The Network operator method was founded by Professor Askhat Diveev in 2006 due to the problem of automatic search system of mathematical expression. Such problem is well known and occurs in different fields of approximation, identification, synthesis of control systems etc.

To automate the search, the researcher defines the sets of operations, variables and parameters. The computer program uses these sets and generates a number of mathematical expressions which are satisfactory to the given restrictions. Then the optimization algorithm finds the structure of appropriate mathematical expression and its parameters. We invented a new data structure called network operator to make this method work properly.

Network operator is a directed graph that corresponds to some mathematical expressions. Every source nodes of the graph are variables or constants of mathematical expression, inner nodes correspond to binary operations and edges correspond to unary operations. The calculation's result of mathematical expression is kept in the last sink node. Any mathematical expression is presented as a network operator if some constrains are followed and sets of operations and variables are given.

To set the network operator in the computer's memory effectively we use an integer network operator matrix (NOM). NOM is an integer matrix where binary operations are located in diagonal elements, and other elements are zeros or numbers of unary operations.

The network operator method with evolutionary algorithms will bring to life the next generation of intelligent computing. Using its ability to learn and solve complex problems the network operator method will challenge the traditional artificial neural networks.

Work has been executed by the support of Russian Fund of Basic Researches on the subject No.10-08-00618-a and No.11-08-00532-a.