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.

翻译：标准进化优化算法假设,对目标和制约功能的评价是直接的,在计算上是廉价的。然而,在许多现实世界优化问题中,这些评价涉及计算费用昂贵的数字模拟或物理实验。代孕辅助进化算法(SAEAs)最近在解决这类问题方面表现得到越来越多的注意。SAEAs的主要想法是将进化算法与一个选定的代算法模型结合起来,该代算法与计算费用高昂的功能相近。在本文中,我们提出了一个基于Lipschitz低估的代算法模型,并用它来发展一种基于不同进化的算法。算法称为Lipschitz代孕辅助差异进化(LSADE),使用基于Lipschitz的代变算法模型,以及一个标准的辐射基代算模型和当地搜索程序。关于30、50、100和200维值的七个基准功能的实验结果显示,拟议的LSADE算法与有限计算预算下的最新算法相比具有竞争力,对于高度复杂的基准功能特别有效。