  Context. The TRAPPIST-1 system hosts seven Earth-sized, temperate exoplanets
orbiting an ultra-cool dwarf star. As such, it represents a remarkable setting
to study the formation and evolution of terrestrial planets that formed in the
same protoplanetary disk. While the sizes of the TRAPPIST-1 planets are all
known to better than 5% precision, their densities have significant
uncertainties (between 28% and 95%) because of poor constraints on the planet's
masses. Aims.The goal of this paper is to improve our knowledge of the
TRAPPIST-1 planetary masses and densities using transit-timing variations
(TTV). The complexity of the TTV inversion problem is known to be particularly
acute in multi-planetary systems (convergence issues, degeneracies and size of
the parameter space), especially for resonant chain systems such as TRAPPIST-1.
Methods. To overcome these challenges, we have used a novel method that employs
a genetic algorithm coupled to a full N-body integrator that we applied to a
set of 284 individual transit timings. This approach enables us to efficiently
explore the parameter space and to derive reliable masses and densities from
TTVs for all seven planets. Results. Our new masses result in a five- to
eight-fold improvement on the planetary density uncertainties, with precisions
ranging from 5% to 12%. These updated values provide new insights into the bulk
structure of the TRAPPIST-1 planets. We find that TRAPPIST-1\,c and e likely
have largely rocky interiors, while planets b, d, f, g, and h require envelopes
of volatiles in the form of thick atmospheres, oceans, or ice, in most cases
with water mass fractions less than 5%.
