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，代理辅助进化算法已被广泛用于求解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急剧下降。本文针对高维昂贵多目标优化问题，提出了一种新型的基于分类器辅助的排序学习与局部模型多目标进化算法（CLMEA）。该算法由三部分组成：基于分类器辅助的排序学习、基于超体积的非支配搜索，以及在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，将子代划分为多个等级。不同等级的子代采用基于排序的学习策略，生成更有前景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近似目标函数。在代理模型辅助搜索非支配解后，选择超体积改进量较大的候选解进行真实评估。此外，为保持解的多样性，基于拥挤距离从非支配解中选择不确定性最大的样本点作为引导父代，以进一步填充前沿的不确定区域。基准问题的实验结果以及地热储层取热优化实际应用表明，与现有最先进的代理辅助多目标进化算法相比，该算法展现出优越性能。本工作的源代码可在https://github.com/JellyChen7/CLMEA获取。