A shortest path-based approach to the multileaf collimator sequencing problem

Hadrien Cambazard (1) , Eoin O'Mahony (2) , O'Sullivan Barry (2)

1 G-SCOP_ROSP - Recherche Opérationnelle pour les Systèmes de Production
2 4C UCC - Cork Constraint Computation Centre

The rnultileaf collimator sequencing problem is an important component in effective cancer treatment delivery. The problem can be formulated as finding a decomposition of an integer matrix into a weighted sequence of binary matrices whose rows satisfy a consecutive ones property. Minimising the cardinality of the decomposition is an important objective and has been shown to be strongly NP-hard, even for a matrix restricted to a single column or row. We show that in this latter case it can be solved efficiently as a shortest path problem, giving a simple proof that the one-row problem is fixed-parameter tractable in the maximum intensity. We develop new linear and constraint programming models exploiting this result. Our approaches significantly improve the best known for the problem, bringing real-world sized problem instances within reach of exact algorithms.

Domaines: Recherche opérationnelle [math.OC]

Hadrien Cambazard, Eoin O'Mahony, O'Sullivan Barry. A shortest path-based approach to the multileaf collimator sequencing problem. Discrete Applied Mathematics, 2012, 160 (1-2), pp.81-99. ⟨10.1016/j.dam.2011.09.008⟩. ⟨hal-00790845⟩