Structures in engineering application may face loads from multiple physical fields. To simultaneously design macroscopic structures that have lower thermal compliance and higher natural frequency, a new multi-objective topology optimization filled with multiple microstructures is proposed based on the weight sum method. To shorten the gap between the optimized results and the design requirement, a self-selected weight sum method that is based on the fitting functions of the result domains and the bisection method is proposed to get the optimized macroscopic structures with specific properties directly. Several numerical examples, including single-phase material and multiple materials cases, are presented to demonstrate the feasibility and practicality of the proposed method. The results show that the employment of multiple materials optimization provides the structures with a wider result domain than the single-phase material situations. The self-selected weight sum method is of high efficiency, good connectivity and easy to implement.
