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Network Operator Method


Network Operator Method

What is Network operator?

Network operator is the directed graph that presents mathematical expression. Network operator has no loops consists of nodes and edges. Every source node corresponds to variables or parameters of mathematical expression. Inner nodes correspond to binary operations. Edges correspond to unary operations. The result of calculation of mathematical expression is in the sink node.

What is NOM?

To present the network operator in PC memory we use an integer network operator matrix (NOM). To construct a NOM let us number the nodes of the network operator so that the number of the node with an outcoming edge would be less than the number of the node which this edge comes in. Thus we receive an upper-triangular integer matrix where binary operations are located in diagonal elements, and other elements are zeros or numbers of unary operations.

To link the parameters or variables to certain source nodes and result values to sink nodes, we define additional integer vectors: vector of numbers of nodes for input variables, vector of numbers of nodes for parameters, vector of numbers of nodes for output variables in case if the network operator describes more than one function, and the node vector. Elements of the node vector contain the values of calculation of mathematical expressions that network operator describes.

What is Basic solution?

To search for the solution to the problem the principle of basic solution was proposed. The principle of basic solution means that initially we define the basic solution (network operator matrix) that is one of admissible solutions. Then we define a set of small variations of basic solution and apply genetic algorithm (GA) that searches for the optimal solution on the vectors of variations (chromosomes in terms of GA). Each vector of variations changes basic solution thus we obtain new solutions. For effective search we change basic solution on the best solution found after some number of generations called epoch.