DFO) is developed
for solving small dimensional problems (less than 100 variables) in which
the computation of an objective function is relatively expensive and the derivatives
of the objective function are not available. Problems of this nature more
and more arise in modern physical, chemical and econometric measurements
and in engineering applications, where computer simulation is employed for the
evaluation of the objective functions.
In this thesis, we give an example of the implementation of DFO in an approach
for optimizing stirrer configurations, including a parametrized grid generator,
a flow solver, and DFO. A derivative free method, i.e., DFO is preferred because
the gradient of the objective function with respect to the stirrer&rsquo / s design variables is not directly available. This nonlinear objective function is obtained
from the flow field by the flow solver. We present and interpret numerical results
of this implementation. Moreover, a contribution is given to a survey and
a distinction of DFO research directions, to an analysis and discussion of these.
We also state a derivative free algorithm used within a clustering algorithm in
combination with non-smooth optimization techniques to reveal the effectiveness
of derivative free methods in computations. This algorithm is applied on
some data sets from various sources of public life and medicine. We compare
various methods, their practical backgrounds, and conclude with a summary
and outlook. This work may serve as a preparation of possible future research.
| Identifer | oai:union.ndltd.org:METU/oai:etd.lib.metu.edu.tr:http://etd.lib.metu.edu.tr/upload/2/12606591/index.pdf |
| Date | 01 July 2005 |
| Creators | Akteke, Basak |
| Contributors | Karasozen, Bulent |
| Publisher | METU |
| Source Sets | Middle East Technical Univ. |
| Language | English |
| Detected Language | English |
| Type | M.S. Thesis |
| Format | text/pdf |
| Rights | To liberate the content for METU campus |
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