This paper proposes the concept of machine-specified ground structures for topology optimization of trusses. Unlike general ground structures with dense and regular connectivity, machine-specified ground structures are sparse stable ground structures with a specified number of members designed by machines. Firstly, the generation process of machine-specified ground structures from a given node-set is formulated as a reinforcement learning task. Graph embedding is used to integrate the structural information into a comprehensive feature matrix to describe the state. By establishing the policy network, the probability of each action, i.e., selecting each node in the node-set, is obtained based on the comprehensive feature matrix. The task is solved using a gradient-based algorithm called REINFORCE. A randomized 4 × 4 node-set is used to train the agent. The policy converges with a high average reward, and generates different yet reasonable structures because a stochastic policy is employed. Besides, the agent can handle different-sized node-sets without re-training. Hence, the machine-specified ground structures generated by the trained agent can be utilized to assist the structural topology design. Subsequently, a method for a typical problem with singular optimal solutions, i.e., topology optimization of binary trusses with stress and displacement constraints, is proposed based on machine-specified ground structures. Finally, through different-sized numerical examples, it is demonstrated that the machine-specified ground structures lead to a variety of optimal solutions, and it is more likely to obtain the global optimum than fully-connected ground structures. It is worth noting that machine-specified ground structures can also be applied to other problems without re-training.

本文提出了用于桁架拓扑优化的机器特定地面结构的概念。与具有密集和规则连接的一般地面结构不同，机器指定的地面结构是由机器设计的具有指定数量的成员的稀疏稳定的地面结构。首先，从给定节点集生成机器指定的地面结构的过程被制定为强化学习任务。图嵌入用于将结构信息整合成一个综合的特征矩阵来描述状态。通过建立策略网络，基于综合特征矩阵获得每个动作的概率，即选择节点集中的每个节点。该任务使用名为REINFORCE的基于梯度的算法解决. 一个随机的 4 × 4 节点集用于训练代理。该策略以高平均奖励收敛，并由于采用了随机策略而产生不同但合理的结构。此外，代理无需重新训练即可处理不同大小的节点集。因此，由受过训练的代理生成的机器指定的地面结构可用于辅助结构拓扑设计。随后，针对具有奇异最优解的典型问题，提出了一种基于机器特定地面结构的具有应力和位移约束的二元桁架拓扑优化方法。最后，通过不同大小的数值例子，证明了机器指定的地面结构导致了多种最优解，并且比全连接的地面结构更有可能获得全局最优。值得注意的是，机器指定的地面结构也可以应用于其他问题而无需重新训练。