CP and IP approaches to cancer radiotherapy delivery optimization

Authors:
Davaatseren Baatar;Natashia Boland;Sebastian Brand;Peter J. Stuckey
Affiliations:
Department of Mathematics, University of Melbourne, Melbourne, Australia;School of Mathematical and Physical Sciences, University of Newcastle, Newcastle, Australia;NICTA Victoria Research Lab, Department of Computer Science and Software Engineering, University of Melbourne, Melbourne, Australia;NICTA Victoria Research Lab, Department of Computer Science and Software Engineering, University of Melbourne, Melbourne, Australia
Venue:
Constraints
Year:
2011

Citing 11
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Abstract

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.