# Multi-objective QUBO Solver: Bi-objective Quadratic Assignment

arXiv: https://arxiv.org/abs/2205.13399 · HTML: https://mlsanity.com/paper/2205.13399/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 35 references that are in the map.
- First posted on arXiv 26 May 2022.

## Builds on (most cited first, 6 of 6)

- [Ising formulations of many NP problems](https://mlsanity.com/paper/1302.5843/) (2013)
- [pymoo: Multi-objective Optimization in Python](https://mlsanity.com/paper/2002.04504/) (2020)
- [Portfolio Optimisation Using the D-Wave Quantum Annealer](https://mlsanity.com/paper/2012.01121/) (2020)
- [Item Listing Optimization for E-commerce Websites based on Diversity](https://mlsanity.com/paper/1903.12478/) (2019)
- [Digital Annealer for quadratic unconstrained binary optimization: a comparative performance analysis](https://mlsanity.com/paper/2012.12264/) (2020)
- [Leveraging Special-Purpose Hardware for Local Search Heuristics](https://mlsanity.com/paper/1911.09810/) (2019)

## Built on by (most cited first, 3 of 3)

- [A Study of Scalarisation Techniques for Multi-Objective QUBO Solving](https://mlsanity.com/paper/2210.11321/) (2022)
- [Projected Stochastic Gradient Descent with Quantum Annealed Binary Gradients](https://mlsanity.com/paper/2310.15128/) (2023)
- [Utilising a Quantum Hybrid Solver for Bi-objective Quadratic Assignment Problems](https://mlsanity.com/paper/2405.17676/) (2024)

## Abstract (arXiv)

Quantum and quantum-inspired optimisation algorithms are designed to solve problems represented in binary, quadratic and unconstrained form. Combinatorial optimisation problems are therefore often formulated as Quadratic Unconstrained Binary Optimisation Problems (QUBO) to solve them with these algorithms. Moreover, these QUBO solvers are often implemented using specialised hardware to achieve enormous speedups, e.g. Fujitsu's Digital Annealer (DA) and D-Wave's Quantum Annealer. However, these are single-objective solvers, while many real-world problems feature multiple conflicting objectives. Thus, a common practice when using these QUBO solvers is to scalarise such multi-objective problems into a sequence of single-objective problems. Due to design trade-offs of these solvers, formulating each scalarisation may require more time than finding a local optimum. We present the first attempt to extend the algorithm supporting a commercial QUBO solver as a multi-objective solver that is not based on scalarisation. The proposed multi-objective DA algorithm is validated on the bi-objective Quadratic Assignment Problem. We observe that algorithm performance significantly depends on the archiving strategy adopted, and that combining DA with non-scalarisation methods to optimise multiple objectives outperforms the current scalarised version of the DA in terms of final solution quality.