  Reliable global optimization is dedicated to finding a global minimum in the
presence of rounding errors. The only approaches for achieving a numerical
proof of global optimality are interval branch and bound methods that
interleave branching of the search-space and pruning of the subdomains that
cannot contain an optimal solution. It is of the utmost importance: i) to
compute sharp enclosures of the objective function and the constraints on a
given subdomain; ii) to find a good approximation (an upper bound) of the
global minimum.
  State-of-the-art solvers are generally integrative methods, that is they
embed local optimization algorithms to compute a good upper bound of the global
minimum over each subspace. In this document, we propose a cooperative
framework in which interval methods cooperate with evolutionary algorithms. The
latter are stochastic algorithms in which a population of candidate solutions
iteratively evolves in the search-space to reach satisfactory solutions.
Evolutionary algorithms, endowed with operators that help individuals escape
from local minima, are particularly suited for difficult problems on which
traditional methods struggle to converge.
  Within our cooperative solver Charibde, the evolutionary algorithm and the
interval-based algorithm run in parallel and exchange bounds, solutions and
search-space via message passing. A novel strategy prevents premature
convergence toward local minima. A comparison of Charibde with state-of-the-art
solvers (GlobSol, IBBA, Ibex) on a benchmark of difficult problems shows that
Charibde converges faster by an order of magnitude. New optimality results are
provided for five multimodal problems, for which few solutions were available
in the literature. Finally, we provide the first numerical proof of optimality
for the open Lennard-Jones cluster problem with five atoms.
