A two-step structural optimization method was proposed to select the transition section of a composite bucket foundation (CBF). In the first step, based on the variable density method, a solid isotropic microstructures with penalization (SIMP) interpolation model was established under specific load conditions and boundary conditions. The solution of force transmission path and the topology of the transition section in six forms (e.g., linear, arc-shaped, linear thin-walled, and arc-shaped thin-walled) were optimized. Afterwards, finite element software ABAQUS was used to verify this model. Results show that the utilization rate of the arc-shaped thin-walled structure was the largest, and its basic transmission force was more straightforward together with smaller cross-section size at the same height and smaller influence on spoiler flow. In the second step, the detailed optimization of CBF was carried out using mathematical programming. Under the premise of minimum total construction cost, the body shape parameters of each part were set as design variables satisfying the corresponding strength, stiffness, and stability conditions; meanwhile, the minimum total structure weight was set as the objective function. MATLAB was used to solve the sequence quadratic programming (SQP) algorithm and hybrid genetic algorithm, and the optimal body parameters were obtained.
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