Abstract
GABLONSKY, J
¨
ORG MAXIMILIAN XAVER. Modifications of the DIRECT Algo-
rithm. (Under the direction of Carl Timothy Kelley.)
This work presents improvements of a global optimization method for bound con-
straint problems along with theoretical results. These improvements are strongly
biased towards local search. The global optimization method known as DIRECT was
modified specifically for small-dimensional problems with few global minima. The
motivation for our work comes from our theoretical results regarding the behavior
of DIRECT. Specifically, we explain how DIRECT clusters its search near a global
minimizer. An additional influence is our explanation of DIRECT’s behavior for both
constant and linear functions.
We further improved the effectiveness of both DIRECT, and our modification, by
combining them with another global optimization method known as Implicit Filtering.
In addition to these improvements the methods were also extended to handle problems
where the objective function is defined solely on an unknown subset of the bounding
box. We demonstrate the increased effectiveness and robustness of our modifications
using optimization problems from the natural gas transmission industry, as well as
commonly used test problems from the literature.
