Main directions and evolution routes of the Central Economics and Mathematics Institute (CEMI) as a leader of domestic economic science in the development and application of economic-mathematical and information-computer models of socio-economic processes and systems were analyzed in the paper. The connection of modeling with such components of the economy as economic theory, economic policy, economic management and economic practice were clarified. It was shown that the economic and mathematical model plays an indispensable role in the integration and systematization of knowledge in the field of economic theory and economic practice. A generalized scheme and the sequence of modeling stages based on the concept of a model as a homomorphic image of a real object in the field of ontology (“the world of things”), ideology (“the world of ideas”), epistemology (“the world of knowledge”) and praxeology (“the world of creation”), were proposed. The evolution of the main components of modeling which had significantly changed over the past 60 years the ideas about the object, subject, goals, apparatus and empirical basis of modeling, were traced. The experience accumulated at CEMI RAS in this area allows us to propose the concept of evidence-based modeling, similar to the ideology of evidence-based medicine, evidence-based policy, evidence-based forecasting, aimed at qualitatively improving the validity and reliability of modeling results for applying in economic theory and practice. The main principles of evidence-based modeling that have to play the role of standards for evidence-based modeling were formulated. The modeling process was considered as an analogue of an innovative project, where every independent stage (likewise the entire project) should be carried out according to these standards. A list of the most important, in our opinion, pioneer works of CEMI RAS in the field of economic-mathematical and computer modeling, which determine significant directions for the further development of this field of science, were given.
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