Recently, evolutionary algorithms have made great achievements in multi-objective optimization problems (MOPs), but there is a little research on how to deal with noisy multi-objective optimization problems (NMOPs), which are quite common in real life. The work in this paper attempts to find the commonality of noises in images/signals and NMOPs and analyzes the effects of several classical smoothing techniques in images/signals on NMOPs. A novel denoising algorithm that embeds the mean and Wiener filters into existing multi-objective optimization algorithms is proposed. In the proposed method, resampling is employed to maintain the accuracy of non-dominated solutions and filters are utilized to denoise dominated solutions, where the mean and Wiener filters are conducive to balance convergence and diversity of the population, respectively. This is the first use of filters in NMOPs, and it will promote the application of denoising methods in images/signals to NMOPs. The empirical results show the superiority of filters to denoise problems with low/medium-intensity noises and continuous Pareto front, compared with several state-of-the-art algorithms.

近来，进化算法在多目标优化问题（MOPs）上取得了很大的成就，但关于如何处理噪声多目标优化问题（NMOPs）的研究很少，这在现实生活中很常见。本文的工作试图找出图像/信号和 NMOP 中噪声的共性，并分析图像/信号中几种经典平滑技术对 NMOP 的影响。提出了一种将均值滤波器和维纳滤波器嵌入到现有多目标优化算法中的新型去噪算法。在所提出的方法中，采用重采样来保持非支配解的准确性，并利用滤波器​​对支配解进行去噪，其中均值和维纳滤波器分别有利于平衡种群的收敛性和多样性。这是 NMOPs 中首次使用滤波器，它将推动图像/信号去噪方法在 NMOPs 中的应用。经验结果表明，与几种最先进的算法相比，滤波器在低/中强度噪声和连续帕累托前沿的降噪问题上具有优越性。