Authors B.K. Lebedev, O.B. Lebedev
Month, Year 06, 2015 @en
Index UDC 621.3.049.771.14
Abstract The problem of symbolic regression is to find mathematical expressions in symbolic form, approximating the relationship between the finite set of values of the independent variables and the corresponding values of the dependent variables. The criterion of quality approach (objective function) is the mean square error: the sum of the squares of the difference between the model and the values of the dependent variable for all values of the independent variable as an argument. Symbolic regression – method of constructing regression models by trying different superpositions of arbitrary functions from a given set. The paper is offered hybrid algorithm for solving symbolic regression. Use the traditional idea of an algebraic formula in the form of syntax tree. Leaf nodes correspond to variables or numeric constants rather than leaf nodes contain the operation that is performed on the child nodes. A distinctive feature of the process tree representation as a linear recording is preclude loss plurality of terminal elements, but the model can be an arbitrary function of the superposition of a set. In the process of synthesis of algebraic formula two problems are solved. The first task is to build a tree structure with anonymous tips. The second task is to specify the values of the tree tops. Leaf nodes are compared with the terminal set, a non-leaf nodes are matched with a functional set. The first problem is solved by ant colony. To solve the second problem is used a genetic algorithm. The rating formula is calculated after solving both problems – the construction of an ant tree unnamed peak and subsequent identification of vertices using ant colony The structure of the graph to find solutions G=(X,U). It is possible to create a solution space in which organized the search process based on the simulation of adaptive behavior of an ant colony. Formulated the necessary conditions under which the built in G route is represented as a legitimate expression D, is a solution of a symbolic regression. Developed heuristic of ant behavior when ant moving in graph to find solutions. For large dimension of time parameters of the algorithm outperformed compared algorithms for the best value of the objective function. Experimental time complexity of the algorithm on a single iteration for fixed values of the control parameters is O(nlgn), where n – the power terminal set.

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Keywords Symbolic regression; syntax tree; terminal set; functional set; ant colony; genetic search; hybrid algorithm
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