Building an iterative heuristic solver for a quantum annealer

TL;DR

This paper introduces an iterative heuristic method that leverages quantum annealing to solve larger and denser QUBO problems by decomposing them into manageable subproblems, demonstrating effectiveness on standard benchmarks.

Contribution

The paper presents a novel meta-heuristic algorithm that enhances quantum annealer capabilities for larger problems through iterative subproblem solving, with detailed analysis of performance and solution quality.

Findings

Effective solution of large QUBO instances up to size 7000.

Dependence of solution quality and time on problem size and desired gap.

Algorithm variants show robustness across different problem types.

Abstract

A quantum annealer heuristically minimizes quadratic unconstrained binary optimization (QUBO) problems, but is limited by the physical hardware in the size and density of the problems it can handle. We have developed a meta-heuristic solver that utilizes D-Wave Systems' quantum annealer (or any other QUBO problem optimizer) to solve larger or denser problems, by iteratively solving subproblems, while keeping the rest of the variables fixed. We present our algorithm, several variants, and the results for the optimization of standard QUBO problem instances from OR-Library of sizes 500 and 2500 as well as the Palubeckis instances of sizes 3000 to 7000. For practical use of the solver, we show the dependence of the time to best solution on the desired gap to the best known solution. In addition, we study the dependence of the gap and the time to best solution on the size of the problems solved by the underlying optimizer.