GROUPING PREDICTORS IN COMBINED PIECEWISE LINEAR REGRESSION
Abstract
The article provides a brief overview of publications on the application of combined structures containing known model forms as constituent elements in mathematical modeling of complex systems. In particular, the following are considered: an algorithm for estimating parameters for creating mathematical models of dynamic systems; structured mathematical models of an oxygen electrode and biological wastewater treatment; a combined model including ion exchange between calcium and copper; a combination of non-standard finite-difference schemes and the Richardson extrapolation method to obtain numerical solutions of two models of biological systems; a mathematical formulation of the problem and a heuristic approach to optimal planning of delivery routes in a multimodal system; a mathematical model for optimizing strategic and tactical decisions in all types of biomass-based supply chains; a method for developing models of various types for elements of chemical-engineering systems taking into account various types of available information and combining these models into a single complex. Two variants of the problem statement for calculating the estimates of the parameters of a combined piecewise linear regression are formulated: with a non-empty and empty intersection of the index sets that define the composition of the independent variables in the linear and piecewise linear components of the model. It is shown that in both cases, when the sum of absolute deviations of approximation errors is selected as the loss function, both variants are reduced to linear-Boolean programming problems. Two versions of a combined piecewise linear regression model of revenue of the mining and metallurgical company Severstal are constructed. The following production volumes are used as independent variables of the model: hot-rolled, cold-rolled and galvanized sheet, sheet with another metal coating, sheet with a polymer coating, rolled products, hardware products.
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