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• This paper presents the optimal design of distillation columns using Set Trimming and Enumeration. • The Set Trimming algorithm reduces the number of design solution candidates to evaluate. • The smart enumeration algorithm guarantees global optimality and has a lower computational effort than complete enumeration. • The scheme Set Trimming followed by Enumeration is robust and does not fail. In this article, we present an alternative approach to the use of metaheuristic methods (GA, PSO, SA, etc.) or mathematical programming (MINLP solvers) for the optimal design of one-feed-two-products distillation columns. We propose the use of Set Trimming followed by candidate enumeration. For the evaluation of the performance of each candidate solution, the method relies on solving the associated system of equations. Three different enumeration procedures are tested: Exhaustive Enumeration, Smart Enumeration, and Segmental Smart Enumeration. Smart Enumeration is an optimization procedure that identifies the solution through a search in the set of candidates organized in ascending order of the objective function lower bound, while Segmental Smart Enumeration is introduced in this article. We compare the results of the proposed procedure with the results using an MINLP approach with different solvers. Numerical results indicate that the best alternative of the enumeration algorithms can identify the global optimum faster than a global solver of mathematical optimization. Numerical tests also showed local solvers which attained optimal solutions quickly but may be trapped in a local optimum. [ABSTRACT FROM AUTHOR]