The objective of this paper is to develop a new framework for the synthesis of process systems that can address the question of how to rigorously combine preliminary screening and MINLP optimization techniques. The proposed method is based on rigorous preliminary screening using aggregated models. These are simplified representations of the MINLP models, may be lower dimensional, and are based on linear, fixed-charge underestimations of the cost and convex overestimations of the feasible region. Thus, the solution to the aggregated model provides a rigorous lower bound to the global optimal solution of the MINLP problem. Furthermore, the objective function evaluated using aggregated models provides a rigorous lower bound to the cost of the NLP subproblem having the identical topology. A screening strategy is outlined that consists of successively solving the aggregated model to identify solutions whose cost is below an upper bound on cost. This upper bound is determined from a base-case design, that is defined as a good, but not necessarily optimal solution to the original MINLP problem. In the second stage a reduced MINLP model is formulated that contains only the alternatives found in the preliminary screening. Application of the proposed search strategy is illustrated with the optimization of a superstructure for heat-integrated distillation columns. This example shows that the size of the superstructure can be reduced, the robustness of the solution improved, the computational efficiency enhanced, and the global optimal solution of the MINLP problem bounded.