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This paper describes an investigation of an optimization-with-constraints method, which uses a hypothetically acceptable level of risk as a constraint, for use in design of liquid metal fast breeder reactor (LMFBR) nuclear power generating stations. No attempt was made during the investigation to define the level of the acceptable risk. Major problems inherent in development of an optimization-with-constraints approach to risk-based design are discussed. Further development of the approach should be along two lines (both of which would require a computer program capable of handling about 50 decision variables): 1. develop a tool for use by product engineers in plant conceptual design; 2. develop a combined risk allocation/optimization-with-constraints methodology.