  We consider the optimal control of a PDE with random source term subject to
probabilistic or almost sure state constraints. In the main theoretical result,
we provide an exact formula for the Clarke subdifferential of the probability
function without a restrictive assumption made in an earlier paper. The focus
of the paper is on numerical solution algorithms. As for probabilistic
constraints, we apply the method of spherical radial decomposition. Almost sure
constraints are dealt with a Moreau--Yosida smoothing of the constraint
function accompanied by Monte Carlo sampling of the given distribution or its
support or even just the boundary of its support. Moreover, one can understand
the almost sure constraint as a probabilistic constraint with safety level one
which offers yet another perspective. Finally, robust optimization can be
applied efficiently when the support is sufficiently simple. A comparative
study of these five different methodologies is carried out and illustrated.
