We propose a new particle swarm optimization algorithm for problems where objective functions are subject to zero-mean, independent, and identically distributed stochastic noise. While particle swarm optimization has been successfully applied to solve many complex deterministic nonlinear optimization problems, straightforward applications of particle swarm optimization to noisy optimization problems are subject to failure because the noise in objective function values can lead the algorithm to incorrectly identify positions as the global/personal best positions. Instead of having the entire swarm follow a global best position based on the sample average of objective function values, the proposed new algorithm works with a set of statistically global best positions that include one or more positions with objective function values that are statistically equivalent, which is achieved using a combination of statistical subset selection and clustering analysis. The new PSO algorithm can be seamlessly integrated with adaptive resampling procedures to enhance the capability of PSO to cope with noisy objective functions. Numerical experiments demonstrate that the new algorithm is able to consistently find better solutions than the canonical particle swarm optimization algorithm in the presence of stochastic noise in objective function values with different resampling procedures.

中文翻译：

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求解噪声优化问题的新粒子群算法

我们针对目标函数受到零均值，独立且均匀分布的随机噪声的问题提出了一种新的粒子群优化算法。虽然粒子群优化已成功应用于解决许多复杂的确定性非线性优化问题，但是粒子群优化在嘈杂的优化问题上的直接应用会失败，因为目标函数值中的噪声会导致算法错误地将位置识别为全局/个人最佳职位。所提出的新算法不是基于目标函数值的样本平均值使整个群体遵循全局最佳位置，而是与一组统计上全局的最佳算法一起工作包括一个或多个位置的目标函数值在统计上相等的位置，这可以通过统计子集选择和聚类分析相结合来实现。新的PSO算法可以与自适应重采样过程无缝集成，以增强PSO应对嘈杂的目标函数的能力。数值实验表明，在目标函数值存在随机噪声且采样过程不同的情况下，新算法能够比经典粒子群优化算法始终找到更好的解决方案。