An Application of the Extended Cutting Angle Method in Radiation Therapy
department or school: Arts and Sciences, Irving K. Barber School of (Okanagan)
department or school: Computer Science, Mathematics, Physics and Statistics, Department of (Okanagan)
data provider: DSpace
degree campus: UBCO
creator: Koch, Valentin
issued: 2010-07-30T19:53:01Z
issued: 2008
description: Global optimization of continuous, non-linear functions are very hard problems, especially when the functions are multivariate and when analytical information is not available. Heuristic methods like simulated annealing provide good results. However, if time is a critical factor, those methods may deliver suboptimal solutions and give little information about the quality of the solutions. Methods of Lipschitz optimization allow one to nd and con rm the global minimum of multivariate Lipschitz functions using a nite number of function evaluations. The Extended Cutting Angle Method (ECAM), proposed by Gleb Beliakov, is a fast method to optimize a Lipschitz function over multiple dimensions. The first objective was to fully implement the proposed algorithm and to test it on a family of classic global optimization problems. A second objective was to apply the algorithm to the problem of optimizing the radiation treatment for cancer patients. In radiotherapy, several x-ray beams are delivered to the tumor from di erent angles around the patient. The ECAM was tested against a simulated annealing algorithm to nd the optimal angles of the beams in order to deliver the prescribed radiation dose to the tumor and to minimize the damage to healthy tissue.
aggregated CHO: https://circle.library.ubc.ca/rest/handle/2429/27046
note: An Application of the Extended Cutting Angle Method in Radiation Therapy by Valentin Koch A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF Bachelor of Science Honours in The I. K. Barber School of Arts & Sciences (Computer Science) The University Of British Columbia April, 2008 c© Valentin Koch 2008 Abstract Global optimization of continuous, non-linear functions are very hard problems, especially when the functions are multivariate and when analytical information is not available. Heuris- tic methods like simulated annealing provide good results. However, if time is a critical factor, those methods may deliver suboptimal solutions and give little information about the quality of the solutions. Methods of Lipschitz optimization allow one to find and confirm the global minimum of multivariate Lipschitz functions using a finite number of function evaluations. The Extended Cutting Angle Method (ECAM), proposed by Gleb Beliakov, is a fast method to optimize a Lipschitz function over multiple dimensions. The first objective was to fully implement the proposed algorithm and to test it on a family of classic global optimization problems. A second objective was to apply the algorithm to the problem of optimizing the radiation treatment for cancer patients. In radiotherapy, several x-ray beams are delivered to the tumor from different angles around the patient. The ECAM was tested against a simulated annealing algorithm to find the optimal angles of the beams in order to deliver the prescribed radiation dose to the tumor and to minimize the damage to healthy tissue. ii Acknowledgements First of all, I would like to thank my supervisor Dr. Yves Lucet for his guidance and coordination towards this thesis. Without his ideas and support, this work would not have been possible. Also, I express a special thank you to Dr. Gleb Beliakov for his infinite patience in answering all of my questions and for the help he provided to implement his algorithm. Th…
has type: Graduating Project
is shown at: 10.14288/1.0052223
language: eng
peer review status: Unreviewed
provider: Vancouver : University of British Columbia Library
rights: Attribution-NonCommercial-NoDerivatives 4.0 International
rights URI: http://creativecommons.org/licenses/by-nc-nd/4.0/
scholar level: Undergraduate
is part of: University of British Columbia. COSC 449
type: Text
identifier URI: http://hdl.handle.net/2429/27046