Existing work on offline data-driven optimization mainly focuses on problems in static environments, and little attention has been paid to problems in dynamic environments. Offline data-driven optimization in dynamic environments is a challenging problem because the distribution of collected data varies over time, requiring surrogate models and optimal solutions tracking with time. This paper proposes a knowledge-transfer-based data-driven optimization algorithm to address these issues. First, an ensemble learning method is adopted to train surrogate models to leverage the knowledge of data in historical environments as well as adapt to new environments. Specifically, given data in a new environment, a model is constructed with the new data, and the preserved models of historical environments are further trained with the new data. Then, these models are considered to be base learners and combined as an ensemble surrogate model. After that, all base learners and the ensemble surrogate model are simultaneously optimized in a multitask environment for finding optimal solutions for real fitness functions. In this way, the optimization tasks in the previous environments can be used to accelerate the tracking of the optimum in the current environment. Since the ensemble model is the most accurate surrogate, we assign more individuals to the ensemble surrogate than its base learners. Empirical results on six dynamic optimization benchmark problems demonstrate the effectiveness of the proposed algorithm compared with four state-of-the-art offline data-driven optimization algorithms. Code is available at https://github.com/Peacefulyang/DSE_MFS.git.

现有的离线数据驱动优化工作主要关注静态环境中的问题，而很少关注动态环境中的问题。动态环境中的离线数据驱动优化是一个具有挑战性的问题，因为收集的数据的分布随时间变化，需要代理模型和随时间跟踪的最优解决方案。本文提出了一种基于知识转移的数据驱动优化算法来解决这些问题。首先，采用集成学习方法来训练代理模型，以利用历史环境中的数据知识并适应新环境。具体来说，给定新环境中的数据，用新数据构建模型，并用新数据进一步训练保留的历史环境模型。然后，这些模型被认为是基础学习器并组合为集成代理模型。之后，所有基础学习器和集成代理模型在多任务环境中同时优化，以找到真实适应度函数的最佳解决方案。这样，可以利用之前环境中的优化任务来加速当前环境中最优值的跟踪。由于集成模型是最准确的代理，因此我们为集成代理分配了比其基础学习器更多的个体。六个动态优化基准问题的实证结果证明了该算法与四种最先进的离线数据驱动优化算法相比的有效性。代码可在 https://github.com/Peacefulyang/DSE_MFS.git 获取。