基于optimization的自动化设计方法
An optimization-based approach to automated design
摘要：
我们提出了一个基于模型的，自动化的，自下而上的设计方法，这是适用于各种物理域，但在这项工作中，我们专注于电气领域。这种自下而上的方法基于元拓扑，其中每个链路由通用组件描述，该通用组件可以被实例化为基本组件（例如，电阻器、电容器）或通过分立开关的基本元件的组合。针对混合整数最优化问题中经常出现的组合爆炸问题，提出了两种算法。在第一种算法中，我们将离散开关转换为连续开关，物理上可实现的，并制定一个参数最优化问题，学习的组件和开关参数，同时通过$L_1$正则项诱导设计稀疏。第二种算法采用了类似于遗传的方法，通过需求成本的排名来指导选择和变异步骤，并结合连续优化来生成最优参数。我们提高了时间复杂度的最优化问题在这两个算法的重建模型时，组件变得冗余，并通过简化拓扑结构，通过折叠组件和删除断开的。为了证明这些算法的有效性，我们将它们应用到各种电路的设计。
英文摘要：
We propose a model-based, automated, bottom-up approach for design, which is applicable to various physical domains, but in this work we focus on the electrical domain. This bottom-up approach is based on a meta-topology in which each link is described by a universal component that can be instantiated as basic components (e.g., resistors, capacitors) or combinations of basic components via discrete switches. To address the combinatorial explosion often present in mixed-integer optimization problems, we present two algorithms. In the first algorithm, we convert the discrete switches into continuous switches that are physically realizable and formulate a parameter optimization problem that learns the component and switch parameters while inducing design sparsity through an $L_1$ regularization term. The second algorithm uses a genetic-like approach with selection and mutation steps guided by ranking of requirements costs, combined with continuous optimization for generating optimal parameters. We improve the time complexity of the optimization problem in both algorithms by reconstructing the model when components become redundant and by simplifying topologies through collapsing components and removing disconnected ones. To demonstrate the efficacy of these algorithms, we apply them to the design of various electrical circuits.
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