提出自适应重采样方法，提升噪声环境下多目标优化效率
Adaptive Resampling with Bootstrap for Noisy Multi-Objective Optimization Problems
- 用自助法估计目标函数均值与支配概率，动态决策是否重采样
- 在多种噪声条件下，显著减少评估次数并逼近帕累托前沿
- 适合高噪声、样本少的工业级多目标优化问题
噪声多目标优化的核心挑战在于平衡探索新决策点与通过重采样提高已知点精度之间的权衡。这一决策需同时考虑目标函数的波动性及当前点对帕累托前沿的估计。由于噪声水平和分布通常未知，理想的决策函数应高度适应问题特性。本文提出一种基于自助法和支配概率的重采样决策函数，利用自助法估计均值实现无分布的支配概率估算。为应对极少数观测的情况，该方法从其他决策点转移分布信息。通过在NSGA-II中引入顺序重采样流程，在多种噪声变化下验证了该方法的高效性。
原文摘要 · Abstract (English)
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.
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