Automated Synthesis of Hardware-implementable Analog Circuits for Constrained Optimization

TL;DR

This paper introduces an automated toolchain that synthesizes analog circuits capable of solving large-scale constrained optimization problems efficiently, leveraging analog parallelism and convergence properties.

Contribution

It presents a novel automated synthesis process that maps high-level optimization problems to scalable, hardware-implementable analog circuits with verified convergence.

Findings

Successfully generates circuits with up to 10,000 variables.

Achieves up to 1,000X scalability improvement over previous analog methods.

Converges to optimal solutions with over 200X speedup compared to digital solvers.

Abstract

This paper presents an automated software toolchain for synthesizing hardware-implementable analog circuits that solve constrained optimization problems. The proposed toolchain supports nonlinear objective functions with linear and quadratic constraints. It maps optimization variables to capacitor voltages, implementing dynamics that enforce Karush-Kuhn-Tucker conditions using operational amplifiers, resistors, capacitors, diodes, and analog multipliers. From high-level problem descriptions in AMPL or MPS, the toolchain generates a SPICE netlist for the analog circuit, simulates it, and verifies that the solutions converge. The projected settling time of the analog circuit depends on circuit parameters, gain-bandwidth product, and slew-rate limits of operational amplifiers, and leverages the inherent parallelism of analog circuits. The proposed toolchain successfully generates circuits with up to 10,000 variables and demonstrates large scalability improvements, achieving up to a 1,000X increase in solvable problem size over prior analog hardware demonstrations. Simulation studies further show that the automatically synthesized circuits converge to optimal solutions, achieving more than a 200X speedup compared to IPOPT, a state-of-the-art digital interior-point solver.