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In recent years generative design techniques have become firmly established in numerous applied fields, especially in engineering. These methods are demonstrating intensive growth owing to promising outlook. However, existing approaches are limited by the specificity of problem under consideration. In addition, they do not provide desired flexibility. In this paper we formulate general approach to an arbitrary generative design problem and propose novel framework called GEFEST (Generative Evolution For Encoded STructure) on its basis. The developed approach is based on three general principles: sampling, estimation and optimization. This ensures the freedom of method adjustment for solution of particular generative design problem and therefore enables to construct the most suitable one. A series of experimental studies was conducted to confirm the effectiveness of the GEFEST framework. It involved synthetic and real-world cases (coastal engineering, microfluidics, thermodynamics and oil field planning). Flexible structure of the GEFEST makes it possible to obtain the results that surpassing baseline solutions.