Digital Annealer for quadratic unconstrained binary optimization: a comparative performance analysis

TL;DR

This paper evaluates the Digital Annealer's performance in solving quadratic unconstrained binary optimization problems and reformulations, demonstrating its competitive speed and solution quality for large instances compared to existing solvers.

Contribution

It provides a comprehensive performance comparison of the Digital Annealer with state-of-the-art solvers across various problem classes, including new applications and heuristics.

Findings

DA delivers high-quality solutions quickly for large instances.

Solution times of DA are unaffected by instance size within its variable limit.

DA shows potential as a competitive technology for combinatorial optimization.

Abstract

Digital Annealer (DA) is a computer architecture designed for tackling combinatorial optimization problems formulated as quadratic unconstrained binary optimization (QUBO) models. In this paper, we present the results of an extensive computational study to evaluate the performance of DA in a systematic way in comparison to multiple state-of-the-art solvers for different problem classes. We examine pure QUBO models, as well as QUBO reformulations of three constrained problems, namely quadratic assignment, quadratic cycle partition, and selective graph coloring, with the last two being new applications for DA. For the selective graph coloring problem, we also present a size reduction heuristic that significantly increases the number of eligible instances for DA. Our experimental results show that despite being in its development stage, DA can provide high-quality solutions quickly and in that regard rivals the state of the art, particularly for large instances. Moreover, as opposed to established solvers, within its limit on the number of decision variables, DA's solution times are not affected by the increase in instance size. These findings illustrate that DA has the potential to become a successful technology in tackling combinatorial optimization problems.