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Minimizing the Number of Apertures in Multileaf Collimator Sequencing with Field Splitting

  • In this paper we consider the problem of decomposing a given integer matrix A into a positive integer linear combination of consecutive-ones matrices with a bound on the number of columns per matrix. This problem is of relevance in the realization stage of intensity modulated radiation therapy (IMRT) using linear accelerators and multileaf collimators with limited width. Constrained and unconstrained versions of the problem with the objectives of minimizing beam-on time and decomposition cardinality are considered. We introduce a new approach which can be used to find the minimum beam-on time for both constrained and unconstrained versions of the problem. The decomposition cardinality problem is shown to be NP-hard and an approach is proposed to solve the lexicographic decomposition problem of minimizing the decomposition cardinality subject to optimal beam-on time.

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Author:Horst W. Hamacher, Ines M. Raschendorfer, Davaatseren Baatar, Matthias Ehrgott
URN (permanent link):urn:nbn:de:hbz:386-kluedo-42065
Serie (Series number):Report in Wirtschaftsmathematik (WIMA Report) (159)
Document Type:Preprint
Language of publication:English
Publication Date:2015/10/26
Year of Publication:2015
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2015/10/28
Tag:Beam-on time; Decomposition cardinality; Field splitting; Intensity modulated radiation therapy; Multileaf collimator sequencing
Number of page:29
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
MSC-Classification (mathematics):90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C10 Integer programming
Licence (German):Standard gemäß KLUEDO-Leitlinien vom 30.07.2015