For offline data-driven multiobjective optimization problems (MOPs), no new data is available during the optimization process. Approximation models (or surrogates) are first built using the provided offline data, and an optimizer, for example, a multiobjective evolutionary algorithm, can then be utilized to find Pareto optimal solutions to the problem with surrogates as objective functions. In contrast to online data-driven MOPs, these surrogates cannot be updated with new data and, hence, the approximation accuracy cannot be improved by considering new data during the optimization process. Gaussian process regression (GPR) models are widely used as surrogates because of their ability to provide uncertainty information. However, building GPRs becomes computationally expensive when the size of the dataset is large. Using sparse GPRs reduces the computational cost of building the surrogates. However, sparse GPRs are not tailored to solve offline data-driven MOPs, where good accuracy of the surrogates is needed near Pareto optimal solutions. Treed GPR (TGPR-MO) surrogates for offline data-driven MOPs with continuous decision variables are proposed in this paper. The proposed surrogates first split the decision space into subregions using regression trees and build GPRs sequentially in regions close to Pareto optimal solutions in the decision space to accurately approximate tradeoffs between the objective functions. TGPR-MO surrogates are computationally inexpensive because GPRs are built only in a smaller region of the decision space utilizing a subset of the data. The TGPR-MO surrogates were tested on distance-based visualizable problems with various data sizes, sampling strategies, numbers of objective functions, and decision variables. Experimental results showed that the TGPR-MO surrogates are computationally cheaper and can handle datasets of large size. Furthermore, TGPR-MO surrogates produced solutions closer to Pareto optimal solutions compared to full GPRs and sparse GPRs.

中文翻译：

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用于解决离线数据驱动的连续多目标优化问题的树状高斯过程回归。

对于离线数据驱动的多目标优化问题（MOP），优化过程中没有新数据可用。首先使用提供的离线数据构建近似模型（或代理），然后可以利用优化器（例如多目标进化算法）以代理作为目标函数找到问题的帕累托最优解。与在线数据驱动的 MOP 相比，这些替代项无法使用新数据进行更新，因此在优化过程中无法通过考虑新数据来提高近似精度。高斯过程回归 (GPR) 模型因其提供不确定性信息的能力而被广泛用作替代模型。然而，当数据集很大时，构建探地雷达的计算成本会变得昂贵。使用稀疏探地雷达可以降低构建代理的计算成本。然而，稀疏探地雷达不适用于解决离线数据驱动的 MOP，其中需要接近帕累托最优解的良好代理精度。本文提出了具有连续决策变量的离线数据驱动 MOP 的树状 GPR (TGPR-MO) 替代方案。所提出的代理首先使用回归树将决策空间划分为子区域，并在决策空间中接近帕累托最优解的区域中顺序构建 GPR，以准确地近似目标函数之间的权衡。TGPR-MO 代理在计算上成本低廉，因为 GPR 仅利用数据子集在决策空间的较小区域中构建。TGPR-MO 代理在具有各种数据大小、采样策略、目标函数数量和决策变量的基于距离的可视化问题上进行了测试。实验结果表明，TGPR-MO 代理的计算成本更低，并且可以处理大尺寸的数据集。此外，与完整 GPR 和稀疏 GPR 相比，TGPR-MO 替代方案产生的解决方案更接近 Pareto 最优解。