A Study of Scalarisation Techniques for Multi-Objective QUBO Solving

TL;DR

This paper compares scalarisation techniques for converting multi-objective QUBO problems into single-objective problems, demonstrating that an iterative method improves performance over naive uniform weighting.

Contribution

It introduces and evaluates an iterative scalarisation method that enhances the efficiency of solving multi-objective QUBO problems.

Findings

Iterative scalarisation improves hypervolume performance.

Uniform weight scalarisation performs less effectively.

Method shows promise for multi-objective combinatorial optimisation.

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 n\"aive approach using uniformly generated weights.