Multi-objective optimisation problems involve finding solutions with varying
trade-offs between multiple and often conflicting objectives. Ising machines
are physical devices that aim to find the absolute or approximate ground states
of an Ising model. To apply Ising machines to multi-objective problems, a
weighted sum objective function is used to convert multi-objective into
single-objective problems. However, deriving scalarisation weights that
archives evenly distributed solutions across the Pareto front is not trivial.
Previous work has shown that adaptive weights based on dichotomic search, and
one based on averages of previously explored weights can explore the Pareto
front quicker than uniformly generated weights. However, these adaptive methods
have only been applied to bi-objective problems in the past. In this work, we
extend the adaptive method based on averages in two ways: (i)~we extend the
adaptive method of deriving scalarisation weights for problems with two or more
objectives, and (ii)~we use an alternative measure of distance to improve
performance.
We compare the proposed method with existing ones and show that it leads to
the best performance on multi-objective Unconstrained Binary Quadratic
Programming (mUBQP) instances with 3 and 4 objectives and that it is
competitive with the best one for instances with 2 objectives.

本文提出一种基于平均值的自适应加权方法，用于解决多目标优化问题中的权衡问题，通过改进距离测量方法，实现多目标问题的 Pareto 前沿探索，并在对比实验中证明该方法在三个或四个目标的优化问题上的性能明显优于现有的方法。

应用 Ising 机解决多目标 QUBOs 问题

Applying Ising Machines to Multi-objective QUBOs

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。