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.

翻译：多目标优化问题涉及在多个且通常相互冲突的目标之间寻找具有不同权衡的解决方案。伊辛机是旨在寻找伊辛模型绝对或近似基态的物理设备。为了将伊辛机应用于多目标问题，采用加权和的目标函数将多目标问题转化为单目标问题。然而，推导出能够实现帕累托前沿均匀分布解的标量化权重并非易事。先前的研究表明，基于二分搜索的自适应权重以及基于先前探索权重平均值的自适应方法，比均匀生成的权重能更快地探索帕累托前沿。然而，这些自适应方法过去仅被应用于双目标问题。在本工作中，我们从两个方面拓展了基于平均值的自适应方法：(i) 我们将推导标量化权重的自适应方法扩展到具有两个或更多目标的问题，并 (ii) 采用替代的距离度量以提高性能。我们将所提出的方法与现有方法进行比较，结果表明，该方法在具有3个和4个目标的多目标无约束二元二次规划（mUBQP）实例上取得了最佳性能，并且在具有2个目标的实例上能与最佳方法相媲美。