Robust optimisation is a well-established framework for optimising functions
in the presence of uncertainty. The inherent goal of this problem is to
identify a collection of inputs whose outputs are both desirable for the
decision maker, whilst also being robust to the underlying uncertainties in the
problem. In this work, we study the multi-objective extension of this problem
from a computational standpoint. We identify that the majority of all robust
multi-objective algorithms rely on two key operations: robustification and
scalarisation. Robustification refers to the strategy that is used to
marginalise over the uncertainty in the problem. Whilst scalarisation refers to
the procedure that is used to encode the relative importance of each objective.
As these operations are not necessarily commutative, the order that they are
performed in has an impact on the resulting solutions that are identified and
the final decisions that are made. This work aims to give an exposition on the
philosophical differences between these two operations and highlight when one
should opt for one ordering over the other. As part of our analysis, we
showcase how many existing risk concepts can be easily integrated into the
specification and solution of a robust multi-objective optimisation problem.
Besides this, we also demonstrate how one can principally define the notion of
a robust Pareto front and a robust performance metric based on our robustify
and scalarise methodology. To illustrate the efficacy of these new ideas, we
present two insightful numerical case studies which are based on real-world
data sets.

基于鲁棒优化的多目标问题，介绍了鲁棒化和标量化两种关键操作之间的哲学差异，展示了风险概念在鲁棒多目标优化问题中的集成，并通过两个基于真实数据集的案例研究验证了这些新思路的有效性。