Estimation of distribution algorithm (EDA) is an efficient population-based stochastic search technique. Since it was proposed, many attempts have been made to improve its performance in the context of nonlinear continuous optimization. However, the success of EDA depends on the accuracy of modeling, the effectiveness of sampling, and the ability of exploration. An effective EDA often needs to take some measures to adjust the model and to guide sampling. In this article, we propose a novel EDA which applies the idea of Kalman filtering to revise the modeling data and a learning strategy to improve sampling. The filtering scheme modifies the modeling data set using an estimation error matrix based on historic solution data. During the sampling process, the learning strategy determines the region to sample next based on the sampling outcomes so far, instead of completely random sampling. The proposed EDA also employs a multivariate probabilistic model based on copula function and can quickly reach the promising area in which the optimal solution is likely to be located. A collection of general benchmark functions are used to test the performance of the proposed algorithm. Computational experiments show that the EDA is effective. Note to Practitioners —In many process industries, there exist black-box operation optimization problems and large-scale nonlinear optimization problems with variable coupling. For these problems, it is difficult to establish mechanism models between input and output. However, real-time data can be measured from the system through sensors. We can utilize this process information to optimize the system so as to attain the desired objective. In this article, we propose a novel estimation of distribution algorithm (EDA) which applies a filtering scheme to revise the modeling data and a learning strategy to improve sampling, which can solve the problems with the characteristics of nonlinearity, variable coupling, and large scale. Computational experiments show that the EDA is effective. In the future, the proposed algorithm can be applied to some practical optimization problems such as operation optimization in blast furnace, which is considered as a continuous production process with variable coupling. The algorithm has the potential to help optimizing the process control parameters.

中文翻译：

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带过滤和学习的分布算法估计

分布估计算法 (EDA) 是一种有效的基于群体的随机搜索技术。自从它被提出以来，已经进行了许多尝试以在非线性连续优化的背景下提高其性能。但是，EDA 的成功取决于建模的准确性、采样的有效性以及探索的能力。一个有效的EDA往往需要采取一些措施来调整模型和指导抽样。在本文中，我们提出了一种新颖的 EDA，它应用卡尔曼滤波的思想来修改建模数据和改进采样的学习策略。过滤方案使用基于历史解数据的估计误差矩阵修改建模数据集。在采样过程中，学习策略根据到目前为止的采样结果确定下一个采样的区域，而不是完全随机抽样。所提出的 EDA 还采用了基于 copula 函数的多元概率模型，可以快速到达最优解可能位于的有希望的区域。一组通用基准函数用于测试所提出算法的性能。计算实验表明EDA是有效的。从业者须知 ——在许多过程工业中，存在着黑箱操作优化问题和变耦合的大规模非线性优化问题。对于这些问题，很难在输入和输出之间建立机制模型。但是，可以通过传感器从系统测量实时数据。我们可以利用这些过程信息来优化系统，以达到预期的目标。在本文中，我们提出了一种新颖的分布估计算法（EDA），该算法应用滤波方案来修正建模数据和学习策略来改进采样，可以解决非线性、可变耦合和大规模等特点的问题。 . 计算实验表明EDA是有效的。将来，所提出的算法可以应用于一些实际优化问题，例如高炉操作优化，高炉​​被认为是一个具有可变耦合的连续生产过程。该算法有可能帮助优化过程控制参数。