The problem of multi-objective synthesis of automatic control systems is considered. A new numerical method of search for control dependence on the coordinates of space conditions is proposed. This functional dependence provides the best values of quality criteria in Pareto relations. The numerical method is based on creation of space of different functional dependences. Solutions that correspond to the best quality criteria are chosen. To construct the space of functional dependences, we use the network operator. The network operator describes mathematical expressions by means of directed graphs. A multi-objective genetic algorithm is used to find the best possible solutions on the space of network operators.