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On column generation approaches for approximate solutions of quadratic programs in intensity-modulated radiation therapy
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.ORCID iD: 0000-0002-6252-7815
2014 (English)In: Annals of Operations Research, ISSN 0254-5330, E-ISSN 1572-9338, Vol. 223, no 1, 471-481 p.Article in journal (Refereed) Published
Abstract [en]

This paper deals with numerical behavior of a recently presented column generation approach for optimization of so called step-and-shoot radiotherapy treatment plans. The approach and variants of it have been reported to be efficient in practice, finding near-optimal solutions by generating only a low number of columns. The impact of different restrictions on the columns in a column generation method is studied, and numerical results are given for quadratic programs corresponding to three patient cases. In particular, it is noted that with a bound on the two-norm of the columns, the method is equivalent to the conjugate-gradient method. Further, the above-mentioned column generation approach for radiotherapy is obtained by employing a restriction based on the infinity-norm and non-negativity. The column generation method has weak convergence properties if restricted to generating feasible step-and-shoot plans, with a "tailing-off" effect for the objective values. However, the numerical results demonstrate that, like the conjugate-gradient method, a rapid decrease of the objective value is obtained in the first few iterations. For the three patient cases, the restriction on the columns to generate feasible step-and-shoot plans has small effect on the numerical efficiency.

Place, publisher, year, edition, pages
2014. Vol. 223, no 1, 471-481 p.
Keyword [en]
Column generation, Conjugate-gradient method, Intensity-modulated radiation therapy, Step-and-shoot delivery
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-158803DOI: 10.1007/s10479-013-1360-1ISI: 000345073400024OAI: oai:DiVA.org:kth-158803DiVA: diva2:785288
Funder
Swedish Research Council
Note

QC 20150202

Available from: 2015-02-02 Created: 2015-01-12 Last updated: 2017-12-05Bibliographically approved

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Forsgren, Anders

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