  In very long baseline interferometry (VLBI) the combination of multiple
antennas permits the synthesis of a virtual telescope with a larger diameter
and consequently higher resolution than the individual antennae. Yet, due to
the sparse nature of the array, recovering an image from the observed data is a
challenging ill-posed inverse problem. The VLBI community is interested in not
only recovering an image in total intensity from interferometric data, but also
to obtain results in the polarimetric and the temporal domain. Only a few
algorithms are able to work in all these domains simultaneously. In particular,
the algorithms based on optimization that consider various penalty terms
specific to static total intensity imaging, time-variability and polarimetry
are restricted to grids the domain of the objective function. In this work we
present a novel algorithm, multiobjective particle swarm optimization, that is
able to recover the optimal weights without any space-gridding, and to obtain
the marginal contribution of each the playing terms. To this end, we utilize
multiobjective optimization together with particle swarm metaheuristics. We let
the swarm of weights to converge together to the best position. We evaluate our
algorithm with representative synthetic data sets focused on the instrumental
configuration of the Event Horizon Telescope Collaboration and its planned
successors. We successfully recover the polarimetric, static and time-dynamic
signature of the ground truth movie, even with relative sparsity, and a set of
realistic data corruptions. This is a novel, fast, weighting space
gridding-free algorithm that successfully recovers static and dynamic
polarimetric reconstructions. Compared to Regularized Maximum Likelihood
methods, it avoids the need for parameter surveys, and it is not limited to the
number of pixels such as recently proposed multiobjective imaging algorithms.
