Multitask Evolution Strategy With Knowledge-Guided External Sampling

Evolutionary multitask optimization employs similarities among tasks via evolutionary algorithms (EAs) with knowledge transfer techniques to address multiple optimization tasks simultaneously. Although existing knowledge transfer techniques achieved success on population-based EAs, they are inappropriate for evolution strategies (ESs) that employ probability distribution sampling. These techniques will face two difficulties when applied to ESs: 1) distribution adaptation errors and 2) convergence difficulties. This article proposes a knowledge-guided external sampling (KGxS) method to provide effective knowledge transfer in multitask ESs (MTESs) for solving multitask optimization problems (MTOPs). KGxS guides the distribution evolution in the target task by transferring solutions from source tasks as external samples. Since these external samples are close to the target distribution, they can handle the difficulty of distribution adaptation errors. In addition, the convergence difficulty caused by negative knowledge transfer is also handled through a mitigation strategy, which adaptively controls the number of external samples. Besides, the external samples carry two kinds of knowledge: 1) domain knowledge which employs the similarity of the optimal domains among tasks and 2) shape knowledge that utilizes the function shapes similarity among tasks. Furthermore, a general boundary constraint handling technique is proposed for ESs to adapt to unconstrained and constrained optimization environments. Empirical results show that KGxS can significantly enhance the positive transfer effect on different types of ES on MTOPs. Moreover, the proposed method obtained superior performance over 20 state-of-the-art algorithms on 38 benchmark problems and three types of real-world applications, including multitask, many-task, and constrained multitask optimization.