Improved proportional topology optimization algorithm for solving minimum compliance problem

The paper proposes four improved proportional topology optimization (IPTO) algorithms which are called IPTO_A, IPTO_B, IPTO_C, and IPTO_D, respectively. The purposes of this work are to solve the minimum compliance optimization problem, avoid the problems of numerical derivation and sensitivity calculation involved in the process of obtaining sensitivity information, and overcome the deficiencies in the original proportional topology optimization (PTO) algorithm. Inspired by the PTO algorithm and ant colony algorithm, combining the advantages of the filtering techniques, the new algorithms are designed by using the compliance proportion filter and the new density variable increment update scheme and modifying the update way of the density variable in the inner and main loops. To verify the effectiveness of the new algorithms, the minimum compliance optimization problem for the MBB beam is introduced and used here. The results show that the new algorithms (IPTO_A, IPTO_B, IPTO_C, and IPTO_D) have some advantages in terms of certain performance aspects and that IPTO_A is the best among the new algorithms in terms of overall performance. Furthermore, compared with PTO and Top88, IPTO_A has some advantages such as improving the objective value and the convergence speed, obtaining the optimized structure without redundancy, and suppressing gray-scale elements. Besides, IPTO_A also possesses the advantage of strong robustness over PTO.