Distribution Direction-Assisted Two-Stage Knowledge Transfer for Many-Task Optimization

Evolutionary many-task optimization (EMaTO) endeavors to solve more than three optimization tasks simultaneously by leveraging similarities among tasks. While existing algorithms have shown promising results, they face significant challenges in low-similarity scenarios. First, existing transfer techniques, which rely on population location and distribution, become ineffective. Second, the difficulty of selecting appropriate knowledge increases significantly. To address these challenges, we introduce a new concept: distribution direction knowledge, i.e., the evolutionary direction (ED) of elite solutions. It enables the target task to learn the search experience of source tasks with similar evolutionary trends. To utilize this knowledge effectively, an EMaTO algorithm with distribution direction-assist two-stage knowledge transfer (DTSKT) is proposed. First, an ED-based multisource selection strategy is proposed to obtain appropriate knowledge in different circumstances. Second, we design a two-stage knowledge transfer (TSKT) strategy to search promising regions, consisting of exploration-oriented and exploitation-oriented knowledge transfer. In addition, to directly obtain distribution direction knowledge, the estimation of distribution algorithm is applied as the basic optimizer, explicitly revealing the ED of populations by employing probability distributions. Afterward, to validate the ability of DTSKT to handle tasks with different similarities, we utilize a test problem generator to create a more challenging many-task benchmark suite, named STOP. The results on the WCCI20 and STOP benchmark suites, along with a real-world application, demonstrate that DTSKT generally outperforms seven state-of-the-art algorithms.