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.

本篇研究探讨将多个目标转化为单一目标的方法，在集合约束均值 - 方差投资组合优化问题上，迭代填充帕累托前沿中最大空间的方法可以显著提高性能。