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• GROUPING PREDICTORS IN COMBINED PIECEWISE LINEAR REGRESSION

  S.I. Noskov , S.V. Belyaev

  120-127

  2025-10-01

  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.

• APPLICATION OF THE MIXED PARAMETER ESTIMATION METHOD IN THE CONSTRUCTION OF A HOMOGENEOUS NESTED PIECEWISE LINEAR REGRESSION OF THE FIRST TYPE

  S.I. Noskov , А. P. Medvedev , I. D. Kirillov

  102-109

  2026-09-10

  Abstract ▼

  The paper is devoted to the development of an algorithm for identifying the parameters of a homogeneous nested piecewise linear regression of the first type – a model that is in demand when analyzing complex systems whose behavior cannot be adequately described by smooth functions. The review part of the work systematizes modern publications illustrating the use of piecewise linear forms in various subject areas: from modeling energy consumption and nonlinear control systems to image processing, reconstruction of genetic networks, and filtering of geophysical data. The novelty of the study lies in the fact that for the first time for this class of models an identification algorithm based on the mixed estimation method (MEM) is proposed, which allows flexible combination of two different quality criteria. It is shown that by introducing additional Boolean variables and auxiliary constraints, the original optimization problem is reduced to a standard linear Boolean programming problem, which makes it possible to use available numerical methods for its solution. The effectiveness of the developed algorithm is demonstrated on real data of the mining and metallurgical company Norilsk Nickel for 2010–2024. The dependent variable is revenue, and the predictors are the production volumes of nickel, palladium, copper and platinum. Two alternative models are constructed – using the classical least absolute deviations method and the proposed mixed estimation method. A comparative analysis shows that the second model has a slightly higher average percentage error, but significantly outperforms in the magnitude of the maximum error on the control subsample, which makes it preferable in conditions where outliers are critical. The results obtained confirm the practical value of MEM for constructing interpretable and robust regression dependencies

• MODEL AND ALGORITHM OF OPERATIONAL PLANNING OF LOGISTIC PROCESSES OF TIMELY DELIVERY OF CARGO WITH THE INTERACTION OF A GROUP OF ROBOTIC COMPLEXES

  Е.D. Grigoreva, V.А. Ushakov

  2025-04-27

  Abstract ▼

  The purpose of the study is to improve the quality of operational planning (program control) of logistics
  processes in the conditions of modern urban systems with the interaction of a group of robotic systems.
  The quality of management in this study will be assessed by the number of deliveries completed after
  established directive deadlines. The goal set during the study is decomposed into the following tasks: system
  analysis of the current state of research in the field of metropolitan logistics, implementation of a
  substantive and formal formulation of the problem of operational planning of logistics processes in a metropolis
  using a group of robotic complexes, development of a model and algorithm for operational planning
  of logistics processes in a metropolis using a grouping of robotic complexes, development of special
  model-algorithmic support and its software prototype for solving the problem of operational planning of
  logistics processes in a metropolis using a grouping of robotic complexes. Proactive (anticipatory) management
  of a group of robotic systems when solving transport and logistics problems in a metropolis within the framework of the “Smart City” concept allows increasing the economic efficiency of cargo delivery.
  The article examines the scientific and technical problem of synthesizing technologies (plans) for the timely
  delivery of small-sized cargo using a group of robotic systems. The scientific significance lies in the
  application of the concept of integrated (system) modeling and proactive (anticipatory) management, and
  the practical significance lies in ensuring timely delivery of goods using a group of robotic complexes in a
  metropolis. The article discusses an example of solving the problem of operational planning of logistics
  processes using the example of Innopolis using the characteristics of Yandex delivery robots (as robotic
  complexes). During the study, an analysis of various options for objective functions was carried out: maximizing
  profit and minimizing delivery time; profit maximization; minimizing time; minimizing the number
  of robotic systems. The following indicators were chosen to evaluate the results obtained: total profit from
  deliveries; the number of deliveries not delivered on time and the total number of completed orders.
  The most suitable objective functions for solving the problem are time minimization or simultaneous time
  minimization and profit maximization. In addition, the conclusion provides directions for further research