A multiobjective genetic algorithm optimization of the extractive distillation process of acetone methanol minimum azeotropic mixture with heavy entrainer water is investigated. The process includes the extractive and entrainer regeneration columns, and the optimization minimizes the energy cost objective function (OF) and total annual cost (TAC) and maximizes efficiency indicators E-ext and e(ext) that describe the ability of the extractive section to discriminate the product between the top and the bottom of that section. Earlier work (You et al. Ind. Eng. Chem. Res. 2015, 54, 491) found that improvement of some designs in the literature led to an increase in those indicators. A two-step optimization strategy for extractive distillation is conducted to find suitable values of the entrainer feed flow rate, entrainer and azeotropic mixture feed locations, total number of trays, two reflux ratios, and two distillates in both the extractive column and the entrainer regeneration column. The first step relies upon the use of a nonsorted genetic algorithm (NSGA) with the four aforementioned criteria. Second, the best design taken from the GA Pareto front is further optimized focusing on decreasing the energy cost by using a sequential quadratic programming (SQP) method. In this way, the most suitable design with optimal efficiency indicators, low energy consumption, and low cost are obtained. Analyzed with respect to thermodynamic insights underlying the extractive section composition profile map, the Pareto front results show that there is maximum E-ext at given reflux ratio, and there is minimum reflux ratio for a given E-ext. There is an optimal efficiency indicator E-ext,E-opt which corresponds to the minimum TAC taken as the best design. In other words, E-ext,E-opt can be a criterion for the comparison between different designs for the same separating system. A SQP-based design is only <1% better in TAC than the best NSGA design, showing that this later method is able to find a consistent design for the extractive process concerning the 1.0-1a class mixture.