This paper introduces the mixed-strategy Harris hawk optimization (MSHHO) algorithm as an enhancement to address the limitations of the conventional Harris hawk optimization (HHO) algorithm in solving complex optimization problems. HHO often faces challenges such as susceptibility to local optima, slow convergence, and inadequate precision in global solution-seeking. MSHHO integrates four innovative strategies to bolster HHO’s effectiveness in both local exploitation and global exploration. These include a positive charge repulsion strategy for diverse population initialization, a nonlinear decreasing parameter to heighten competitiveness, the introduction of Gaussian random walk, and mutual benefit-based position updates to enhance mobility and escape local optima. Empirical validation on 12 benchmark functions from CEC2005 and comparison with 10 established algorithms affirm MSHHO’s superior performance. Applications to three real-world engineering problems and UAV flight trajectory optimization further demonstrate MSHHO’s efficacy in overcoming complex optimization challenges. This study underscores MSHHO as a robust framework with enhanced global exploration capabilities, significantly improving convergence accuracy and speed in engineering applications.