When designing modern cellular networks, it is challenging to account for many contradictory criteria and constantly changing external conditions of the networks (e.g., traffic). We need to solve multicriteria problems with high-dimensional vectors of parameters. A prerequisite to solution of these problems is correct determination of the feasible solution set, which is directly related to the statement of optimization problem. This is a major challenge in all multicriteria engineering optimization problems and represents significant difficulties for the expert. In this paper, we show how to define the feasible solution set for cellular network optimal design problems and thus answer the fundamental question of where to search for optimal solutions in such problems. We use the Parameter Space Investigation (PSI) method implemented in the Multicriteria Optimization and Vector Identification (MOVI) software system and apply it to a mathematical model of cellular network. In addition to developing methodology for stating and solving the problem of multicriteria optimization of cellular network, we have found that 1) defining the feasible solution set is directly related to the correct statement of the optimization problem, 2) once the feasible solution set has been determined, the criteria convolution can be applied to find the optimal solution in the feasible solution set, 3) it is possible to perform online tuning of the cellular network parameters.