One of the ways to solve the conditionally ill-posed problem for ranking quality criteria of the multiobjective system, whose regularization is made by applying the fractal formalism, is hereby considered. Ranking quality criteria by their importance is based on the definition of the area of self-similarity for partial criteria. At the first stage of research, the key parameter is identified under the defined initial conditions by ranking quality criteria with the use of the fractal formalism. Ranking the criteria by importance is based on the estimation of the comparative value of areas of their self-similarity. The self-similarity coefficients of these areas appear as the regularization parameter at this stage of research. These areas are estimated by means of definitions of their relative values as the ratio of the range for existence of each partial criterion referred to its upper boundary. The second stage of research is initiated by the need to determine the optimal combinations of the target product properties in the working area, depending on the customer conditions. For this purpose, the sub-compromise regions are defined in the working area of partial criteria under consideration (compromise criteria). The sub-compromise partial regions are regions of the optimal combinations of properties. Thus, the regularization at the second stage is made in co-ordination with the requirements of the customer. In this connection, the example of solving the conditionally ill-posed problem for optimizing the multicriteria and multiparametric technologies of fabrication of cast iron rolls is given.