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Article . 2022
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Pure University of Manchester
Part of book or chapter of book . 2023
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A Study of Scalarisation Techniques for Multi-objective QUBO Solving

Authors: Ayodele, Mayowa; Allmendinger, Richard; López-Ibáñez, Manuel; Parizy, Matthieu;

A Study of Scalarisation Techniques for Multi-objective QUBO Solving

Abstract

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 näive approach using uniformly generated weights.

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Keywords

FOS: Computer and information sciences, QUBO, Digital Annealer, Computer Science - Artificial Intelligence, I.2.8, G.2.1, 90C29, 90C20, 90C27, Artificial Intelligence (cs.AI), Multi-objective optimisation, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), G.2.1; I.2.8

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
Average
Average
Average
Green