CP and IP approaches to cancer radiotherapy delivery optimization

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 mod...

• Type: Journal
• Year: 2011
• Where: CONSTRAINTS
• Authors: Davaatseren Baatar, Natashia Boland, Sebastian Brand, Peter J. Stuckey
• Keywords: Cancer Radiation Therapy, Communications, CONSTRAINTS 2011, Integer Programming Formulations, Radiation Therapy Treatment