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Designing a lightweight and durable engine is universally important from the standpoints of fuel economy, vehicle dynamics and cost. However, it is challenging to theoretically find an optimal solution which meets both requirements in products such as the cylinder head, to which various thermal loads and mechanical loads are simultaneously applied. In our research, we focused on “non-parametric optimization” and attempted to establish a new design approach derived from the weight reduction of a cylinder head. Our optimization process consists of topology optimization and shape optimization. In the topology optimization process, we explored an optimal structure with the theoretically-highest stiffness in the given design space. This is to provide an efficient structure for pursuing both lightweight and durable characteristics in the subsequent shape optimization process.