An optimization problem of packing objects of arbitrary geometry with generalization in dimension is considered. It is proposed to use a discrete representation of objects of complex shape in the form of orthogonal polyhedra, which are compound objects obtained by combining rectangles or parallelepipeds depending on the dimension of the problem. The model of potential containers is used to form and describe the placement schemes of orthogonal polyhedra. The paper proposes algorithms that provide a qualitative increase in the speed of formation of the placement schemes by reducing the number of potential containers processed when placing each compound object. A fast algorithm for updating sets of potential containers is presented, which is based on the use of the set-theoretic operation of intersection. An additional increase in the speed of the potential containers model is achieved by removing potential containers that cannot be used to place new objects in all possible orientations. It is shown that with an increase in the number of objects placed using the proposed algorithms, the time spent on placing one object is reduced. The proposed optimization makes it possible to solve the problems of placing objects of complex shape, specified with a higher degree of detail, which will provide a denser packing in the allotted time. The results of the computational experiments carried out on the problems of packing flat and volumetric objects of irregular shape are presented, confirming the effectiveness of the developed algorithms.