Several practical applications of evolutionary computation possess objective functions that receive the design variables and externally given parameters. Such problems are termed contextual optimization problems. These problems require finding the optimal solutions corresponding to the given context vectors. Existing contextual optimization methods train a policy model to predict the optimal solution from context vectors. However, the performance of such models is limited by their representation ability. By contrast, warm starting methods have been used to initialize evolutionary algorithms on a given problem using the optimization results on similar problems. Because warm starting methods do not consider the context vectors, their performances can be improved on contextual optimization problems. Herein, we propose a covariance matrix adaptation evolution strategy with contextual warm starting (CMA-ES-CWS) to efficiently optimize the contextual optimization problem with a given context vector. The CMA-ES-CWS utilizes the optimization results of past context vectors to train the multivariate Gaussian process regression. Subsequently, the CMA-ES-CWS performs warm starting for a given context vector by initializing the search distribution using posterior distribution of the Gaussian process regression. The results of the numerical simulation suggest that CMA-ES-CWS outperforms the existing contextual optimization and warm starting methods.

翻译：进化计算在若干实际应用中具有接收设计变量与外部给定参数的目标函数，此类问题被称为上下文优化问题。这类问题需要针对给定的上下文向量寻找对应的最优解。现有的上下文优化方法通过训练策略模型来根据上下文向量预测最优解，但此类模型的性能受限于其表征能力。相比之下，热启动方法利用相似问题的优化结果在给定问题上初始化进化算法。由于热启动方法未考虑上下文向量，其在上下文优化问题中的性能仍有提升空间。本文提出一种具有上下文热启动的协方差矩阵自适应进化策略（CMA-ES-CWS），以针对给定上下文向量高效优化上下文优化问题。CMA-ES-CWS利用历史上下文向量的优化结果训练多元高斯过程回归模型，进而通过高斯过程回归的后验分布初始化搜索分布，实现对给定上下文向量的热启动。数值仿真结果表明，CMA-ES-CWS在性能上优于现有的上下文优化方法与热启动方法。