Combination of BESO and harmony search for topology optimization of microstructures for materials

•Design of material microstructures based on a metaheuristic algorithm.•Combination of BESO and harmony search methodologies.•Materials with maximum bulk and shear modulus.•Higher convergence speed in topology optimization. This paper introduces a metaheuristic algorithm for topology optimization of microstructures for cellular materials. It combines the harmony search (HS) algorithm with bi-directional evolutionary structural optimization (BESO) features. It is assumed that the cellular material comprises periodic base cells. Bulk and shear moduli are selected as the objectives of topology optimization with a volume constraint on the material solid phase. Each element in the base cell ground structure is treated as a discrete design variable and sensitivity numbers are calculated using homogenization theory. Through an iterative process, new sets of design variables are selected and the volume constraint is imposed using the BESO principals. Algorithm parameters such as filter radius, harmony memory considering rate (HMCR) and pitch adjusting rate (PAR) are selected experimentally. Numerical examples show the capability of the algorithm in designing microstructures of 2D and 3D materials with a high convergence speed. The proposed algorithm can also be easily extended to design of materials with other functional properties.