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This paper compares the advantages and shortcomings of shape optimization method and topology optimization method for HTS solenoid design. For both methods critical current condition of superconducting material is taken into account for accurate analysis and design. Details of each method are explained including design variables and sensitivity analysis. With these methods, it is possible to design HTS solenoid that makes efficient use of superconducting material. Design results show that it is best to use topology optimization method for basic layout design and use shape optimization method for the fine-tuning of the basic layout.