  The only rigorous approaches for achieving a numerical proof of optimality in
global optimization are interval-based methods that interleave branching of the
search-space and pruning of the subdomains that cannot contain an optimal
solution. State-of-the-art solvers generally integrate 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.
  Within our cooperative solver Charibde, the evolutionary algorithm and the
interval-based algorithm run in parallel and exchange bounds, solutions and
search-space in an advanced manner via message passing. A comparison of
Charibde with state-of-the-art interval-based solvers (GlobSol, IBBA, Ibex) and
NLP solvers (Couenne, BARON) on a benchmark of difficult COCONUT problems shows
that Charibde is highly competitive against non-rigorous solvers and converges
faster than rigorous solvers by an order of magnitude.
