Recently, the concept of equal thermodynamic distance (ETD) has been proposed to minimize entropy production in a distillation process using a diabatic column. ETD gives the optimal temperature profile to first-order in N-1, where N is the number of trays. ETD, however, does not generally give the true minimum for distillation columns with few trays. We therefore apply a fully numerical, multidimensional optimization routine to determine minimum entropy production. Since this method does not depend on an underlying theory, we expect a true minimum to be revealed. We then compare the performance of ETD and numerical optimization by varying the number of trays and the purity requirements. Our results show a surprisingly good agreement between the ETD results and those obtained numerically.