caa a22 4500 445879319 CHVBK 20180317145537.0 cr unu---uuuuu 170323e20110401xx s 000 0 eng 10.1007/s10601-010-9104-1 doi (NATIONALLICENCE)springer-10.1007/s10601-010-9104-1 CP and IP approaches to cancer radiotherapy delivery optimization [Elektronische Daten] [Davaatseren Baatar, Natashia Boland, Sebastian Brand, Peter Stuckey] We consider the problem of decomposing an integer matrix into a positively weighted sum of binary matrices that have the consecutive-ones property. This problem is well-known and of practical relevance. It has an important application in cancer radiation therapy treatment planning: the sequencing of multileaf collimators to deliver a given radiation intensity matrix, representing (a component of) the treatment plan. Two criteria characterise the efficacy of a decomposition: the beam-on time (the length of time the radiation source is switched on during the treatment), and the cardinality (the number of machine set-ups required to deliver the planned treatment). Minimising the former is known to be easy. However finding a decomposition of minimal cardinality is NP-hard. Progress so far has largely been restricted to heuristic algorithms, mostly using linear programming, integer programming and combinatorial enumerative methods as the solving approaches. We present a novel model, with corresponding constraint programming and integer programming formulations. We compare these computationally with previous formulations, and we show that constraint programming performs very well by comparison. Springer Science+Business Media, LLC, 2010 Modelling nationallicence Symmetry-breaking nationallicence Search nationallicence Integer programming nationallicence Intensity-modulated radiation therapy nationallicence Multileaf collimator leaf sequencing nationallicence Baatar Davaatseren Department of Mathematics, University of Melbourne, Melbourne, Australia aut Boland Natashia School of Mathematical and Physical Sciences, University of Newcastle, Newcastle, Australia aut Brand Sebastian NICTA Victoria Research Lab, Department of Computer Science and Software Engineering, University of Melbourne, Melbourne, Australia aut Stuckey Peter NICTA Victoria Research Lab, Department of Computer Science and Software Engineering, University of Melbourne, Melbourne, Australia aut Constraints Springer US; http://www.springer-ny.com 16/2(2011-04-01), 173-194 1383-7133 16:2<173 2011 16 10601 https://doi.org/10.1007/s10601-010-9104-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10601-010-9104-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Baatar Davaatseren Department of Mathematics, University of Melbourne, Melbourne, Australia aut NATIONALLICENCE 700 1- Boland Natashia School of Mathematical and Physical Sciences, University of Newcastle, Newcastle, Australia aut NATIONALLICENCE 700 1- Brand Sebastian NICTA Victoria Research Lab, Department of Computer Science and Software Engineering, University of Melbourne, Melbourne, Australia aut NATIONALLICENCE 700 1- Stuckey Peter NICTA Victoria Research Lab, Department of Computer Science and Software Engineering, University of Melbourne, Melbourne, Australia aut NATIONALLICENCE 773 0- Constraints Springer US; http://www.springer-ny.com 16/2(2011-04-01), 173-194 1383-7133 16:2<173 2011 16 10601 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer