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An air-conditioner compressor-mounting bracket is a structural component of an engine, on which bolts attach an air-conditioner compressor. In this paper, the shape of the air-conditioner compressor-mounting bracket of a passenger car is optimized using a finite element software, and the optimized bracket is manufactured and verified by tests. An objective function for the shape optimization of the bracket is the weight of the bracket. Two design constraints on the bracket are the first resonant frequency of the compressor assembly and the need not to fracture during the workbench durability test. The compressor assembly, which consists of a compressor, a bracket and connection bolts, is modeled using finite elements. The bracket is modeled by solid elements and the swash-plate-type compressor is represented by rigid masses and beam elements in order to consider the elastic effects of the compressor.