###### Abstract
proposed an improved Harris hawks method based on the random replace method and Laplace crossover to address the issues of the algorithm's poor convergence speed and increase its local exploitation capability [39]. [PERSON] et al. put forward that HHO was widely employed in optimization issues, which might efficiently eliminate unnecessary characteristics and enhance the algorithm's classification performance [40]. The ability of the offered methodologies to identify the ideal feature subset was demonstrated by [PERSON] et al. 's new HHO, which used an energetic learning method and memory storage update mechanism [41]. Although many experts have conducted extensive research and improvements on HHO, significant room for development remains. To further enhance HHO's performance, this article proposes a mixed-strategy Harris hawk optimization (MSHHO) algorithm. Firstly, a novel initialization algorithm is proposed, which utilizes the principle of positive charge repulsion to enhance the population's diversity. Secondly, a non-linear decreasing escape strategy is adopted during the Harris hawk hunting process to improve the precision and stability of the algorithm. Thirdly, a Gaussian random walk strategy and position update strategy based on mutual benefit and symbiosis are incorporated to greatly improve the algorithm's ability to escape local extremum. The simulation results show that MSHHO has significant advantages in precision, convergence speed, and stability compared to other popular algorithms. The major contributions of this article are as follows. 1. Four strategies were implemented to enhance the performance of HHO. Firstly, the positive charge repulsion initialization enriches population diversity, fostering a broader exploration of solution space. Secondly, the nonlinear escape factor enhances optimization capabilities by facilitating efficient movement towards optimal solutions. Thirdly, the Gaussian random walk strategy improves movement abilities, introducing randomness to explore diverse solution paths effectively. Lastly, the position update strategy, based on mutual benefit and symbiosis, promotes algorithmic development by exchanging beneficial information among individuals. Together, these strategies bolster global exploration and mitigate the risk of getting trapped in local optima, thereby enhancing overall algorithm performance. 2. The MSHHO is comprehensively tested on 12 unconstrained benchmark functions, three constrained optimization issues, and a UAV flight trajectory optimization and compared with popular algorithms. The statistical results indicate that the MSHHO algorithm has significant superiority in solving optimization issues. 3. Population initialization is an important step in MAs, which can be achieved through various methods such as random initialization, uniform initialization, clustering initialization, chaotic mapping, etc. This article innovatively uses the principle of positive charge repulsion to initialize the population, solving the problem of local aggregation and loss of population, making the population distribution more uniform and stable while satisfying randomness. Here is the structure for the remainder of the paper. Section 2 explores the foundational theory of HHO, elucidating its core principles. Section 3 introduces the mathematical model of MSHHO, highlighting key enhancements to the original algorithm. Section 4 presents empirical results from applying MSHHO across various optimization scenarios, illustrating its efficacy. Section 5 rigorously tests MSHHO on three distinct real-world engineering challenges and UAV flight trajectory optimization, underscoring its practical utility and performance. Finally, Section 6 synthesizes the study's findings and conclusions.