The problem of the automatic synthesis of design of complex component-based systems is treated using fuzzy constraints and genetic algorithm (GA). The approach is demonstrated with a heating, ventilating and air-conditioning (HVAC) systems design, but it can easily be extended to other component-based systems such as VLSI. The complex problem of system design that involves human decisions, especially at its early stages, is treated as a fuzzy constraints satisfaction problem. GA and problem-specific operators are used to solve numerically this fuzzy optimization problem. The use of GA is motivated by the complex nature of the design problem, which results in the use of different types of variables (real and integer) that represent both the physical and the topological properties of the system. The ultimate objective of this fuzzy optimization problem is to design a feasible and efficient system. A software realization is in Java and it fully automates the design process. An interactive supervision by a human-designer is also possible using a specialized GUI. An example of automatic design of HVAC system is presented which does not limit the range of possible applications in a variety of other types of component-based systems such as VLSI.