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.

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 paper 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.

Ensemble of constraint handling techniques (CHTs) is an effective way for solving constrained optimization problems (COPs). However, the use of multiple CHTs might cause more resource overhead. How to make reasonable resource allocation and cooperation among different CHTs is the issue that requires much more attention to improve the effectiveness of the ensemble of CHTs. Based on this consideration, we tried to handle the issue with adaptive resource allocation and population co-evolution for competition and cooperation among different CHTs. First, the competitive and cooperative evolutionary framework (CCEF) was proposed to construct multiple populations for CHTs. It assigns separate populations to each CHT and performs resource allocation based on success history records calculated by the performance of each CHT population. In addition, it promotes population co-evolution through parent recombination and offspring diffusion. Second, four CHTs with different types were chosen to compose a technique pool for the implementation of CCEF. Third, to obtain stronger search ability, we designed a heuristic and historical-based differential evolutionary operator (EO) embedded into CCEF. Experimental results on five COP benchmark suites (116 COPs in total) and 33 real-world COPs demonstrated that the proposed CCEF outperforms other advanced algorithms. The results revealed that CCEF can absorb the advantages of different CHTs and appropriately allocate resources to the more suitable CHTs.

Solving nonlinear equations (NEs) requires the algorithm to locate multiple roots of NEs in one run. In this article, a generic framework based on two-stage reinforcement learning (RL) and differential evolution (DE) is proposed to effectively deal with NEs problems. The major advantage of our approach are: 1) different niching methods and mutation strategies are integrated into the DE algorithm to assist evolution; 2) the diversity is maintained by utilizing the search characteristics of different niching methods at population level; 3) additionally, each individual is regarded as an agent, and three classical mutation strategies are used as the agent’s alternative actions; and 4) different state settings and reward function can be easily integrated into this framework. To verify the performance of our approach, 30 problems and 18 new NEs are selected as the test suite. The experimental results demonstrate that RL can facilitate the algorithm and improve the problem-solving ability. Moreover, the proposed method also obtains competitive performance compared with other peer algorithms.