# A Study of Scalarisation Techniques for Multi-Objective QUBO Solving

arXiv: https://arxiv.org/abs/2210.11321 · HTML: https://mlsanity.com/paper/2210.11321/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 14 references that are in the map.
- First posted on arXiv 20 Oct 2022.

## Builds on (most cited first, 4 of 4)

- [Portfolio Optimisation Using the D-Wave Quantum Annealer](https://mlsanity.com/paper/2012.01121/) (2020)
- [Penalty Weights in QUBO Formulations: Permutation Problems](https://mlsanity.com/paper/2206.11040/) (2022)
- [Multi-objective QUBO Solver: Bi-objective Quadratic Assignment](https://mlsanity.com/paper/2205.13399/) (2022)
- [Comparing the Digital Annealer with Classical Evolutionary Algorithm](https://mlsanity.com/paper/2205.13586/) (2022)

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

- [Applying Ising Machines to Multi-objective QUBOs](https://mlsanity.com/paper/2305.11648/) (2023)
- [Utilising a Quantum Hybrid Solver for Bi-objective Quadratic Assignment Problems](https://mlsanity.com/paper/2405.17676/) (2024)
- [Standardization of Multi-Objective QUBOs](https://mlsanity.com/paper/2504.12419/) (2025)

## Abstract (arXiv)

In recent years, there has been significant research interest in solving Quadratic Unconstrained Binary Optimisation (QUBO) problems. Physics-inspired optimisation algorithms have been proposed for deriving optimal or sub-optimal solutions to QUBOs. These methods are particularly attractive within the context of using specialised hardware, such as quantum computers, application specific CMOS and other high performance computing resources for solving optimisation problems. These solvers are then applied to QUBO formulations of combinatorial optimisation problems. Quantum and quantum-inspired optimisation algorithms have shown promising performance when applied to academic benchmarks as well as real-world problems. However, QUBO solvers are single objective solvers. To make them more efficient at solving problems with multiple objectives, a decision on how to convert such multi-objective problems to single-objective problems need to be made. In this study, we compare methods of deriving scalarisation weights when combining two objectives of the cardinality constrained mean-variance portfolio optimisation problem into one. We show significant performance improvement (measured in terms of hypervolume) when using a method that iteratively fills the largest space in the Pareto front compared to a n"aive approach using uniformly generated weights.