Control Systems and Computers, N2, 2017, Article 5


Upr. sist. maš., 2017, Issue 2 (268), pp. 58-73.

UDC 621.513.8

Stepashko Volodymyr S., Doctor of Eng. Sciences, Head of the department, International Research and Training Center for Information Technologies and Systems NAS and MES of Ukraine, Glushkov ave., 40, Kyiv, 03187, Ukraine, E-mail:

The Achievements and Prospects of Inductive Modeling

Introduction. Inductive modelling as the scientific school was formed by academician Alexey Ivakhnenko and is still actively being developed. The worldwide known Group method of data handling (GMDH) as a means of self-organizing models keeps the central place in this studying. The concept “inductive modelling” can be defined as a self-organizing process of evolutionary transition from primary data to mathematical models reflecting patterns of the simulated systems functioning, implicitly contained in the available experimental or statistical data.

Purpose. The typical problems solved by means of inductive modelling are described, information on this scientific school in Ukraine and abroad is presented, the fundamental basic and the technological achievements are defined, the most promising ways of further research are formulated.

Methods. The goal of this article is being achieved by presenting a comprehensive survey of the main publications in this area and structuring the material in accordance with the historical, fundamental, technological and applied aspects of the inductive modelling.

Results. As a result of the references survey in the field of inductive modelling, it can be stated that the GMDH is a promising basis of modern information technology for discovering knowledge from data, or one of original and efficient methods of data mining.

Conclusion. The further development of the model assumes the improvement of the theory of inductive modelling, the development and implementation of new high-performance algorithms in up-to-date computer technologies and the application of these technologies to solve a wide range of real-life problems of modelling, forecasting, control and decision-making in systems of different fields – economic, ecological, technological and others.

Keywords: Inductive modeling, GMDH, self-organization, structural-parametric identification, data mining, decision-making.

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  1. Ivakhnenko, A.G, 1968. “Group Method of Data Handling as a Rival of Stochastic Approximation Method”, Journal Soviet Automatic Control, 3, pp. 58-72. (In Russian).
  2. Ivakhnenko, A.G., 1971. Systems of heuristic self-organization in engineering cybernetics. Kiev: Tekhnika, 392 p. (In Russian).
  3. Ivakhnenko, A.G., 1975. Long-term forecasting and control of complex systems. Kiev: Tekhnika, 311 p. (In Russian).
  4. Ivakhnenko, A.G., 1982. Inductive method of self-organization of complex systems. Kiev: Naukova dumka, 296 p. (In Russian).
  5. Ivakhnenko, A.G., Peka, Yu.P., Vostrov, N.P., 1984. “ Combined method for modeling water and oil fields. Kiev: Naukova dumka, 1984. (In Russian).
  6. Ivakhnenko, A.G., Muller, J.A., 1985. Self-organization of forecasting models. Kiev: Tekhnika, 223 p. (In Russian).
  7. Ivachnenko, A.G., Müller, J.A., 1984. Selbstorganisation von Vorhersagemodellen. Berlin: VEB Verlag Technik, 223 p.
  8. Selforganizing methods in modeling: GMDH type algorithms. New York, Basel: Marcel Decker Inc., 1984. 350 p.
  9. Ivakhnenko, A.G., Karpinsky, A.M., 1982. “Self-organization of models on computers in terms of the general theory of communication (information theory)”. Automation, 4, pp. 7–26.
  10. Ivakhnenko, A.G., Stepashko, V.S., 1985. Noise-immunity of modeling. Kiev: Naukova dumka, 216 p. (In Russian).
  11. Ivakhnenko, A.G., Yurachkovskiy, Yu.P., 1987. Modeling of complex systems from experimental data. Moscow: Radio i svyaz, 120 p. (In Russian).
  12. Madala, H.R., Ivakhnenko, A.G., 1994. Inductive learning algorithms for complex systems modeling. New York: Boca Raton, CRC Press, 384 p.
  13. Ivakhnenko, A.G., Kostenko, Yu.V., Goleusov, I.V., 1983. “Systems analysis and long-term quantitative forecasting of quasistatic systems based on self-organizing models. Part 2. Objective system analysis without a priori indication of external influences”. Automation. 3. pp. 3–11.
  14. Ivakhnenko, A.G., 1987. “Objective computer clustering based on the theory of model self-organization”. Automation, 5, pp. 1–9.
  15. Ivakhnenko, A.G., Krotov, G.I., Strokova, T.I., 1984. “Self-organization of dimensionless harmonic-exponential and correlation predictive models of standard structures”.  Soviet J. of Automation and Information Sciences, 4, pp. 18–29.
  16. Ivakhnenko, A.G., 1991. “Inductive Sorting Method for the Forecasting of Multidimensional Random Processes and Events with the Help of Analogs Forecast Complexing”. Pattern Recognition and Image Analysis, 1 (1), pp. 99–108.
  17. Kondo, T., 1998. “GMDH Neural Network Algorithm Using the Heuristic Self-Organization Method and its Application to the Pattern Identification Problem”. Proc. of the 37th SICE Annual Conf. – SICE’98. Tokyo: IEEE, pp. 1143–1148.
  18. Ivakhnenko, A.G., Ivakhnenko, G.A., Mueller, J.A., 1994. “Self-Organization of Neuronets with Active Neurons. Pattern Recognition and Image Analysis”, 4 (4), pp. 177–188.
  19. Muller, J.-A., Lemke, F., 1999. Self-Organizing Data Mining. An Intelligent Approach to Extract Knowledge from Data. Berlin, Dresden, 225 p.
  20. Stepashko, V.S., 1983. “Potential noise immunity of modelling us
    ing a combinatorial GMDH algorithm without information
    regarding the noise”. Soviet Automatic Control, 16, 3, pp. 15-25.
  21. Kocherga, Yu.L., 1988. “J-optimal Reduction of Model Structure in the Gauss-Markov Scheme”. Soviet J. of Automation and Information Sciences, 21 (4), pp.34-36.
  22. Aksenova, T.I., Yurachkovsky, Yu.P., 1988. “A Characterization at Unbiased Structure and Conditions of Their J-Optimality”. Sov. J. of Automation and Information Sciences, 21 (4), pp.36-42.
  23. Stepashko, V.S., 1988. “Asymptotic Properties of External Criteria for Model Selection”. Soviet Journal of Automation and Information Sciences, 21 (6), pp.84-92.
  24. Dyshin, O.A., 1989. “Asymptotic noise immunity properties of model accuracy criteria”. Soviet Journal of Automation and Information Sciences, 21 (6), pp. 53–56.
  25. Aksenova, T.I., 1989. “Sufficient conditions for the convergence of external criteria for the choice of models”. Soviet Journal of Automation and Information Sciences, 21 (6), pp. 53–56.
  26. Sarychev, A.P., 2006. “System Regularity Criterion of Group Method of Data Handling”. Journal of Automation and Information Sciences, 38 (11), pp. 25–37. Automat Inf Scien.v38.i11.30
  27. Sarychev, A.P., 2008. Identification of states of structurally uncertain systems. Dnepropetrovsk: In-t tech. mechanics of NASU and NSAU, 268 p.
  28. Stepashko, V.S., 1991. “Investigation of the predictive properties of the recurrent structural-parametric identifier”. Soviet J. of Automation and Information Sciences, 3, pp. 33–41.
  29. Stepashko, V.S., 1992. “Structural identification of predictive models in the conditions of the planned experiment”. Soviet J. of Automation and Information Sciences, 1, pp. 26–35.
  30. Stepashko, V.S., 1994. “Efficiency analysis of criteria of structural identification of forecasting models”. Journal of Automation and Information Sciences, 3-4, pp.13-22.
  31. Stepashko, V.S., 2008. “Method of Critical Variances as Analytical Tool of Theory of Inductive Modeling”. Journal of Automation and Information Sciences, 40 (2), pp. 4-22.
  32. Stepashko, V.S, 1981. “Combinatorial Algorithm of the Group Method of Data Handling with Optimal Model Scanning Scheme”, Soviet Automatic Control, 14 (3), pp. 24-28.
  33. Stepashko, V.S., 1983. “A Finite Selection Procedure for Pruning an Exhaustive Search of Models”, Soviet Automatic Control, 16 (4), pp. 88-93.
  34. Stepashko, V.S., Yefіmenko, S.M., Savchenko, Ye.A., 2014. Computer experiment in inductive modeling. K .: Naukova dumka, 222 p.
  35. Moroz, O.G., Stepashko, V.S., 2016.Portive analogous generators of model structures for the interdisciplinary algorithms of GMDH”. Inductive modeling of complex systems, 8, K .: IRTC ITandS NASU, pp. 133–148.
  36. Pavlov, A.V., Stepashko, V.S., Kondrashova, N.V., 2014. Effective methods of self-organization models. K .: Academperiodika, 200 p.
  37. Stepashko, V.S., Bulgakova, O.S., 2013. “Generalized iterational algorithm of the group method of data handling”. Upravlausie sistemy i masiny, 2, 2013, pp. 9-26.
  38. Kondo, T., Ueno, J., 2007. “Feedback GMDH-Type Neural Network Self-Selecting Optimum Neural Network Architecture and Its Application to 3-Dimensional Medical Image Recognition of the Lungs”. Proc. of the II Int. Workshop on Inductive Modelling IWIM–2007, 19–23 Sept. 2007. Prague: Czech Techn. Univ., pp. 63–70. ISBN 978-80-01-03881-9.
  39. Kordik, P., 2006. Fully automated knowledge extraction using group of adaptive model evolution: Ph.D. thesis. Electrical Engineering and Inform. Techn. Prague: CTU, 150 p.
  40. Onwubolu, G., Sharma, A., Dayal  A. et al., 2008. Hybrid Particle Swarm Optimization and Group Method of Data Handling for Inductive Modeling. Proc. of 2nd Int. Conf. on Inductive Modelling (ICIM’2008). Kyiv: IRTC ITS NASU, 2008. pp.95–103.
  41. Bodyanskiy, Ye., Zaychenko, Yu., Pavlikovskaya, Ye., 2009. “The Neo-Fuzzy Neural Network Structure Optimization Using the GMDH for the Solving Forecasting and Classification Problems”. Proc. of the 3rd Int. Workshop on Inductive Modelling IWIM–2009, 14–19 Sept. 2009, Krynica, Poland. Prague: Czech Techn. Univ., pp. 100–107.
  42. Lytvynenko, V., 2013. “Hybrid GMDH Cooperative Immune Network For Time Series Forecasting”. Proc. of the 4th Int. Conf. on Inductive Modelling ICIM–2013, Sept. 16–20, 2013, Kyiv. Kyiv: IRTC ITS NASU, pp. 179–187.
  43. Dyvak, M.P., 2011. Problems of modeling of static systems with interval data. Ternopil: Economic Thought, 216 p.
  44. Stepashko, V., Yefimenko, S., 2009. “Parallel algorithms for solving combinatorial macromodelling problems”. Przegląd Elektrotechniczny (Electrical Review), 85 (4), pp. 98–99.
  45. Valkman, Yu.R., Stepashko, P.V., 2015. “On the way of building an ontology of intellectual modeling”. Inductive modeling of complex systems, 7, K .: IRTC ITandS NASU, pp. 101–115.
  46. Stepashko, V.S., 2010.Elements of the theory of inductive modeling”. The state and prospects of the development of computer science in Ukraine. K .: Science. opinion, 1008 p., pp. 481-496.
  47. Stepashko, V.S., 2013. “Self-organization of predictive models of complex processes and systems”. XV Vseros. scientific and technical conf. “Neuroinformatics 2013”: Lectures on neuroinformatics. M .: NIIUU MEPI, pp. 150-170.
  50. Ivakhnenko, A.G., Savchenko, E.A., 2008. “Investigation of Efficiency of Additional Determination Method of the Model
    Selection in the Modeling Problems by Application of the GMDH Algorithm”. Journal of Automation and Information sciences. Begell House. Inc. Publishers. 40 (3), pp. 47-58.
  51. Samoilenko, A.A., 2013. “A weight criterion for determining the informativeness of arguments in the methods for constructing models with a consistent selection of variables”.  Upravlausie sistemy i masiny, 2, pp. 33–39.
  52. Stepashko, V.S., Melnyk, I.M., Voloshchuk, R.V., 2006. “Models of synthesis of integral assessment of a complex system of interconnected primary indicators”. Modeling and control of the state of ecological-economic systems of the region: Zb. sciences works, 3, K .: IRTC ITandS NASU, pp. 275-284.
  53. Yefimenko, S., Stepashko, V., 2015. “Intelligent Recurrent-and-Parallel Computing for Solving Inductive Modeling Problems”. Proc. of 16th Int. Conf. on Computational Problems of Electrical Engineering CPEE’2015, Lviv, Ukraine, Sept. 2–5, Lviv: Lvivska politekhnika, pp. 236–238.
  54. Stepashko V.S., 2016. “Conceptual Fundamentals of Intelligent Modeling”. Upravlausie sistemy i masiny, 4, pp. 3-15.
  55. Yefimenko S.M. System Modeling and Prediction of the Multidimensional Interrelated Processes. Upravlausie sistemy i masiny, 4, pp. 80-85.
  56. Stepashko, V.S., Kopa, Yu.V., 1998.Experience of using the ASTRID system for modeling economic processes according to statistical data”. Cybernetics and Computer Engineering, 117, pp. 24–31.
  57. Samoilenko, O.A., 2011. “Designing of the GMGM preemptive algorithms as the main components of the simulation subsystem”. Inductive modeling of complex systems, 3, K .: IRTC ITandS NASU, pp. 191-208.
  58. Bulgakova, O.S., Zosimov, V.V., Stepashko, V.S., 2014. “Software complex of modeling of complex systems on the basis of iterative algorithms of GMDH with the possibility of network access”. Systemni doslidzhennya ta informatsiyni tekhnolohiyi, 1, pp. 43-55.
  59. Pavlov, A.V., 2015. “Designing a system for automated structural-parametric identification”. Inductive modeling of complex systems, 7, K .: IRTC ITandS NASU, pp. 202–219.
  60. Stepashko, V., Samoilenko, O., Voloschuk, R., 2014. “Informational Support of Managerial Decisions as a New Kind of Business Intelligence Systems”. Computational Models for Business and Engineering Domains. Rzeszow, Poland; Sofia, Bulgaria: ITHEA, pp. 269–279.
  61. Iuutinska, G.O., Koppa, Yu.V., Stepashko, V.S., 2002. “Modeling of the dynamics of microorganisms in soil contaminated with heavy metals”. Microbiological journal, 64 ( 3), pp. 59-67.
  62. Alomov, S.V., Bulgakova, O.S., Stepashko, V.S., 2011. “Modeling the influence of the Black Sea contamination on the total number of species of benthic organisms“. Zb. sciences works SNUYaEtaP. 3 (39), pp. 54-62.
  63. Tokova, O.V., Savchenko, Ye.A., 2916. “Approach to the development of information support solutions for foundry production”. Inductive modeling of complex systems, 8, K .: IRTC ITandS NASU, pp. 111-118.

Received 27.04.2017