  We consider the following problem: to decompose a nonnegative integer matrix
into a linear combination of binary matrices that respect the consecutive ones
prop- erty. This problem occurs in the radiotherapy treatment of cancer. The
nonnegative 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 in- homogeneous 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
efficient decompositions that simultaneously minimize the irradiation time, the
cardinality of the decomposition and the setup-time to configure the multi-leaf
collimator at each step of the decomposition. We propose for this NP-hard
multiobjective combinatorial problem a heuristic, based on the adaptation of
the two-phase Pareto local search. Experiments are carried out on different
size instances and the results are reported.
