The use of commercial flowsheeting programs enables straight-forward use of rigorous, but user hidden, mathematical formulations of chemical processes. The optimization of such black-box models is a challenging task due to nonconvexity, absence of accurate derivatives, and simulation convergence failures which can prevent classical optimization procedures from continuing the search. Here, we present an optimization framework based on the extended cutting plane algorithm with additional heuristic techniques and strategies designed to improve its practical performance for solving nonconvex simulation-based MINLP problems. The new algorithmic features include two approaches for dealing with nonconvexities; the first technique expands the search space to restore feasibility of the MILP subproblems, and the second is a restarting technique to avoid premature termination to non-optimal solutions. We also propose two approaches for handle simulation failures, based on no-good cuts and backtracking. The proposed optimization framework is successfully applied to four case studies dealing with the economic optimization of distillation processes.