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Title: Modifications of the DIRECT Algorithm.
Authors: Gablonsky, Jorg M.
Advisors: C. T. Kelley, Chair
J. C. Dunn, Member
P.A. Gremaud, Member
M. Shearer, Member
Issue Date: 22-May-2001
Degree: PhD
Discipline: Applied Mathematics
Abstract: This work presents improvements of a global optimization method for boundconstraint problems along with theoretical results. These improvements arestrongly biased towards local search. The global optimization method known asDIRECT was modified specifically for small-dimensional problems with few globalminima. The motivation for our work comes from our theoretical results regarding thebehavior of DIRECT. Specifically, we explain how DIRECT clusters its search neara 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, bycombining them with another global optimization method known as ImplicitFiltering. In addition to these improvements the methods were also extended tohandle problems where the objective function is defined solely on an unknownsubset of the bounding box. We demonstrate the increased effectiveness androbustness of our modifications using optimization problems from the natural gastransmission industry, as well as commonly used test problems from theliterature.
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