数据驱动的高维复杂进化优化方法研究

The computationally cheap surrogate models, which are trained using the historical data that have been evaluated using the computationally expensive exact objective function, are paid more and more attentions in recent years for assisting evolutionary optimization algorithms to solve computationally expensive complex problems, and have been applied in different fields, such as aerodynamic optimization design, structural optimization design, et al.. However, when the dimension of the optimization problems increases, more training data or labeled data that evaluated using the real time-consuming objective function are required, which put great difficulties to train a correct surrogate model because of the lack of labeled data as it requires more time to obtain a labeled data when the optimization problem becomes more complex. In this project, based on the previous research achievements, we first propose to study on the strategy of adaptive feature selection by analyzing the expected contributions of the surrogate model in the algorithm, and correspondingly implement the dynamic decomposition on the high dimensional problems so as to improve the efficiency of training a model. Then, new strategies for adaptive selecting unlabeled data to assist training the surrogate models after dimension reduction will be studied. Third, multi-tasking optimization methods will be adopted for simultaneously optimizing lower-dimensional simple problems or lower-dimensional models and the original high-dimensional complex problem, and corresponding implement the transfer optimization based on simple problems or surrogate models. Finally, all achievements will be applied in the optimization of storage density of dielectric glass-ceramic composite. The achievements of the proposed project is expected to significantly enlarge the applicability range of evolutionary optimization algorithms, which is of very high practical values.

近几年，基于历史数据建立计算廉价的代理模型以辅助进化优化算法求解计算费时的复杂优化问题受到了越来越多的关注，在气动优化、结构优化等方面获得了较多的应用。然而，当优化问题的维度进一步提高，训练模型需要的训练样本增多且对样本的一次标注耗时增加，导致获得标注样本困难，从而建立的模型准确度降低。为此，本项目针对计算费时的高维复杂优化优化问题，在以往研究的基础上，首先基于模型所需发挥作用研究自适应的特征选择策略，实现对高维问题的动态分解，以提高模型的训练效率。其次，基于降维后模型的用途引入无标注样本的自适应选择策略，以提高模型的范化能力。第三，利用多任务优化学习方法，将低维简单问题或低维模型和原高维复杂问题同时优化，实现基于简单问题或代理模型的迁移优化。最后，将研究成果应用于玻璃陶瓷介电材料储能密度的优化设计中。本课题的研究成果将进一步扩大进化优化算法的求解范围，具有重要的实际应用价值。

近年来，数据驱动的进化优化算法在求解评价昂贵的黑盒问题方面获得了越来越多的关注。然而，随着优化问题决策变量的增多，一方面，搜索空间增大，增加了找到最优解的难度，另一方面，训练模型所需的样本数增多，而对于昂贵问题来说很难获得较多的评价数据；另外，随着优化问题目标空间维度的增大，估值的不确定度随之累加，迫切需要合适的模型管理策略。本项目针对大规模优化问题、高维昂贵优化问题、多目标/高维多目标优化问题等问题展开研究。针对大规模单目标计算廉价问题和大规模多目标计算廉价问题，分别提出了新的种群更新策略和方向采样策略。针对大规模单目标计算昂贵问题，基于随机特征选择策略和随机分组策略实现对大规模问题的降维，通过对代理模型辅助的低维子问题优化实现对大规模问题的求解。针对高维昂贵优化算法，提出了不同的模型集成策略、基于不确定度以及多目标选择策略的填充采样方法、无标记个体的选用策略以及多任务优化策略。基于多理想点引导和问题转化策略，提出了不同的高维多目标优化算法。针对昂贵多目标优化问题，分别采用对目标函数建模和对性能指标建模来引导优化搜索。此外，通过实验分析对比了贝叶斯优化方法和代理模型辅助的进化多目标优化方法的性能。该项目的研究不仅为高维复杂工程问题的优化设计提供了新的有效方法，而且可进一步为实际复杂工程问题的优化设计提供技术和理论依据。该项目所取得的成果已发表在《IEEE Transactions on Evolutionary Computation》、《Information Sciences》、《Knowledge-based Systems》等该领域知名期刊以及PPSN、CEC、SSCI等知名国际会议上，发表与录用30篇、在审4篇，在写专著一部。