Abstract:
In this paper we propose a modification of Benson’s algorithm for solving
multiobjective linear programmes in objective space in order to approximate
the true nondominated set. We first summarize Benson’s original algorithm
and propose some small changes to improve computational performance. We
then introduce our approximation version of the algorithm, which computes
an inner and an outer approximation of the nondominated set. We prove that
the inner approximation provides a set of ε-nondominated points. This work
is motivated by an application, the beam intensity optimization problem of
radiotherapy treatment planning. This problem can be formulated as a multiobjective
linear programme with three objectives. The constraint matrix of
the problem relies on the calculation of dose deposited in tissue. Since this
calculation is always imprecise solving the MOLP exactly is not necessary
in practice. With our algorithm we solve the problem approximately within
a specified accuracy in objective space. We present results on four clinical
cancer cases that clearly illustrate the advantages of our method.
