Many expensive optimization problems exist in various real-world applications. However traditional evolutionary algorithms are inadequate for solving these problems directly. Surrogate-assisted evolutionary algorithm (SAEA) can effectively solve expensive optimization problems using computationally inexpensive surrogate models. However, both the Kriging and ensemble models most SAEAs adopted have limited uncertainty of prediction, especially for expensive multiobjective optimization problems (EMOPs). To enhance the optimization performance of SAEA for EMOPs, this paper proposes a new XGBoost-assisted evolutionary algorithm, calling XGBEA. Specifically, XGBoost is used as the surrogate model, and a neighborhood density selection strategy based on a mixed population and archive space (NDS-MPA) is proposed to measure the uncertainties of individuals. XGBoost helps to best fit objective functions with different fitness landscapes. NDS-MPA selects non-dominated individuals with minimal density for re-evaluation, incorporating considerations of convergence, diversity and uncertainty. Experimental results on two well-studied benchmarks demonstrated the superiority of XGBEA over seven state-of-the-art SAEAs.

中文翻译：

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用于解决昂贵的多目标优化问题的 XGBoost 辅助进化算法

各种实际应用中存在许多昂贵的优化问题。然而传统的进化算法不足以直接解决这些问题。替代辅助进化算法（SAEA）可以使用计算成本低廉的替代模型有效地解决昂贵的优化问题。然而，大多数 SAEA 采用的克里金法和集成模型的预测不确定性有限，特别是对于昂贵的多目标优化问题 (EMOP)。为了增强 SAEA 对 EMOP 的优化性能，本文提出了一种新的 XGBoost 辅助进化算法，称为 XGBEA。具体来说，使用XGBoost作为代理模型，提出基于混合群体和档案空间（NDS-MPA）的邻域密度选择策略来衡量个体的不确定性。 XGBoost 有助于最佳地适应不同健身环境的目标函数。 NDS-MPA选择密度最小的非支配个体进行重新评估，综合考虑收敛性、多样性和不确定性。两个经过充分研究的基准测试的实验结果证明了 XGBEA 相对于七个最先进的 SAEA 的优越性。