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 L1​ 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