Discrete Mathematics
CP '99 Proceedings of the 5th International Conference on Principles and Practice of Constraint Programming
Nonnegative integral subset representations of integer sets
Information Processing Letters
Selected Topics in Column Generation
Operations Research
Minimum Cardinality Matrix Decomposition into Consecutive-Ones Matrices: CP and IP Approaches
CPAIOR '07 Proceedings of the 4th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Computers and Operations Research
The sum-of-increments constraint in the consecutive-ones matrix decomposition problem
Proceedings of the 2009 ACM symposium on Applied Computing
A Shortest Path-Based Approach to the Multileaf Collimator Sequencing Problem
CPAIOR '09 Proceedings of the 6th International Conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Sequencing and Counting with the multicost-regular Constraint
CPAIOR '09 Proceedings of the 6th International Conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Discrete Applied Mathematics
Decomposition of integer matrices and multileaf collimator sequencing
Discrete Applied Mathematics
A new algorithm for optimal multileaf collimator field segmentation
Discrete Applied Mathematics
Discrete Applied Mathematics
Optimal Multileaf Collimator Leaf Sequencing in IMRT Treatment Planning
Operations Research
A note on improving the performance of approximation algorithms for radiation therapy
Information Processing Letters
A shortest path-based approach to the multileaf collimator sequencing problem
Discrete Applied Mathematics
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The multileaf collimator sequencing problem is an important component of the effective delivery of intensity modulated radiotherapy used in the treatment of cancer. 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. In this paper we extend the state-of-the-art optimisation methods for this problem, which are based on constraint programming and decomposition. Specifically, we propose two alternative hybrid methods: one based on Lagrangian relaxation and the other on column generation. Empirical evaluation on both random and clinical problem instances shows that these approaches can out-perform the state-of-the-art by an order of magnitude in terms of time. Larger problem instances than those within the capability of other approaches can also be solved with the methods proposed.