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During the design of engineering systems under the conditions of the partial uncertainty of physical, chemical, and economical information, the determination of a design at which its control system would ensure the performance of all constraints (exactly or with somewhat probability) is an essential problem despite the change of internal and external factors at operation stage. In this paper, one- and two-stage optimization problems with hard and soft constraints have been considered that must be solved during the design of flexible optimal systems. Approaches that enable one to avoid the procedures of multidimensional integration at each iteration of the solution of problems have been suggested.