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<p>This work proposes a non-gradient proportional topology optimization method applying evolutionary strategy (PTO-ES) and a proportion filtering technique. The traditional interpolation function and the polarized interpolation function derived from logistic function are also employed into the PTO-ES, and the corresponding topology optimization results are discussed. As a non-gradient method without the evaluation of sensitivity, PTO-ES is easy to implement and simple to understand. The compliance minimization problem is solved through a range of two-dimensional (2D) and three-dimensional (3D) numerical examples to illustrate the effectiveness of the proposed approach. Furthermore, PTO-ES is compared with solid isotropic material with penalization (SIMP), proportional topology optimization (PTO), and bi-directional evolutionary structural optimization (BESO) methods concerning the 2D and 3D examples of cantilever and half-MBB beams. The results show that PTO-ES has obvious advantages over BESO, PTO, and SIMP in many aspects (e.g., convergence speed and the ability to acquire minimum objective function value and ideal topology structure without redundancy and intermediate density elements). Furthermore, PTO-ES integrates the respective advantages of PTO and BESO; that is, sensitivity calculation is not required during the optimization process, and there is no intermediate density material in the obtained topological configuration.</p>

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A non-gradient proportional topology optimization method applying evolutionary strategy

  • 期刊论文

  • 发表日期：

    2025年3月1日

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  • Xiong Rao,
  • Wenming Cheng,
  • Run Du

摘要

This work proposes a non-gradient proportional topology optimization method applying evolutionary strategy (PTO-ES) and a proportion filtering technique. The traditional interpolation function and the polarized interpolation function derived from logistic function are also employed into the PTO-ES, and the corresponding topology optimization results are discussed. As a non-gradient method without the evaluation of sensitivity, PTO-ES is easy to implement and simple to understand. The compliance minimization problem is solved through a range of two-dimensional (2D) and three-dimensional (3D) numerical examples to illustrate the effectiveness of the proposed approach. Furthermore, PTO-ES is compared with solid isotropic material with penalization (SIMP), proportional topology optimization (PTO), and bi-directional evolutionary structural optimization (BESO) methods concerning the 2D and 3D examples of cantilever and half-MBB beams. The results show that PTO-ES has obvious advantages over BESO, PTO, and SIMP in many aspects (e.g., convergence speed and the ability to acquire minimum objective function value and ideal topology structure without redundancy and intermediate density elements). Furthermore, PTO-ES integrates the respective advantages of PTO and BESO; that is, sensitivity calculation is not required during the optimization process, and there is no intermediate density material in the obtained topological configuration.