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.
翻译:近些年来,人们对于解决四压不限制的二进制优化(QUBO)问题有着巨大的研究兴趣。提出了物理学启发的优化算法,为QUBO提出最佳或亚最佳的解决方案。这些方法在使用专用硬件,如量子计算机、应用特定CMOS和其他高性能计算资源解决优化问题的背景下特别有吸引力。这些解算器随后应用于QUBO的组合优化问题配方。量子和量子驱动的优化算法在应用学术基准和现实世界问题时显示出有良好的性能。然而,QUBO解算法是单一的客观解决者。为了使这些方法在解决多种目标的问题方面更加有效,需要做出如何将这类多目标问题转换为单一目标问题的决定。在这项研究中,我们将将将受限制的中位差组合优化问题的两个目标结合到一个目标时的定量加权计算方法进行了比较。我们用一个最大程度的性能改进来填补一个比重的比重方法。我们用一个具有最高性能的比重的方法来填补一个比重的方法。