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.

Beluga whale optimization (BWO) is a swarm-based metaheuristic algorithm inspired by the group behavior of beluga whales. BWO suffers from drawbacks such as an insufficient exploration capability and the tendency to fall into local optima. To address these shortcomings, this paper proposes augmented multi-strategy beluga optimization (AMBWO). The adaptive population learning strategy is proposed to improve the global exploration capability of BWO. The introduction of the roulette equilibrium selection strategy allows BWO to have more reference points to choose among during the exploitation phase, which enhances the flexibility of the algorithm. In addition, the adaptive avoidance strategy improves the algorithm’s ability to escape from local optima and enriches the population quality. In order to validate the performance of the proposed AMBWO, extensive evaluation comparisons with other state-of-the-art improved algorithms were conducted on the CEC2017 and CEC2022 test sets. Statistical tests, convergence analysis, and stability analysis show that the AMBWO exhibits a superior overall performance. Finally, the applicability and superiority of the AMBWO was further verified by several engineering optimization problems.