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.

本文提出了四种改进的比例拓扑优化（IPTO）算法，分别称为IPTO_A，IPTO_B，IPTO_C和IPTO_D。这项工作的目的是解决最小依从性优化问题，避免在获取敏感度信息的过程中涉及数值推导和敏感度计算的问题，并克服原始比例拓扑优化（PTO）算法中的缺陷。受PTO算法和蚁群算法的启发，结合滤波技术的优势，通过使用依从比例滤波器和新的密度变量增量更新方案并修改内部和内部密度变量的更新方式来设计新算法。主循环。为了验证新算法的有效性，本文介绍并使用了MBB梁的最小柔度优化问题。结果表明，新算法（IPTO_A，IPTO_B，IPTO_C和IPTO_D）在某些性能方面具有一些优势，而IPTO_A在总体性能方面是新算法中最好的。此外，与PTO和Top88相比，IPTO_A具有一些优点，例如，提高了目标值和收敛速度，获得了没有冗余的优化结构，并且抑制了灰度元素。此外，IPTO_A还具有优于PTO的强大鲁棒性的优势。和IPTO_D）在某些性能方面具有一些优势，而IPTO_A在整体性能方面是新算法中最好的。此外，与PTO和Top88相比，IPTO_A具有一些优点，例如，提高了目标值和收敛速度，获得了没有冗余的优化结构，并且抑制了灰度元素。此外，IPTO_A还具有优于PTO的强大鲁棒性的优势。和IPTO_D）在某些性能方面具有一些优势，而IPTO_A在整体性能方面是新算法中最好的。此外，与PTO和Top88相比，IPTO_A具有一些优点，例如，提高了目标值和收敛速度，获得了没有冗余的优化结构，并且抑制了灰度元素。此外，IPTO_A还具有优于PTO的强大鲁棒性的优势。