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An engine bracket is one of the most critical components of the engine used for mounting and supporting the engine in the vehicles. Today, the automobile industry requires lightweight components, which will reduce the car's overall weight when fitted into the vehicle. Topology optimization is a technique with the help of which the surface of a component is optimized to get the required shape for having reduced weight. The weight is reduced by optimizing the material on the surface of the details. In this paper, the work done is the application of topology optimization on the surface of the engine bracket arm. Then the optimized model is tested computationally using realistic conditions. Bi-directional evolutionary structural optimization is used as a technique for topology optimization. With the help of the BESO method, the material optimization is done, and then the weights are compared with the original component. A new algorithm is developed using MATLAB codes. The sensitivity ratio is considered using the von Mises strength as a critical parameter for the BESO method for optimization. The optimized bracket model is then assembled with the hub of the component, and then the assembly is simulated for verification using standard conditions. A comparison of weight reduction is there using topology optimization. [ABSTRACT FROM AUTHOR]