  Imaging in radioastronomy is an ill-posed inverse problem. Particularly the
Event Horizon Telescope (EHT) Collaboration investigated the fidelity of their
image reconstructions convincingly by large surveys solving the problem with
different optimization parameters. This strategy faces a limitation for the
existing methods when imaging the active galactic nuclei (AGN): large and
expensive surveys solving the problem with different optimization parameters
are time-consumptive. We present a novel nonconvex, multiobjective optimization
modeling approach that gives a different type of claim and may provide a
pathway to overcome this limitation. To this end we used a multiobjective
version of the genetic algorithm (GA): the Multiobjective Evolutionary
Algorithm Based on Decomposition, or MOEA/D. GA strategies explore the
objective function by evolutionary operations to find the different local
minima, and to avoid getting trapped in saddle points. First, we have tested
our algorithm (MOEA/D) using synthetic data based on the 2017 Event Horizon
Telescope (EHT) array and a possible EHT + next-generation EHT (ngEHT)
configuration. We successfully recover a fully evolved Pareto front of
non-dominated solutions for these examples. The Pareto front divides into
clusters of image morphologies representing the full set of locally optimal
solutions. We discuss approaches to find the most natural guess among these
solutions and demonstrate its performance on synthetic data. Finally, we apply
MOEA/D to observations of the black hole shadow in Messier 87 (M87) with the
EHT data in 2017. MOEA/D is very flexible, faster than any other Bayesian
method and explores more solutions than Regularized Maximum Likelihood methods
(RML).
