A Shortest Path-Based Approach to the Multileaf Collimator Sequencing Problem

Authors:
Hadrien Cambazard;Eoin O'Mahony;Barry O'Sullivan
Affiliations:
Cork Constraint Computation Centre Department of Computer Science, University College Cork, Ireland;Cork Constraint Computation Centre Department of Computer Science, University College Cork, Ireland;Cork Constraint Computation Centre Department of Computer Science, University College Cork, Ireland
Venue:
CPAIOR '09 Proceedings of the 6th International Conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Year:
2009

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Abstract

The multileaf 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 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 line problem is fixed-parameter tractable in the maximum intensity. This result was obtained recently by [9] with a complex construction. We develop new linear and constraint programming models exploiting this idea. Our approaches significantly improve the best known for the problem, bringing real-world sized problem instances within reach of complete methods.