Utilising a Quantum Hybrid Solver for Bi-objective Quadratic Assignment Problems

TL;DR

The paper addresses solving a bi-objective quadratic assignment problem (QAP) using a quantum-hybrid solver based on constrained quadratic models (CQM). It formulates the bi-objective QAP with two objectives weighted by scalarisation parameters $\lambda_1$ and $\lambda_2$ (where $\lambda_1+\lambda_2=1$) and enforces permutation constraints via $g_{1,i}(x)$ and $g_{2,j}(x)$. Three scalarisation strategies—uniform, adaptive-averages, adaptive-dichotomic—are evaluated and compared using hypervolume as the performance metric. Findings show adaptive methods outperform uniform in certain objective-correlation regimes and align with prior work on Ising machines, supporting a general framework for multi-objective quantum optimisation and guiding weight selection.

Abstract

The intersection between quantum computing and optimisation has been an area of interest in recent years. There have been numerous studies exploring the application of quantum and quantum-hybrid solvers to various optimisation problems. This work explores scalarisation methods within the context of solving the bi-objective quadratic assignment problem using a quantum-hybrid solver. We show results that are consistent with previous research on a different Ising machine.

Figures (1)

• Figure 1: Comparing a single run of all scalarisation methods with the known Pareto Optimal