There are several ways of using three-dimensional printing techniques in the construction industry. One method that seems quite feasible is the concreting of walls and structural components starting at the bottom and progressing up in layers according to the principles of additive manufacturing. The goal of this study is to optimize the movements of a nozzle at one level that will result in this operation. This study considers that the movements of the nozzle can be of two types: rectangular only (i.e., only in x and y directions) or more freely, including moving in diagonal directions. Applications are performed on four hypothetical flats (with 7, 8, 14, and 31 walls, respectively) and a structural component with 17 members. It is shown that as the number of walls and members increase, the problem of optimizing the movements of the nozzle becomes increasingly difficult due to exponentially increasing path combinations. A comparison is presented in terms of the ratio of movements of the nozzle without concreting to total distances traveled. The optimization process is conducted using the Harmony Search algorithm with a special coding and encoding system.