Multiobjective Multitask Optimization With Manifold Structure-Driven Knowledge Transfer

Evolutionary multitasking (EMT) endeavors to solve multiple optimization tasks simultaneously via knowledge transfer (KT) among tasks. While several EMT algorithms have obtained promising results, they still encounter uncertainties and challenges in the complex field of multiobjective multitask optimization (MO-MTO). A key limitation of existing approaches is the insufficient attention to manifold structures of the Pareto set (PS), which represent the local regularities of multiobjective optimization problems. Ignoring these structures prevents the algorithm from capturing local features, thereby limiting the efficiency and accuracy of KT. To alleviate this issue, this article proposes a new EMT algorithm for MO-MTO with manifold structure-driven KT, namely EMT-MSKT. EMT-MSKT aims to improve optimization performance by leveraging both global and local structural information. In particular, KT in EMT-MSKT consists of two key strategies: global structure learning (GSL) and local structure learning (LSL). GSL exploits global structural similarity to provide population-level directional information that drives broad exploration across tasks. LSL exploits local structural similarity to support fine-grained exploitation based on manifold features. To implement these two strategies, the global and local search directions are extracted as knowledge, reflecting how solutions evolve within these structures. Moreover, to further enhance transfer efficiency in the LSL process, a local source selection (LSS) strategy is developed to identify relevant knowledge sources based on local manifold similarities. Comprehensive results on four benchmark suites (including a newly constructed suite for complex problems) and three real-world applications demonstrate that EMT-MSKT consistently outperforms other state-of-the-art algorithms.