Surrogate-assisted evolutionary algorithms have been widely developed to solve complex and computationally expensive multi-objective optimization problems in recent years. However, when dealing with high-dimensional optimization problems, the performance of these surrogate-assisted multi-objective evolutionary algorithms deteriorate drastically. In this work, a novel Classifier-assisted rank-based learning and Local Model based multi-objective Evolutionary Algorithm (CLMEA) is proposed for high-dimensional expensive multi-objective optimization problems. The proposed algorithm consists of three parts: classifier-assisted rank-based learning, hypervolume-based non-dominated search, and local search in the relatively sparse objective space. Specifically, a probabilistic neural network is built as classifier to divide the offspring into a number of ranks. The offspring in different ranks uses rank-based learning strategy to generate more promising and informative candidates for real function evaluations. Then, radial basis function networks are built as surrogates to approximate the objective functions. After searching non-dominated solutions assisted by the surrogate model, the candidates with higher hypervolume improvement are selected for real evaluations. Subsequently, in order to maintain the diversity of solutions, the most uncertain sample point from the non-dominated solutions measured by the crowding distance is selected as the guided parent to further infill in the uncertain region of the front. The experimental results of benchmark problems and a real-world application on geothermal reservoir heat extraction optimization demonstrate that the proposed algorithm shows superior performance compared with the state-of-the-art surrogate-assisted multi-objective evolutionary algorithms. The source code for this work is available at https://github.com/JellyChen7/CLMEA.

翻译：近年来，代理辅助进化算法被广泛用于解决复杂且计算昂贵的多目标优化问题。然而，在处理高维优化问题时，这些代理辅助多目标进化算法的性能会显著下降。本文提出了一种新颖的分类器辅助秩学习与局部模型多目标进化算法（CLMEA），用于解决高维昂贵多目标优化问题。该算法由三部分组成：分类器辅助的秩学习、基于超体积的非支配搜索，以及相对稀疏目标空间中的局部搜索。具体而言，构建概率神经网络作为分类器，将子代划分为若干秩。不同秩的子代采用基于秩的学习策略，生成更具潜力和信息量的候选解用于真实函数评估。随后，构建径向基函数网络作为代理模型来逼近目标函数。在通过代理模型搜索非支配解后，选择具有更高超体积改进的候选解进行真实评估。此外，为保持解集的多样性，从非支配解中选取由拥挤距离度量的最不确定样本点作为引导父代，进一步填充前沿的不确定区域。基准问题测试以及地热储层热提取优化这一实际应用的实验结果表明，所提算法相较于最先进的代理辅助多目标进化算法表现出更优性能。本工作源代码可从 https://github.com/JellyChen7/CLMEA 获取。