Heat integration, such as multi-effect distillation (MED), can often help save considerable energy in distillation processes. With the increasing level of heat integration and consequent flowsheet complexity, the chemical industry calls for systematic design procedures. Usually, MED synthesis is followed by heuristic rules, such as arbitrarily set pressure level based on temperature-pressure relationship. No systematic design procedure driven by economic criterion has been established so far. As a solution, an enumeration-based MED process synthesis framework is therefore suggested for optimization using column pressure as an independent decision variable. The framework firstly includes 43 potentially useful MED configurations to generate a search space, followed by mathematical formulation of a short-cut nonlinear programming for each configuration. Then rapid screening is performed to evaluate all the design variants in the search space. The solution provides a rank-list of all feasible configurations in total annualized cost (TAC) criterion, from which top preferred candidates are verified through a genetic algorithm (GA) based rigorous optimization in the third step. The validity of this framework is illustrated with three case studies. Results show the MED can generally save approximately 50% of energy and up to 30% of TAC, compared to a conventional distillation column. (C) 2019 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.