Abstract: An adaptive weighted sum algorithm proposed for multiple objective problems is presented to optimize
the topology of the microst ructure with periodic two2phase materials. The microst ructure of porous composite with a certain volume f raction of solid materials and st ructural symmet ry is studied. By means of the homogenization method and method of moving approximating (MMA) , the equivalent elastic module of cell is calculated and maxi2 mized , based on the finite element method. The relative density of each element of the cell is defined as the design variable based on the finite element method , with SIMP density2stiffness scheme which has the effect of penalizing to element s with intermediate density. During the process of iteration , the weighing coefficient is adaptively adjusted according to the variety of the objective function. Several microst ructure topologies are obtained by the adaptive weighting algorithm with different combinations of equivalent elastic module and weighing coefficient s. Numerical result s verify the validity of the proposed adaptive weighted sum algorithm in the multiple objective topology design of microst ructures.