This study introduces the constraint‐aware optimization model (CAOM), a novel optimization framework designed to optimize the size, shape, and topology of plane truss structures simultaneously. Unlike traditional optimization models, which rely on gradient descent and frequently struggle with managing various constraints due to their dependence on a single optimization agent, CAOM effectively addresses this challenge. It does so by incorporating a variety of assistant modules along with the Adam optimizer, a variant of the gradient descent method. Uniquely, CAOM employs the leaky rectified linear unit (ReLU) activation function beyond its conventional use in neural networks, applying it as a mechanism to integrate constraints and losses seamlessly. The model's effectiveness was validated through two numerical examples and a practical application, demonstrating that CAOM can reduce structural weight by up to 84% compared to unoptimized designs while fully adhering to structural, dimensional, and moveable constraints. Furthermore, the study found that while shape optimization plays a key role for stiffness‐governed structures, size optimization is crucial for strength‐governed structures. Optimizing size, shape, and topology together consistently leads to the most weight‐efficient designs. This emphasizes the significance of a holistic approach in the optimization processes.

中文翻译：

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基于单智能体梯度下降的平面桁架结构约束感知优化模型

本研究介绍了约束感知优化模型（CAOM），这是一种新颖的优化框架，旨在同时优化平面桁架结构的尺寸、形状和拓扑。传统的优化模型依赖于梯度下降，并且由于依赖于单个优化代理而经常难以管理各种约束，与此不同，CAOM 有效地解决了这一挑战。它通过将各种辅助模块与 Adam 优化器（梯度下降法的一种变体）结合起来来实现这一点。独特的是，CAOM 采用了泄漏修正线性单元 (ReLU) 激活函数，超出了神经网络中的常规用途，将其用作无缝集成约束和损失的机制。该模型的有效性通过两个数值示例和实际应用得到了验证，表明与未优化的设计相比，CAOM 可以减少高达 84% 的结构重量，同时完全遵守结构、尺寸和可移动约束。此外，研究发现，虽然形状优化对于刚度控制结构起着关键作用，但尺寸优化对于强度控制结构至关重要。尺寸、形状和拓扑的共同优化可以带来最轻量化的设计。这强调了优化过程中整体方法的重要性。