Multiobjective Decomposition of Positive Integer Matrix: Application to Radiotherapy

Authors:
Thibaut Lust;Jacques Teghem
Affiliations:
Laboratory of Mathematics & Operational Research, Facultéé Polytechnique de Mons, Mons, Belgium 7000;Laboratory of Mathematics & Operational Research, Facultéé Polytechnique de Mons, Mons, Belgium 7000
Venue:
EMO '09 Proceedings of the 5th International Conference on Evolutionary Multi-Criterion Optimization
Year:
2009

Citing 5
Cited 0

Mixed integer programming approaches to exact minimization of total treatment time in cancer radiotherapy using multileaf collimators

Computers and Operations Research
Decomposition of integer matrices and multileaf collimator sequencing

Discrete Applied Mathematics
A new algorithm for optimal multileaf collimator field segmentation

Discrete Applied Mathematics
First vs. best improvement: An empirical study

Discrete Applied Mathematics - Special issue: IV ALIO/EURO workshop on applied combinatorial optimization
Realization of intensity modulated radiation fields using multileaf collimators

General Theory of Information Transfer and Combinatorics

Quantified Score

Hi-index	0.03

Visualization

Abstract

We consider the following problem: to decompose a positive integer matrix into a linear combination of binary matrices that respect the consecutive ones property. The positive integer matrix corresponds to fields giving the different radiation beams that a linear accelerator has to send throughout the body of a patient. Due to the inhomogeneous dose levels, leaves from a multi-leaf collimator are used between the accelerator and the body of the patient to block the radiations. The leaves positions can be represented by segments, that are binary matrices with the consecutive ones property. The aim is to find a decomposition that minimizes the irradiation time, and the setup-time to configure the multi-leaf collimator at each step of the decomposition. We propose for this NP-hard multiobjective problem a heuristic method, based on the Pareto local search method. Experimentations are carried out on different size instances and the results are reported. These first results are encouraging and are a good basis for the design of more elaborated methods.