Group Method of Data Handling is the realization of inductive approach for mathematical modeling of complex systems. The contents of the "Soviet Journal of Automation and Information Sciences" (previously "Soviet Automatic Control", and then "Journal of Automation and Information Sciences" - full translation of the ukrainian journal "Avtomatica") reflect to some extent the history and facilitate the tracking of the experimental and analytical development of the GMDH technique.

The first investigation of GMDH abroad had been made by R.Shankar in 1972 [39]. Later different variants were published by japanese [16] and polish scientists. Their conclusion was following: GMDH is the best method for solving of the AI problems - identification, short-term and long-term forecast of random processes and pattern recognition in complex systems. Mathematical GMDH theory showed that regression analysis can be described as the particular case of GMDH [25].

Many scientists are join to development of GMDH theory and applications now. It is property not of the author Prof. A.G.Ivakhnenko, but many other. This method was developed since 1968 in the Combined Control Systems (CCS) group of the Institute of Cybernetics in Kyiv (Ukraina). Contributions to the field have come from many research areas of different disciplines. More than 220 candidate (Ph.D.) and 27 doctoral dissertations were defended in this approach by scientists from several countries. Different 19 monographs devoted to this method have been published in 10 countries.

Period 1968-1971 is characterized by application of one regularity criterion for solving of the problems of identification, pattern recognition and short-term forecasting. As reference functions polynomials, logical nets, fuzzy Zadeh sets and Bayes probability formulas were used. Authors were staggered by high accuracy of forecastings. Noiseimmunity was not investigated.

Period 1972-1975. The problem of modeling of noised data and with incomplete information basis was solved. Multicriteria selection and utilization of additional apriory information for noiseimmunity increasing were proposed. Best experiments showed that with extended definition of the optimal model by additional criterion noise level can be ten times more than signal. Then it was improved using Shennon's theorem of General Communication theory.

Period 1976-1979. The convergence of multilayered GMDH algorithms was investigated. It was shown that some multilayered algorithms have "multilayerness error" - analogical to static error of control systems. In 1977 solution of objective systems analysis problems by multilayered GMDH algorithms was proposed. It turned out that sorting-out by criteria ensemble allow to choose the only optimal system of equations and therefore to show complex object elements, their main input and output variables.

Period 1980-1988. Many important theoretical results were received. It became clear that full (contentative) physical models cannot be used for long-term forecasting. It was proved, that non-physical models of GMDH are more accurate for approximation and forecast than physical models of regression analysis. Two-level algorithms which use two different time scales for modeling were developed.

Period 1989-to present time. New algorithms (AC, OCC,PF) for non-parametric modeling of fuzzy objects and SLP for expert systems were developed and investigated. Present stage of work is devoted to development and implementation, mainly into economical systems, of twice-multilayered neuronets, which open a new solution to the problem of self-organization of artificial neuronets - models of human brains. Among the last it is possible to point out recent work with title "Inductive computer advisor for current forecasting of ukrainian macroeconomy".

At present time it can be noted that further increase of accuracy of artificial intelligence problems may need application of preliminary working up of experimental data by the Objective Computer Clusterization (OCC) algorithm. Then the main Combinatorial (COMBI) algorithm should be used. Further increase of accuracy can be finished by implementation at the output of processing system of the neural nets with active neurons (TMNN), which is found their input connections by self-organization themselves.

Glushkov Institute of Cybernetics is one of the principal centers of research in the field of control theory and applications in exUSSR. There was created the first on the Europe continent electronic computer MESM in 1950.