Inverse radiation therapy planning: a multiple objective optimization approach
Discrete Applied Mathematics - Special issue: Third ALIO-EURO meeting on applied combinatorial optimization
Mathematical Programming: Series A and B
A Column Generation Approach to Radiation Therapy Treatment Planning Using Aperture Modulation
SIAM Journal on Optimization
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
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
Hybrid methods for the multileaf collimator sequencing problem
CPAIOR'10 Proceedings of the 7th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
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We consider a problem dealing with the efficient delivery of intensity modulated radiation therapy (IMRT) to individual patients. IMRT treatment planning is usually performed in three phases. The first phase determines a set of beam angles through which radiation is delivered, followed by a second phase that determines an optimal radiation intensity profile (or fluence map). This intensity profile is selected to ensure that certain targets receive a required amount of dose while functional organs are spared. To deliver these intensity profiles to the patient, a third phase must decompose them into a collection of apertures and corresponding intensities. In this paper, we investigate this last problem. Formally, an intensity profile is represented as a nonnegative integer matrix; an aperture is represented as a binary matrix whose ones appear consecutively in each row. A feasible decomposition is one in which the original desired intensity profile is equal to the sum of a number of feasible binary matrices multiplied by corresponding intensity values. To most efficiently treat a patient, we wish to minimize a measure of total treatment time, which is given as a weighted sum of the number of apertures and the sum of the aperture intensities used in the decomposition. We develop the first exact algorithm capable of solving real-world problem instances to optimality within practicable computational limits, using a combination of integer programming decomposition and combinatorial search techniques. We demonstrate the efficacy of our approach on a set of 25 test instances derived from actual clinical data and on 100 randomly generated instances.