The challenge of noisy multi-objective optimization lies in the constant trade-off between exploring new decision points and improving the precision of known points through resampling. This decision should take into account both the variability of the objective functions and the current estimate of a point in relation to the Pareto front. Since the amount and distribution of noise are generally unknown, it is desirable for a decision function to be highly adaptive to the properties of the optimization problem. This paper presents a resampling decision function that incorporates the stochastic nature of the optimization problem by using bootstrapping and the probability of dominance. The distribution-free estimation of the probability of dominance is achieved using bootstrap estimates of the means. To make the procedure applicable even with very few observations, we transfer the distribution observed at other decision points. The efficiency of this resampling approach is demonstrated by applying it in the NSGA-II algorithm with a sequential resampling procedure under multiple noise variations.

翻译：噪声多目标优化的核心挑战在于探索新决策点与通过重采样提升已知点精度之间的持续权衡。该决策需同时考虑目标函数的变异特性以及当前解相对于帕累托前沿的估计位置。由于噪声的强度与分布通常未知，理想的决策函数应具备对优化问题特性的高度自适应性。本文提出一种结合Bootstrap方法与支配概率的重采样决策函数，通过概率化建模捕捉优化问题的随机本质。基于Bootstrap均值估计实现了对支配概率的无分布估计。为使方法在极少观测数据下仍具适用性，我们引入了跨决策点的分布迁移机制。通过将本方法嵌入NSGA-II算法并采用序列重采样流程，在多种噪声变异场景下验证了该重采样策略的有效性。