粒子滤波优化：一种用于全局随机优化的贝叶斯方法
Particle Filter Optimization: A Bayesian Approach for Global Stochastic Optimization
AI总结：
提出基于粒子滤波的全局随机优化算法PFO，将优化重构为状态估计，用协方差椭球转移模型替代采集函数，结合无迹变换抗噪，实现探索与利用统一，优于现有黑箱多模态优化方法。
摘要：
本文提出了一种新颖的全局优化算法——基于粒子滤波的优化（Particle Filter-Based Optimization, PFO），该算法针对一类目标函数缺乏解析形式且评估带有噪声的随机优化问题而设计。PFO利用粒子滤波（Particle Filters, PF）的贝叶斯推断框架，将优化任务重新表述为状态估计问题。在此背景下，目标函数的评估被解释为测量值，并引入了一种基于协方差椭球的自定义转移模型来引导粒子传播。该模型作为经典采集函数的替代，赋予粒子滤波框架局部搜索能力，并支持对全局最优解的高效探索。为了减轻测量噪声的不利影响，采用无迹变换（Unscented Transform, UT）来近似目标函数的潜在均值，从而提高粒子更新的准确性。该算法在针对黑箱多模态目标函数的现有随机优化算法基础上提供了显著改进。首先，PFO提供了粒子权重的完全概率性定义，增强了适应性和鲁棒性。其次，PFO在统一的贝叶斯框架内整合了探索与利用，确保在整个优化过程中对未探索区域进行采样的概率非零。这种方法与主要用于状态估计的传统粒子滤波方法以及缺乏理论保证的启发式优化算法形成对比。PFO的新颖之处在于其将粒子滤波与动态搜索空间预测独特地结合起来，为贝叶斯优化（Bayesian Optimization, BO）中的采集函数提供了一种具有理论基础的替代方案。
英文摘要：
This paper proposes a novel global optimization algorithm, Particle Filter-Based Optimization (PFO), designed for a class of stochastic optimization problems in which the objective function lacks an analytical form and is subject to noisy evaluations. PFO utilizes the Bayesian inference framework of Particle Filters (PF) by reformulating the optimization task as a state estimation problem. In this context, evaluations of the objective function are interpreted as measurements, and a customized transition model based on covariance ellipsoids is introduced to guide particle propagation. This model serves as a surrogate for classical acquisition functions, equipping the PF framework with local search capabilities and supporting efficient exploration of the global optimum. To mitigate the adverse effects of measurement noise, the Unscented Transform (UT) is employed to approximate the underlying mean of the objective function, enhancing the accuracy of particle updates. The algorithm offers notable improvements over existing stochastic optimization algorithms for black-box multi-modal objective functions. First, PFO provides a fully probabilistic definition of particle weights, enhancing adaptability and robustness. Second, PFO integrates exploration and exploitation within a unified Bayesian framework, ensuring a non-zero probability of sampling from unexplored regions throughout the optimization process. This approach contrasts with traditional particle filter methods that are primarily used for state estimation, and heuristic optimization algorithms that lack theoretical guarantees. The novelty of PFO lies in its unique integration of particle filtering with a dynamic search space prediction, offering a theoretically grounded alternative to acquisition functions in Bayesian Optimization (BO).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
