论文标题
将Lipschitz和RBF替代模型结合在一起，以解决高维昂贵的问题
Combining Lipschitz and RBF Surrogate Models for High-dimensional Computationally Expensive Problems
论文作者
论文摘要
标准进化优化算法假定，对目标和约束函数的评估是直接且计算便宜的。但是，在许多实际优化问题中，这些评估涉及计算昂贵的数值模拟或物理实验。替代辅助进化算法（SAEAS）最近因其在解决这些类型的问题方面的表现而引起了人们的关注。 SAEAS的主要思想是将进化算法与所选的替代模型的集成，该模型近似于计算量昂贵的函数。在本文中，我们提出了一个基于Lipschitz低估的替代模型，并使用它来开发基于差异进化的算法。该算法称为Lipschitz替代辅助差异进化（LSADE），利用了基于Lipschitz的替代模型，以及标准的径向基函数替代模型和局部搜索程序。在有限的计算预算下，与最先进的算法相比，与最先进的算法相比，提出的LSADE算法的七个基准函数的实验结果表明，所提出的LSADE算法具有竞争力，对于在高维度中非常复杂的基准功能特别有效。
Standard evolutionary optimization algorithms assume that the evaluation of the objective and constraint functions is straightforward and computationally cheap. However, in many real-world optimization problems, these evaluations involve computationally expensive numerical simulations or physical experiments. Surrogate-assisted evolutionary algorithms (SAEAs) have recently gained increased attention for their performance in solving these types of problems. The main idea of SAEAs is the integration of an evolutionary algorithm with a selected surrogate model that approximates the computationally expensive function. In this paper, we propose a surrogate model based on a Lipschitz underestimation and use it to develop a differential evolution-based algorithm. The algorithm, called Lipschitz Surrogate-assisted Differential Evolution (LSADE), utilizes the Lipschitz-based surrogate model, along with a standard radial basis function surrogate model and a local search procedure. The experimental results on seven benchmark functions of dimensions 30, 50, 100, and 200 show that the proposed LSADE algorithm is competitive compared with the state-of-the-art algorithms under a limited computational budget, being especially effective for the very complicated benchmark functions in high dimensions.
