Fast Design Space Exploration of Nonlinear Systems: Part I

TL;DR

This paper introduces CNMA, a novel approach combining neural networks, MILPs, and learning from failures to efficiently solve inverse design problems in nonlinear systems, outperforming traditional methods especially in high-dimensional and mixed-variable scenarios.

Contribution

The paper presents CNMA, a new method for inverse design that overcomes challenges of blackbox evaluation, high dimensionality, and mixed variables, with a parallel version enhancing efficiency and solution quality.

Findings

CNMA solves all tested nonlinear design problems, including high-dimensional and mixed-variable cases.

CNMA outperforms Bayesian Optimization, Nelder Mead, and Random Search, with up to 87% better performance.

Parallel CNMA improves solution quality and efficiency over the sequential version.

Abstract

System design tools are often only available as input-output blackboxes: for a given design as input they compute an output representing system behavior. Blackboxes are intended to be run in the forward direction. This paper presents a new method of solving the inverse design problem namely, given requirements or constraints on output, find an input that also optimizes an objective function. This problem is challenging for several reasons. First, blackboxes are not designed to be run in reverse. Second, inputs and outputs can be discrete and continuous. Third, finding designs concurrently satisfying a set of requirements is hard because designs satisfying individual requirements may conflict with each other. Fourth, blackbox evaluations can be expensive. Finally, blackboxes can sometimes fail to produce an output. This paper presents CNMA, a new method of solving the inverse problem that overcomes these challenges. CNMA tries to sample only the part of the design space relevant to solving the problem, leveraging the power of neural networks, Mixed Integer Linear Programs, and a new learning-from-failure feedback loop. The paper also presents a parallel version of CNMA that improves the efficiency and quality of solutions over the sequential version, and tries to steer it away from local optima. CNMA's performance is evaluated against conventional optimization methods for seven nonlinear design problems of 8 (two problems), 10, 15, 36 and 60 real-valued dimensions and one with 186 binary dimensions. Conventional methods evaluated are off-the-shelf implementations of Bayesian Optimization with Gaussian Processes, Nelder Mead and Random Search. The first two do not solve problems that are high-dimensional, have discrete and continuous variables or whose blackboxes can fail to return values. CNMA solves all problems, and surpasses the performance of conventional methods by up to 87%.