Computational Models based on Synchronized Oscillators for Solving Combinatorial Optimization Problems

TL;DR

This paper develops synchronized oscillator-based dynamical models capable of solving a wide range of combinatorial optimization problems, expanding the scope of oscillator-based analog computing.

Contribution

It introduces a general framework for designing oscillator networks to solve various combinatorial problems, beyond previously studied cases.

Findings

Oscillator dynamics can be tailored to solve Max-K-Cut and Traveling Salesman Problem.

Proper coupling and external injection enable the mapping of optimization problems to oscillator states.

The approach broadens the potential of oscillator-based analog accelerators.

Abstract

The equivalence between the natural minimization of energy in a dynamical system and the minimization of an objective function characterizing a combinatorial optimization problem offers a promising approach to designing dynamical system-inspired computational models and solvers for such problems. For instance, the ground state energy of coupled electronic oscillators, under second harmonic injection, can be directly mapped to the optimal solution of the Maximum Cut problem. However, prior work has focused on a limited set of such problems. Therefore, in this work, we formulate computing models based on synchronized oscillator dynamics for a broad spectrum of combinatorial optimization problems ranging from the Max-K-Cut (the general version of the Maximum Cut problem) to the Traveling Salesman Problem. We show that synchronized oscillator dynamics can be engineered to solve these different combinatorial optimization problems by appropriately designing the coupling function and the external injection to the oscillators. Our work marks a step forward towards expanding the functionalities of oscillator-based analog accelerators and furthers the scope of dynamical system solvers for combinatorial optimization problems.