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

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.

Multi-spin-flip engineering in an Ising machine

“…They are NP-hard problems [17], [18]. It has been reported that existing Isingmachine hardware is unable to provide even a near-optimal solution of them [32], [33]. Section 5.2 shows the assignment process of {m i } and {s i } for each combinatorial optimization problem.…”

Multi-objective QUBO Solver: Bi-objective Quadratic Assignment

“…As a benchmark problem, we consider the bi-objective Quadratic Assignment Problem (QAP). The DA has been shown to present competitive performance on single-objective QAP instances [Şeker et al, 2020b[Şeker et al, , Matsubara et al, 2020. In [Matsubara et al, 2020], the DA was able to solve QAPLIB [Burkard et al, 1997] instances to optimality up to 165,000 times faster than CPLEX.…”