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CADSYS is an interactive computer-aided decision support system which interfaces a designer with a mathematical, rather than graphic, model of a design problem. Multiple design goals can be imposed in the form of equality and inequality constraints, whose levels can be manipulated. A numerical search is used to find designs which meet the constraints. CADSYS has now been applied to two real and current design problems: the hydraulic system of a novel inertial navigation unit and the financial, technical, and logistical problem of liquified natural gas tanker design and operation. Both of these studies returned new understanding of the problems themselves and of the capabilities of CADSYS.