This work addresses the optimal design of catalytic distillation (CD) columns taking into account discrete design variables, i.e., the number of stages and location of feed stages and reactive stages. This optimization problem is challenging due to the combinatorial complexity introduced by these discrete decisions. In this work, the binary variables of the superstructure are expressed as a function of a reduced variable set: the external variables, which allows the use of a local algorithm that solves a series of master and primal sub-problems introduced in our previous study (Part I). The master problem is constructed from the reduced variable set and solved with a Discrete-Steepest Descent Algorithm (D-SDA). The primal sub-problem is a nonlinear programming problem obtained by fixing the binary terms in accordance with the reduced variable set. This strategy avoids finding multiple local minimizers, thus making this methodology more practical and efficient than existing Mixed-Integer Nonlinear Programming (MINLP) local and global optimization solvers. The proposed approach was evaluated on a catalytic column used for the production of ethyl tert-butyl ether (ETBE). It was found that an alternating distribution pattern of the reactive trays, the optimization of the location of feed stages, and the optimization of the total number of trays results in a more cost-effective CD column.