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Harris hawks optimization (HHO) algorithm inspired by the cooperative behavior and chasing style of harris' hawks in nature called surprise pounce is a relatively novel swarm intelligent optimization algorithm. Due to its simplicity and efficiency, the canonical HHO has displayed promising performance on a large number of continuous optimization problems and real-world optimization problems. However, how to balance contradictions between the exploration and exploitation capabilities and alleviate the premature convergence are two critical concerns that need to be dealt with in the HHO study. To address these two drawbacks, improve the optimization performance, and broaden its application domain, a dynamic multi-swarm differential learning Harris hawks optimizer (DMSDL-HHO) is proposed in this paper. To efficiently maintain the population diversity, the whole population is divided into many small sub-swarms, which are regrouped periodically, and information is exchanged among the swarms. In each generation, the differential evolution operator (including mutation, crossover, and selection operators) based on the personal historical best position is merged into each sub-swarm to augment the exploration capability, while the Quasi-Newton method as a local searcher is used to enhance the exploitation capability. Besides, aiming to prevent the algorithm from falling into local optima to some extent, the differential mutation operator candidate pool strategy is introduced into the late stage of the search process. Thus, different individuals in the same population can conduct distinct search behaviors in each generation, and the same individual can perform various search behaviors in different generations. The proposed algorithm is tested on 23 classic test functions and 30 CEC2014 benchmark functions and is compared with quite a few state-of-the-art algorithms in terms of often-used performance metrics with the help of statistical analysis, diversity measurement, exploration–exploitation investigations, ranking statistics, and Wilcoxon Signed Rank Test (WSRT). The experimental results verify the superior performance of the embedded strategies on balancing the exploration capability and the exploitation capability. In addition, the DMSDL-HHO is applied to the optimal dispatch problem of cascade hydropower stations (ODPCHS) based on a novel constraints handling method designed in this paper to demonstrate its good practicability and performance. The experimental results of a case study on the optimal dispatch problem of China's Wujiang cascade hydropower stations show that DMSDL-HHO can obtain better and more reliable optimal results than the canonical HHO and other compared algorithms. Moreover, the convergence speed of DMSDL-HHO is also competitive in contrast to other algorithms. Therefore, it can be concluded that DMSDL-HHO is a promising alternative tool for solving complex continuous optimization problems and real-world optimization problems with complex constraints. [ABSTRACT FROM AUTHOR]