  Proton therapy is a modality in fast development. Characterized by a maximum
dose deposition at the end of the proton trajectory followed by a sharp
fall-off, proton beams can deliver a highly conformal dose to the tumor while
sparing organs at risk and surrounding healthy tissues. New treatment planning
systems based on spot scanning techniques can now propose multi-field
optimization. However, in most cases, this optimization only processes the
field fluences whereas the choice of ballistics (field geometry) is left to the
oncologist and medical physicist.
  In this work, we investigate a new optimization framework based on a genetic
approach. This tool is intended to explore new irradiation schemes and to
evaluate the potential of actual or future irradiation systems. We propose to
optimize simultaneously the target points and beam incidence angles in a
continuous manner and with a variable number of beams. No \textit{a priori}
technological constraints are taken into account, \textit{i.e.}~the beam energy
values, incidence directions and target points are free parameters.
  The proposed algorithm is based on a modified version of classical genetic
operators: mutation, crossover and selection. We use the real coding associated
with random perturbations of the parameters to obtain a continuous variation of
the potential solutions. We also introduce a perturbation in the exchange
points of the crossover to allow variations of the number of beams. These
variations are controlled by introducing a beam fluence lower limit.
  In this paper, we present a complete description of the algorithm and of its
behaviour in an elementary test case. The proposed method is finally assessed
in a clinically-realistic test case.
