面向噪声优化的进化算法动态重采样策略研究

In real-world optimization problems, the solution or the evaluation of a solution may be affected by noise. Noisy optimization is the optimization of objective functions corrupted by noise, aiming at searching for solutions that achieve optimal expected objective value. In real-world applications, the noise come from various uncertainties that can affect the evaluation of a solution. As a consequence of a lack of knowledge of the uncertainties, black-box noisy optimization is considered. Evolutionary computation techniques are suitable for black-box noisy optimization as they do not require knowledge about the problems. However, there is still a risk of mis-ranking solutions due to the noise, which probably leads to the divergence or slow convergence of algorithms. Resampling, i.e. evaluating a given solution multiple times, can be used to reduce the effect of noise. Designing resampling strategies is a difficult challenge. Existed works usually assume Gaussian noise, the asymmetric noise models are rarely investigated. current research assumes that the noisy objective values are independent and identically distributed random variables, this is sometimes not the case in real-world applications. Additionally, some state-of-the-art resampling strategies are usually designed for specific noise models. When the noise model is unknown or complicated, it is not possible to design particularly efficient resampling strategy based on the noise model. In this project, we aim at designing dynamic resampling strategies that enhance evolutionary techniques and are self-adaptive, robust to noisy optimization problems, using stochastic optimization, automatic algorithm configuration and reinforcement learning techniques.

实际优化问题中，对解或决策的评估往往被问题的噪声影响。噪声优化主要研究在有噪声情况下高效搜索一个或多个最优解使得其目标函数的期望值达到最优。噪声来自于多种可能影响决策评估结果的不确定性因素，其对评估解的具体影响多是未知的。进化算法由于其不对待求解问题做过多假设而备受青睐。然而，解的比较可能因为噪声引起错判，导致算法不收敛或收敛速率过慢。一个直接的降噪方法是重采样解。对于噪声的先验知识的缺失为重采样策略的设计带来了巨大的挑战，主要包括：现有研究往往假设噪声是个对称分布的随机过程，缺少对非对称噪声的研究；现有研究通常假设一个解的多次重采样值是独立同分布的，此假设在一些实际应用中是不现实的；经典的重采样策略往往是针对单一噪声模型量身定制的，难以适应求解实际的复杂噪声优化问题的需求。本项目针对这些挑战，结合随机优化、自动算法设计和强化学习的思想，展开面向噪声优化的进化算法动态重采样策略研究。

噪声优化或不确定最优化是指给定解的目标函数值被噪声或不确定性影响的情况下，高效搜索一个或多个最优解使得其目标函数的期望值达到最优。这类问题广泛存在于实际场景、智能优化算法的自动配置以及机器学习模型的评估中。在不同的场景下，噪声来自于多种可能影响解或决策（如调度方案、发动机模型参数、优化算法的配置方案、神经网络结构或权重等）评估结果的不确定性因素，导致优化算法不收敛或收敛速率过慢。面向此类问题的一个直接处理方法是对解进行重采样或重评估。然而，重评估次数的判定存在探索-利用困境。本项目面向复杂噪声下的动态重采样开展研究，将随机优化、自动算法设计和强化学习的思想应用于设计面向复杂噪声优化问题的动态重采样策略，并验证本项目研究的动态重采样策略，不仅在通用的算法验证问题集进行验证，也选取了两个实际工业场景进行建模和算法验证。本项目研究的抽象问题广泛存在于多种多样的含有不确定性的优化问题，这些问题主要区别于对于解的定义和建模、以及关于噪声的假设。因此，本项目的研究成果可以用于含有不确定性的优化问题或评估过程会被不确定性干扰的问题，被重采样/评估的对象可以是一个具体的调度方案、一个机器学习模型、一个算法的优化算子或者配置等等，具有重要的科学意义和广泛的应用前景。