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The problem of the optimal design of a rectifying column system of a given topology is presented as a problem of discrete-continuous nonlinear programming. The branch-and-bound method is suggested for solving the problem. To find the values of the lower bound of the optimality criterion, minimum cost, we suggest an approach that proceeds from discrete variables (the number of trays in the reinforcing and exhaustive parts of the columns) to continuous variables. The efficiency of this approach is demonstrated on the example of the design of a rectifying system composed of three rectifying columns for separating a four-component mixture.