A Study of Scalarisation Techniques for Multi-Objective QUBO Solving
This work addresses the inefficiency of single-objective QUBO solvers for multi-objective problems, specifically in finance, but is incremental as it compares existing scalarisation methods.
The study tackled the problem of converting multi-objective optimization into single-objective for QUBO solvers by comparing scalarisation techniques for a portfolio optimization problem, showing significant performance improvement in hypervolume compared to a naive approach.
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.